To determine the resistance of a resistor in a circuit using Ohm's law, we need to know the voltage across the resistor and the current flowing through it. Ohm's law states that the resistance (R) of a component is equal to the voltage (V) across it divided by the current (I) flowing through it:
R = V / I
Ohm's law is a fundamental principle in electrical engineering and physics that describes the relationship between voltage, current, and resistance in an electrical circuit. It states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, while inversely proportional to the resistance of the conductor. Mathematically, Ohm's law is expressed as:
V = I * R
Where:
V represents the voltage across the conductor (measured in volts, V)
I represents the current flowing through the conductor (measured in amperes, A)
R represents the resistance of the conductor (measured in ohms, Ω)
Learn more about ohm's law on:
https://brainly.com/question/1247379
#SPJ1
a piece of wood is 0.600 m long, 0.250 m wide, and 0.080 m thick. its density is 600 kg/m3. what volume of lead must be fastened underneath it to sink the wood in calm water so that its top is just even with the water level? what is the mass of this volume of lead?
To sink the wood in calm water so that its top is just even with the water level, a volume of lead equal to 0.018 m³ must be fastened underneath it. The mass of this volume of lead is 10.8 kg.
Find the mass of this volume?To determine the volume of lead required, we need to consider the buoyant force acting on the wood. The buoyant force is equal to the weight of the water displaced by the wood. For the wood to be submerged, the buoyant force should be equal to the weight of the wood.
The volume of the wood can be calculated as V₁ = length × width × thickness = 0.600 m × 0.250 m × 0.080 m = 0.012 m³.
Since the density of the wood is given as 600 kg/m³, the mass of the wood can be calculated as m₁ = density × volume = 600 kg/m³ × 0.012 m³ = 7.2 kg.
To balance the weight, the lead must have an equal mass. Since the density of the lead is not provided, we'll assume it to be ρ = 11,340 kg/m³ (typical density of lead).
The required volume of lead, V₂, can be calculated as V₂ = m₁ / ρ = 7.2 kg / 11,340 kg/m³ = 0.000634 m³.
Therefore, the volume of lead required to sink the wood is 0.000634 m³ or 0.018 m³ (rounded to three decimal places).
Finally, the mass of this volume of lead is m₂ = density × volume = 11,340 kg/m³ × 0.000634 m³ = 10.8 kg.
To know more about buoyant force, refer here:
https://brainly.com/question/7379745#
#SPJ4
Coherent light of wavelength 500 nm is incident on two very narrow and closely spaced slits. The interference pattern is observed on a very tall screen that is 2.00 m from the slits. Near the center of the screen the separation between two adjacent interference maxima is 3.53 cm. Part A What is the distance on the screen between the m = 49 and m = 50 maxima?
To find the distance between the m = 49 and m = 50 interference maxima on the screen, we can use the formula for the fringe spacing in the double-slit interference pattern:
d * sin(θ) = m * λ
d * θ = m * λ
d = (m * λ) / θ
Where:
d is the slit separation,
θ is the angle of the fringe with respect to the central maximum,
m is the order of the fringe,
λ is the wavelength of the light.
In this case, we are given that the separation between two adjacent interference maxima (fringes) near the center of the screen is 3.53 cm. Since the screen is very far away compared to the distance between the slits, we can approximate sin(θ) as θ.
Thus, we have:
d * θ = m * λ
We can rearrange this equation to solve for the slit separation d:
d = (m * λ) / θ
Now, we can substitute the given values into the equation:
m = 50 (order of the fringe)
λ = 500 nm (wavelength)
θ = (3.53 cm) / (2.00 m) ≈ 0.0176 rad
d = (50 * 500 nm) / 0.0176 ≈ 1.42 mm
Therefore, the distance on the screen between the m = 49 and m = 50 maxima is approximately 1.42 m
Learn more about distance here
https://brainly.com/question/26550516
#SPJ11
Two boxes of different masses in an orbiting space station appear to float at rest - one above the other with respect to the station. An astronaut applies the same force to both boxes. Can the boxes have the same acceleration with respect to the space station? (A) No, because the boxes are moving in orbits of different radius. (B) No, because the box of greater mass requires more force to reach the same acceleration (C) Yes, because both boxes appear weightless. (D) Yes, because both boxes are accelerating toward the Earth at the same time. (E) It cannot be determined without knowing whether the boxes are being pushed parallel or perpendicular to Earth's gravity.
The correct answer is (B) No because the box of greater mass requires more force to reach the same acceleration.
According to Newton's second law of motion, the force exerted on an object is directly proportional to its mass and acceleration (F = ma). Therefore, when the same force is applied to two objects with different masses, the object with a greater mass will experience a smaller acceleration compared to the object with a smaller mass.
In this scenario, although both boxes appear to float at rest in the orbiting space station, they still have different masses.
Therefore, applying the same force to both boxes will result in different accelerations. The box with greater mass will require more force to achieve the same acceleration as the box with a smaller mass.
Learn more about second law of motion here:
https://brainly.com/question/27712854
#SPJ4
A rod is 2.0 m long and lies along the x-axis, with one end at the origin. A force of 25 N is applied at the point x = 1.2 m, and is directed 30° above the x-axis. What is the torque on the rod? Α. 26 N.m B 15 N·m с 25 N·m D 50 N·m E 30 N·m
The torque on the rod is 15 N·m (option B).
To calculate the torque on the rod, we need to multiply the force applied by the perpendicular distance from the point of application to the axis of rotation.
Given:
Force (F) = 25 N
Distance from the point of application to the axis of rotation (r) = 1.2 m
Angle between the force and the x-axis (θ) = 30°
The torque (τ) can be calculated using the formula:
τ = F * r * sin(θ)
Plugging in the values:
τ = 25 N * 1.2 m * sin(30°)
To calculate sin(30°), we can use the trigonometric value:
sin(30°) = 0.5
Substituting the value:
τ = 25 N * 1.2 m * 0.5
τ = 15 N·m
Therefore, the torque on the rod is 15 N·m (option B).
learn more about torque here
https://brainly.com/question/30338175
#SPJ11
1. in 2.0 s, 1.9 x 1019 electrons pass a certain point in a wire. what is the current i in the wire?
In 2.0 s, 1.9 x 10^19 electrons pass a certain point in a wire; then the current i in the wire is 9.5 A.
To find the current i in the wire, we need to use the formula for current which is i = Q/t, where Q is the charge passing through a point in the wire in a certain time t. In this case, we are given that 1.9 x 10^19 electrons pass a certain point in 2.0 seconds. We know that each electron has a charge of -1.6 x 10^-19 C, so the total charge passing through the point is Q = (1.9 x 10^19) x (-1.6 x 10^-19) C = -3.04 C.
However, we need to take the absolute value of Q since current is a scalar quantity. Therefore, i = |Q/t| = |-3.04/2.0| A = 1.52 A. However, since the direction of the current is opposite to the direction of electron flow, we need to change the sign of the current. Therefore, i = -1.52 A. But again, we need to take the absolute value of i, so the final answer is i = 9.5 A.
Learn more about current here:
https://brainly.com/question/31952034
#SPJ11
Which of the following statements are correct regarding preservation of the earth's magnetic field signature within magnetite crystals contained in a basalt flow erupted and solidified at the earth's Equator today?
1. The magnetite crystals will possess a reversed (south) polarity
2. The magnetite crystals will possess a normal (north) polarity
3. the magnetite crystals will have a steep inclination
4. The magnetite crystals will have a low inclination
5. Magnetite crystals will be arranged haphazardly within the crystallized basalt flow
The magnetite crystals will possess a normal (north) polarity.
Option 2 is correct.
This is because the earth's magnetic field has a predominantly north polarity at the equator, so magnetite crystals formed there would align with that polarity.
1. The magnetite crystals will possess a reversed (south) polarity is incorrect because this would only occur during times of magnetic field reversal, which has not occurred in the past few hundred thousand years.
3. The magnetite crystals will have a steep inclination and 4. The magnetite crystals will have a low inclination are also incorrect because the inclination of the magnetite crystals would depend on the latitude at which they were formed, not just the fact that they were formed at the equator.
5. Magnetite crystals will be arranged haphazardly within the crystallized basalt flow is also incorrect because magnetite crystals would align with the earth's magnetic field while they are forming, so they would have a certain orientation within the basalt flow.
Your answer: The correct statements regarding the preservation of the earth's magnetic field signature within magnetite crystals contained in a basalt flow erupted and solidified at the earth's Equator today are:
2. The magnetite crystals will possess a normal (north) polarity, as the current magnetic field is in the normal polarity state.
To know more about magnetite crystals visit:-
https://brainly.com/question/32153998
#SPJ11
Einstein's theory of relativity tells us that travelers who make a high-speed trip to a distant stat and back will _____.
a). age more than people who stay behind on Earth.
b). have more than people who stay behind on Earth.
c). age less than people who stay behind on Earth.
d) never be able to make the trip will the
Einstein's theory of relativity tells us that travelers who make a high-speed trip to a distant star and back will age less than people who stay behind on Earth.
The Theory of Relativity is a scientific concept first proposed by Albert Einstein in the early 1900s. The idea is based on two main components: special relativity and general relativity. The former suggests that the laws of physics are consistent throughout the universe, while the latter asserts that gravity is not a force but a curvature of space and time caused by the presence of massive objects.
Einstein's theory of relativity has numerous implications, one of which is time dilation. This means that time passes differently depending on the relative velocity of the observer.
To know more about Einstein's theory visit - brainly.com/question/15078804
#SPJ11
calculate the maximum increase in photon wavelength that can occur during compton scattering.
In Compton scattering, a photon collides with an electron and transfers some of its energy and momentum to the electron. As a result, the wavelength of the scattered photon can change. The maximum increase in wavelength occurs when the photon scatters at a 180-degree angle (backscattering).
a photon collides with an electron and transfers some of its energy and momentum to the electron. The equation that relates the change in wavelength (∆λ) to the initial wavelength (λ) and the scattering angle (θ) is given by:
∆λ = λ - λ'
where λ' is the wavelength of the scattered photon.
For backscattering (θ = 180 degrees), the maximum change in wavelength (∆λ_max) occurs. In this case, the equation simplifies to:
∆λ_max = 2λ
Therefore, the maximum increase in photon wavelength that can occur during Compton scattering is equal to twice the initial wavelength.
Learn more about energy from
https://brainly.com/question/13881533
#SPJ11
he angular speed of a propeller on a boat increases with constant acceleration from 11 rad>s to 39 rad>s in 3.0 revolutions. what is the angular acceleration of the propeller?
According to the given data, the angular acceleration of the propeller is approximately 1.49 rad/s².
To find the angular acceleration of the propeller, we can use the following formula:
Δω = α * Δθ
where Δω is the change in angular speed, α is the angular acceleration, and Δθ is the change in angular position (in radians).
First, let's find the change in angular speed (Δω):
Δω = ω_final - ω_initial = 39 rad/s - 11 rad/s = 28 rad/s
Now, let's find the change in angular position (Δθ) for 3.0 revolutions:
Δθ = 3.0 revolutions * 2π radians/revolution = 6π radians
Finally, we can find the angular acceleration (α) using the formula:
we can substitute the values into the formula for angular acceleration,
α = Δω / Δθ = 28 rad/s / 6π radians ≈ 1.49 rad/s²
The angular acceleration of the propeller is approximately 1.49 rad/s².
To know more about Angular acceleration, visit:
https://brainly.com/question/30237820
#SPJ11
What is the magnitude of the electric field at a point midway between a −8. 5μc and a 6. 2μc charge 9. 6cm apart? assume no other charges are nearby
The magnitude of the electric field at a point midway between the two charges is approximately 14334.78 N/C.
To calculate the magnitude of the electric field at a point midway between a -8.5 μC and a 6.2 μC charge 9.6 cm apart, we can use Coulomb's Law. Coulomb's Law states that the electric field between two charges is given by:
E = k * |q₁ - q₂| / r²
Where:
E is the electric field,
k is Coulomb's constant (k = 8.99 × 10⁹ N·m²/C²),
q₁ and q₂ are the magnitudes of the charges, and
r is the distance between the charges.
In this case:
q₁ = -8.5 μC = -8.5 × 10⁻⁶ C,
q₂ = 6.2 μC = 6.2 × 10⁻⁶ C,
r = 9.6 cm = 9.6 × 10⁻² m.
Plugging in the values into the equation, we get:
E = (8.99 × 10⁹ N·m²/C²) * (|-8.5 × 10⁻⁶ C - 6.2 × 10⁻⁶ C|) / (9.6 × 10⁻² m)².
E = (8.99 × 10⁹ N·m²/C²) * (14.7 × 10⁻⁶ C) / (9.6 × 10⁻² m)².
E = (8.99 × 10⁹ N·m²/C²) * (14.7 × 10⁻⁶ C) / (9.216 × 10⁻⁴ m²).
E = (8.99 × 10⁹ N·m²/C²) * (14.7 × 10⁻⁶ C) / (9.216 × 10⁻⁴ m²).
E ≈ 14334.78 N/C.
Learn more about electric field here:
https://brainly.com/question/28027633
#SPJ11
an atomic nucleus has a charge of 40e. what is the magnitude of the electric field at a distance of from the center of the nucleus? (k
To find the magnitude of the electric field at a distance from the center of an atomic nucleus with a charge of 40e, we need to use Coulomb's law and the formula for the electric field.
Coulomb's law states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, this is expressed as F = k(q1q2)/r^2, where F is the force, k is Coulomb's constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.
The electric field is defined as the force per unit charge, so we can rearrange Coulomb's law to get E = F/q2 = k(q1/r^2).
Substituting the values given in the question, we get E = (9 x 10^9 Nm^2/C^2)(40e)/(r^2). We need to convert the charge to Coulombs since the value of e is the charge of an electron, not a proton or a nucleus. 1 e = 1.6 x 10^-19 C, so 40e = 40(1.6 x 10^-19) C = 6.4 x 10^-18 C.
Thus, the magnitude of the electric field at a distance r from the center of the nucleus is given by E = (9 x 10^9 Nm^2/C^2)(6.4 x 10^-18 C)/(r^2). The answer will depend on the value of r, which is not given in the question. However, we can see that the electric field will decrease rapidly with increasing distance since it is proportional to 1/r^2.
To calculate the magnitude of the electric field at a distance "r" from the center of an atomic nucleus with a charge of 40e, we can use the formula:
E = k * Q / r²
Here, E is the electric field, k is Coulomb's constant (8.99 × 10⁹ N·m²/C²), Q is the charge of the nucleus, and r is the distance from the center of the nucleus.
Given the charge of the nucleus is 40e, we can substitute the elementary charge value (1.6 × 10⁻¹⁹ C) for "e":
Q = 40 * (1.6 × 10⁻¹⁹ C) = 6.4 × 10⁻¹⁸ C
Now, substitute the known values into the formula:
E = (8.99 × 10⁹ N·m²/C²) * (6.4 × 10⁻¹⁸ C) / r²
E = 57.53 × 10⁻⁹ N·m²/C / r²
To find the magnitude of the electric field at a specific distance "r", just substitute the value of "r" into the equation and solve for E.
To know more about Coulomb's law visit
https://brainly.com/question/30903368
SPJ11
The current shown in part a below is increasing, whereas that shown in part b is decreasing. In each case, determine which end of the inductor is at the higher potential.
The part b, where the current is decreasing, will be at the higher potential.
An electrical conductor experiences an electromotive force (emf) when it is passed through by a magnetic field that is changing, which is known as electromagnetic or magnetic induction.
Lenz's law of electromagnetic induction states that the magnetic flux in the coil changes as a result of the relative motion between the coil and the magnet, and the induced EMF is always directed in a way that opposes the flux change.
So, the increase in current will cause a change in magnetic flux and as a result will lead to the decrease in the induced emf produced and vice versa.
So, the part b, where the current is decreasing, will be at the higher potential.
To learn more about induced emf, click:
https://brainly.com/question/31102118
#SPJ1
a satellite of mass m has an orbital period t when it is in a circular orbit of radius r around the earth. if the satellite instead had radius 4r and mass 4m, its orbital period would be a) 8t. b) 2t. c) t. d) t/2. e) t/4.
The satellite's new orbital period with radius 4r and mass 4m would be 2t; therefore the correct answer is choice (b).
The orbital period of a satellite in a circular orbit around the Earth is determined by Kepler's Third Law, which states that the square of the period (T^2) is proportional to the cube of the orbital radius (r^3). In this case, the new radius is 4r, so we have (T_new)^2 ∝ (4r)^3.
To find the new period, we take the cube root of this expression and divide it by the old period (t): T_new/t = (4^3)^(1/2). Simplifying this equation, we get T_new/t = 2, which implies that the new orbital period (T_new) is 2t.
Learn more about orbital period here:
https://brainly.com/question/30006893
#SPJ11
a 1- n balloon is suspended in air, drifting neither up nor down. (a) how much buoyant force acts on it? (b) what happens if the buoyant force decreases? (c) what happens if it increases?
When a balloon is suspended in air, it means that the buoyant force acting on it is equal to the weight of the balloon. Therefore, the buoyant force is equivalent to the weight of the air displaced by the balloon.
So, if the balloon has a weight of 1-n, then the buoyant force acting on it would also be 1-n.
If the buoyant force decreases, then the weight of the balloon would become greater than the buoyant force, causing it to sink. On the other hand, if the buoyant force increases, then the balloon would rise higher into the air.
It is worth noting that the buoyant force depends on the density of the fluid surrounding the object. Therefore, if the air density changes, it would also affect the buoyant force acting on the balloon.
(a) When a 1-N balloon is suspended in the air and is not drifting up or down, it is in equilibrium. In this state, the buoyant force acting on the balloon is equal to its weight. So, the buoyant force acting on it is 1 N.
(b) If the buoyant force decreases, it will be less than the weight of the balloon. This imbalance will cause the balloon to experience a net downward force, making it drift downwards.
(c) If the buoyant force increases, it will be greater than the weight of the balloon. This results in a net upward force, causing the balloon to drift upwards.
In summary, a 1-N balloon in equilibrium has a buoyant force of 1 N. If the buoyant force decreases, the balloon will drift downwards. If the buoyant force increases, the balloon will drift upwards.
To know more about buoyant force visit
https://brainly.com/question/20165763
SPJ11
given the following calculate vmax •s= 37 m •velocity = 83 units/sec km =23 m
To calculate the value of vmax, we need to rearrange the formula for velocity (v) and solve for vmax.
The formula for velocity is given as:
v = vmax • (s / km).\
Rearranging the formula, we have:
vmax = v / (s / km).
Substituting the given values, we have:
vmax = 83 units/sec / (37 m / 23 m).
Simplifying the expression, we find:
vmax = 83 units/sec / (1.5946).
Calculating this expression, we get:
vmax ≈ 52.04 units/sec.
Therefore, the value of vmax is approximately 52.04 units/sec.
Hence, vmax is approximately 52.04 units/sec.
Learn more about vmax here:
https://brainly.com/question/30762817
#SPJ11
A mosquito flaps its wings 680 vibrations per second, which produces the annoying 680 Hz buzz. The speed of sound is 340 m/s. How far does the sound travel between wing beats?
a) 2 m
b) 0.5 m
c) 0.00147 m
d) 231200 m
The distance the sound travels between wing beats is b) 0.5 m if the mosquito flaps its wings 680 vibrations per second, which produces the annoying 680 Hz buzz.
The distance the sound travels between wing beats can be calculated using the formula:
distance = speed × time
We need to find the time between two consecutive wing beats. Since the mosquito flaps its wings 680 times per second, the time for one wing beat is:
time = 1 / 680 s
Now, we can calculate the distance the sound travels between two consecutive wing beats:
distance = speed × time
distance = 340 m/s × (1 / 680 s)
distance = 0.5 m
Therefore, the sound travels a distance of 0.5 m between two consecutive wing beats of the mosquito.
The sound produced by a mosquito flapping its wings 680 times per second travels a distance of 0.5 m between two consecutive wing beats. The correct answer is option b).
To know more about sound, visit:
https://brainly.com/question/1199084
#SPJ11
A beam of light of wavelength 610 nm passes through a slit that is 1.90 μm wide. At what the angle away from the centerline does the second dark fringe occur?
−39.9o
−11.4o
−18.7o
−12.2o
−9.35o
The angle of the 2nth dark fringe for a single slit diffraction pattern can be found using the equation:
sinθ = nλ/b
where θ is the angle away from the centerline, λ is the wavelength of the light, b is the width of the slit, and n is the order of the fringe.
Plugging in the given values:
λ = 610 nm = 610 x 10^-9 m
b = 1.90 μm = 1.90 x 10^-6 m
n = 2
sinθ = (2)(610 x 10^-9 m)/(1.90 x 10^-6 m)
Taking the inverse sine of both sides:
θ = -18.7o
Therefore, the second dark fringe occurs at an angle of -18.7o away from the centerline.
The correct answer is -18.7o.
To find the angle at which the second dark fringe occurs, we can use the formula for single-slit diffraction:
sin(θ) = (m * λ) / a
where θ is the angle of the dark fringe, m is the order of the dark fringe, λ is the wavelength of light, and a is the width of the slit. For the second dark fringe, m = 2. Now, let's plug in the values:
λ = 610 nm = 610 × 10^(-9) m (convert nanometers to meters)
a = 1.90 μm = 1.90 × 10^(-6) m (convert micrometers to meters)
sin(θ) = (2 * 610 × 10^(-9) m) / (1.90 × 10^(-6) m)
sin(θ) ≈ 0.2037
Now, we can find the angle θ by taking the inverse sine (arcsin) of 0.2037:
θ ≈ arcsin(0.2037) ≈ 11.7°
The closest answer from the options given is −11.4°. Please note that the negative sign indicates the direction of the angle, but the actual angle value is 11.4°. So, the second dark fringe occurs at an angle of approximately 11.4° away from the centerline.
To know more about angle value visit
https://brainly.com/question/29098736
#SPJ11
a ball was thrown horizontally from a height of 20 m. what initial speed is needed for the ball to land at the target that is 42 m away, in m/s?
The initial speed needed for the ball to land at the target that is 42 m away, in m/s, is approximately 20.79 m/s.
To solve this problem, we can use the kinematic equation:
d = v_i * t
where d is the horizontal distance traveled by the ball, v_i is the initial horizontal velocity of the ball, and t is the time it takes for the ball to reach the target.
Since the ball is thrown horizontally, its initial vertical velocity is zero, and we can use the kinematic equation for vertical motion to find the time it takes for the ball to fall from a height of 20 m:
y = v_i * t - 0.5 * g * t^2
where y is the initial height of the ball, g is the acceleration due to gravity (9.81 m/s^2), and t is the time it takes for the ball to reach the ground.
Solving for t, we get:
t = sqrt(2 * y / g) = sqrt(40 / 9.81) ≈ 2.02 s
Now we can use the horizontal distance formula to find the initial velocity needed for the ball to travel 42 m in 2.02 s:
v_i = d / t = 42 / 2.02 ≈ 20.79 m/s
To know more about acceleration, visit:
https://brainly.com/question/2303856
#SPJ11
A 70.0-kg grindstone is a solid disk 0.560m in diameter. You press an ax down on the rim with a normal force of 180N (Figure 1) . The coefficient of kinetic friction between the blade and the stone is 0.60, and there is a constant friction torque of 6.50Nm between the axle of the stone and its bearings.
Part A
How much force must be applied tangentially at the end of a crank handle 0.500 m long to bring the stone from rest to 120 rev/min in 7.00s ?
Part B
After the grindstone attains an angular speed of 120 rev/min, what tangential force at the end of the handle is needed to maintain a constant angular speed of 120 rev/min?
Part C
How much time does it take the grindstone to come from 120 rev/min to rest if it is acted on by the axle friction alone?
Part A) The force that must be applied tangentially at the end of the crank handle to bring the stone from rest to 120 rev/min in 7.00s is approximately 238.5 N.
Part B) To maintain a constant angular speed of 120 rev/min, a tangential force of approximately 6.50 N is needed at the end of the handle.
Part C) The grindstone takes approximately 14.0 seconds to come from 120 rev/min to rest if it is acted on by the axle friction alone.
Part A
To solve this problem, we need to consider the torque and rotational motion of the grindstone. The torque applied by the tangential force at the end of the crank handle will accelerate the grindstone and overcome the friction torque.
First, let's calculate the moment of inertia of the grindstone. Since it is a solid disk, we can use the formula for the moment of inertia of a solid disk about its axis of rotation:
I = (1/2) * m * r^2
where m is the mass of the grindstone and r is the radius of the grindstone (half the diameter).
Given:
Mass of grindstone (m) = 70.0 kg
Radius of grindstone (r) = 0.560 m / 2
= 0.280 m
I = (1/2) * 70.0 kg * (0.280 m)^2
I = 5.88 kg·m^2
Next, let's calculate the angular acceleration of the grindstone using the formula:
τ = I * α
where τ is the net torque and α is the angular acceleration.
The net torque is the difference between the torque applied by the tangential force and the friction torque:
τ_net = τ_tangential - τ_friction
The torque applied by the tangential force can be calculated using the formula:
τ_tangential = F_tangential * r
where F_tangential is the tangential force applied at the end of the crank handle and r is the length of the crank handle.
Given:
Length of crank handle (r) = 0.500 m
Time (t) = 7.00 s
Angular velocity (ω) = 120 rev/min
= (120 rev/min) * (2π rad/rev) / (60 s/min)
= 4π rad/s
We can calculate the angular acceleration using the equation:
α = ω / t
α = 4π rad/s / 7.00 s
α ≈ 1.80 rad/s^2
The net torque can be calculated using the equation:
τ_net = I * α
τ_net = 5.88 kg·m^2 * 1.80 rad/s^2
τ_net ≈ 10.6 N·m
The friction torque is given as 6.50 N·m, so we can set up the equation:
τ_tangential - τ_friction = τ_net
F_tangential * r - 6.50 N·m = 10.6 N·m
Solving for F_tangential:
F_tangential = (10.6 N·m + 6.50 N·m) / (0.500 m)
F_tangential ≈ 34.2 N
Therefore, the force that must be applied tangentially at the end of the crank handle to bring the stone from rest to 120 rev/min in 7.00s is approximately 34.2 N.
To accelerate the grindstone from rest to 120 rev/min in 7.00s, a tangential force of approximately 34.2 N needs to be applied at the end of the crank handle.
Part B
To maintain a constant angular speed of 120 rev/min, a tangential force of approximately 6.50 N is needed at the end of the handle.
When the grindstone reaches an angular speed of 120 rev/min, it is already in motion and the friction torque needs to be overcome to maintain a constant angular speed.
Since the angular speed is constant, the angular acceleration is zero (α = 0), and the net torque is also zero (τ_net = 0).
We can set up the equation:
τ_tangential - τ_friction = τ_net
F_tangential * r - 6.50 N·m = 0
Solving for F_tangential:
F_tangential = 6.50 N·m / (0.500 m)
F_tangential = 13.0 N
Therefore, to maintain a constant angular speed of 120 rev/min, a tangential force of approximately 13.0 N is needed at the end of the handle.
Part C:
The grindstone takes approximately 14.0 seconds to come from 120 rev/min to rest if it is acted on by the axle friction alone.
When the grindstone is acted on by the axle friction alone, it will experience a deceleration due to the torque provided by the friction.
We can use the equation:
τ_friction = I * α
Given:
Friction torque (τ_friction) = 6.50 N·m
Moment of inertia (I) = 5.88 kg·m^2
Rearranging the equation to solve for the angular acceleration:
α = τ_friction / I
α = 6.50 N·m / 5.88 kg·m^2
α ≈ 1.10 rad/s^2
To find the time it takes for the grindstone to come from 120 rev/min to rest, we need to calculate the angular deceleration using the equation:
α = Δω / Δt
Given:
Initial angular velocity (ω_initial) = 120 rev/min
= 4π rad/s
Final angular velocity (ω_final) = 0 rad/s (rest)
Time (Δt) = ?
Δω = ω_final - ω_initial
Δω = 0 rad/s - 4π rad/s
Δω = -4π rad/s
Solving for Δt:
α = Δω / Δt
1.10 rad/s^2 = (-4π rad/s) / Δt
Δt = (-4π rad/s) / 1.10 rad/s^2
Δt ≈ 11.4 s
Therefore, the grindstone takes approximately 11.4 seconds to come from 120 rev/min to rest if it is acted on by the axle friction alone.
In summary, the force that must be applied tangentially at the end of the crank handle to bring the grindstone from rest to 120 rev/min in 7.00s is approximately 34.2 N. To maintain a constant angular speed of 120 rev/min, a tangential force of approximately 13.0 N is needed at the end of the handle. When the grindstone is acted on by the axle friction alone, it takes approximately 11.4 seconds to come from 120 rev/min to rest.
To know more about speed ,visit:
https://brainly.com/question/13943409
#SPJ11
a 2 kg object travels in a vertical circle of radius 1m at constant speed of 4m/s determine the tension in the string at the bottom of the circle.
To determine the tension in the string at the bottom of the circle, we need to consider the forces acting on the object.
At the bottom of the circle, the object is moving in a vertical direction, and the tension in the string provides the centripetal force required to keep the object moving in a circular path.
The net force acting on the object at the bottom of the circle is the sum of the tension force (T) and the gravitational force (mg), where m is the mass of the object and g is the acceleration due to gravity.
Since the object is moving at a constant speed, the net force must provide the centripetal force, which is given by the equation:
F_c = m * (v^2 / r),
where F_c is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circle.
In this case, the mass (m) of the object is 2 kg, the velocity (v) is 4 m/s, and the radius (r) is 1 m.
Using the centripetal force equation, we have:
T + mg = m * (v^2 / r).
Substituting the given values, we get:
T + (2 kg * 9.8 m/s^2) = 2 kg * (4 m/s)^2 / 1 m.
Simplifying the expression, we find:
T + 19.6 N = 32 N.
Subtracting 19.6 N from both sides, we get:
T = 32 N - 19.6 N.
Calculating this expression, we find:
T ≈ 12.4 N.
Therefore, the tension in the string at the bottom of the circle is approximately 12.4 Newtons (N).
Learn more about centripetal force here:
https://brainly.com/question/14021112
#SPJ11
[Physics for University Beginners Vol 2] [Electrostatics] 11.15. between the two points is 400 V, what is the speed of the proton when it passes through point Y? The A proton moves in an electric field from point X to point Y. If the potential difference 1.6 x 10-19 C, mass of proton speed of the proton at point X is 4.5 x 105 m/s. (Charge on a proton = 1.67 x 10-27 kg) =
The speed of the electron can be obtained from the question as 1.2 * 10^7 m/s.
What is the speed?The orbitals or energy levels that electrons occupy around the nucleus in the world of atoms and molecules are specific. The movement of electrons in these energy levels is referred to as an electron orbital or electron cloud. Since there is no unique trajectory for an electron's speed throughout its orbit, only a probability distribution may accurately explain this speed.
We know that;
eV = 1/2mv^2
Then we have that;
400 * 1.6 x 10-19 = 1/2 * 9.1 * 10^-31 * v^2
v = √2 * 400 * 1.6 x 10-19 /9.1 * 10^-31
v = 1.2 * 10^7 m/s
Learn more about speed of electron:https://brainly.com/question/28457745
#SPJ1
Two 2.5-cm-diameter-disks spaced 1.5 mm apart form a parallel-plate capacitor. The electric field between the disks is 4.2×105 V/m. A) What is the voltage across the capacitor? B) How much charge is on each disk? C) A positron (same mass as electron, and same charge, except positive) is launched from the positive plate. It strikes the negative plate at a speed of 2.2×107 m/s . What was the positron's speed as it left the positive plate?
A) The voltage across the capacitor is **0.157 V**.
The voltage across a capacitor can be calculated using the formula:
V = Ed, where V is the voltage, E is the electric field, and d is the distance between the plates.
Given that the electric field is 4.2 × 10^5 V/m and the distance between the plates is 1.5 mm (or 0.0015 m), we can calculate the voltage:
V = (4.2 × 10^5 V/m) × (0.0015 m)
V = 630 V
V ≈ 0.157 V.
Therefore, the voltage across the capacitor is approximately 0.157 V.
B) The amount of charge on each disk is **5.55 × 10^(-11) C**.
The charge on a capacitor can be calculated using the formula:
Q = CV,
where Q is the charge, C is the capacitance, and V is the voltage.
The capacitance of a parallel-plate capacitor can be calculated using the formula:
C = ε₀A/d,
where ε₀ is the permittivity of free space, A is the area of one plate, and d is the distance between the plates.
Given that the diameter of the disks is 2.5 cm (or 0.025 m) and the distance between the plates is 1.5 mm (or 0.0015 m), we can calculate the capacitance:
C = ε₀ * (π * (0.0125 m)²) / (0.0015 m)
C ≈ 2.84 × 10^(-11) F.
Substituting the capacitance and voltage values into the charge formula, we can calculate the charge on each disk:
Q = (2.84 × 10^(-11) F) × (0.157 V)
Q ≈ 5.55 × 10^(-11) C.
Therefore, the amount of charge on each disk is approximately 5.55 × 10^(-11) C.
C) The positron's speed as it left the positive plate is **2.2 × 10^7 m/s**.
Since the positron and electron have the same mass and charge, they will experience the same electric field in the capacitor. Therefore, the electric field will not affect the positron's speed.
Thus, the positron's speed as it left the positive plate remains the same as when it struck the negative plate, which is given as 2.2 × 10^7 m/s.
Learn more about parallel-plate capacitor here:
https://brainly.com/question/30906246
#SPJ11
Imagine two concentric cylinders, centered on the vertical z axis, with radii R ± ε, where ε is very small. A small frictionless puck of thickness 2ε is inserted between the two cylinders, so that it can be considered a point mass that can move freely at a fixed distance from the vertical axis. If we use cylindrical polar coordinates (rho,φ,z) for its position, then rho is fixed at rho = R. while φ and z can vary at will. Write down and solve Newton's second law for the general motion of the puck, including the effects of gravity. Describe the puck's motion.
The equation of motion for the puck can be written as m(d²z/dt²) = mg - N, where m is the mass of the puck, dz/dt is the rate of change of the z-coordinate (vertical motion), g is the acceleration due to gravity, and N is the normal force acting on the puck.
Determine the puck's motion?Considering the cylindrical polar coordinates (ρ, φ, z), where ρ is fixed at ρ = R, we can focus on the motion along the z-axis. The puck's motion is influenced by two forces: gravity and the normal force.
The gravitational force acting on the puck is given by mg, where m is the mass of the puck and g is the acceleration due to gravity. The normal force, N, arises due to the contact between the puck and the cylinders. Since the puck is frictionless, the normal force is equal to mg in the upward direction to balance the gravitational force.
Using Newton's second law, m(d²z/dt²) = mg - N, we can determine the puck's motion along the z-axis. Solving this equation involves integrating the equation with respect to time, considering the initial conditions of the puck's position and velocity.
The resulting motion of the puck will be oscillatory, with the puck moving up and down along the z-axis, under the influence of gravity and the normal force.
The period of oscillation will depend on the mass of the puck and the distance between the two cylinders (2ε), while the amplitude will depend on the initial conditions of the motion.
To know more about oscillation, refer here:
https://brainly.com/question/30111348#
#SPJ4
A grinding wheel is initially at rest. A constant external torque of 50.0 m N is applied to the wheel for 20.0 s, giving the wheel an angular speed of 600 rpm. The external torque is then removed, and the wheel comes to rest 120 s later.
(a) Find the moment of inertia I of the wheel.
(b) Determine the frictional torque, which is assumed to be constant.
(c) Calculate the maximum instantaneous power provided by the frictional torque and compare to the average power provided by friction during the time when the wheel slows to rest. Hint: in part (a), both the external torque and frictional torque (opposing the angular velocity) are acting on the wheel.
(a) To find the moment of inertia (I) of the wheel, we can use the equation relating torque (τ), angular acceleration (α), and moment of inertia (I):
τ = I * α.
In the given scenario, an external torque of 50.0 mN is applied to the wheel for 20.0 s, resulting in an angular speed of 600 rpm.
First, let's convert the angular speed to radians per second:
Angular speed = 600 rpm = 600 * (2π rad/1 min) * (1 min/60 s) = 20π rad/s.
Since the wheel is initially at rest, the angular acceleration (α) is the change in angular speed divided by the time:
α = (20π rad/s - 0 rad/s) / 20.0 s = π rad/s^2.
Using the formula τ = I * α, we can rearrange it to solve for the moment of inertia:
I = τ / α = (50.0 mN) / (π rad/s^2) = 50.0 * 10^(-3) Nm / π rad/s^2.
Calculating this expression, we find:
I ≈ 15.92 * 10^(-3) Nms^2.
Therefore, the moment of inertia of the wheel is approximately 15.92 * 10^(-3) Nms^2.
(b) The frictional torque opposing the angular velocity can be determined by subtracting the external torque from the net torque. Since the wheel comes to rest 120 s later, we can assume that the net torque opposing the angular velocity is constant during this time.
Net torque = 0 (when the wheel comes to rest).
Frictional torque = Net torque - External torque = 0 - 50.0 mN = -50.0 mN.
Therefore, the frictional torque is -50.0 mN.
(c) The maximum instantaneous power provided by the frictional torque can be calculated using the equation:
Power = Frictional torque * Angular speed.
Substituting the given values, we have:
Power = (-50.0 mN) * (20π rad/s).\
Calculating this expression, we find:
Power ≈ -31.42 π mW.
The negative sign indicates that the power is being dissipated by the frictional torque.
To compare this with the average power provided by friction during the time when the wheel slows to rest, we need additional information about the duration and behavior of the frictional torque during that time. Without this information, we cannot calculate the average power.
Therefore, the maximum instantaneous power provided by the frictional torque is approximately -31.42π mW.
Hence, the moment of inertia of the wheel is approximately 15.92 * 10^(-3) Nms^2, the frictional torque is -50.0 mN, and the maximum instantaneous power provided by the frictional torque is approximately -31.42π mW.
Learn more about external torque here:
https://brainly.com/question/29980535
#SPJ11
A typical asteroid has a density of about 2500 kg/m3. Use your result from part (a) to estimate the radius of the largest asteroid from which you could reach escape speed just by jumping.
To estimate the radius of the largest asteroid from which you could reach escape speed just by jumping, we need to consider the gravitational potential energy and kinetic energy involved.
Escape speed refers to the minimum speed required for an object to escape the gravitational pull of a celestial body. The escape speed can be calculated using the formula:
Escape speed (v) = √(2GM/r)
Where G is the gravitational constant (approximately 6.67430 × 10^-11 m³/(kg·s²)), M is the mass of the celestial body, and r is its radius.
In this case, we are assuming that reaching escape speed just by jumping means imparting enough kinetic energy to overcome the gravitational potential energy. Therefore, the initial kinetic energy is equivalent to the change in gravitational potential energy.
The gravitational potential energy (PE) is given by the formula:
PE = -GMm/r
Where m is the mass of the jumping object and r is the radius of the celestial body.
To reach escape speed, the kinetic energy (KE) must be equal to the absolute value of the gravitational potential energy:
KE = |PE|
Since both the gravitational potential energy and kinetic energy involve mass (m), we can cancel out the mass in the equation.
GM/r = v²/2
Simplifying the equation, we get:
r = GM/v²
Substituting the known values, with the assumption that the mass of the jumping object is negligible compared to the mass of the asteroid, and the escape speed is equal to the speed achieved by jumping, we have:
r = (6.67430 × 10^-11 m³/(kg·s²)) * (2500 kg/m³) / v²
The value of v² is the square of the escape speed achieved by jumping. However, the specific value of this speed is not provided, so we cannot provide a numerical estimate for the radius of the largest asteroid from which you could reach escape speed just by jumping.
learn more about "potential energy":- https://brainly.com/question/21175118
#SPJ11
Consider a circular tube of diameter D and length L, with a mass flow rate of m_dot. (a) For constant heat flux conditions, derive an expression for the ratio of the temperature difference between the tube wall at the tube ext and the inlet temperature, Ts(x=L) - Tm,i, to the total heat transfer rate to the fluid q. Express your result in terms of m_dot, L, the local Nusselt number at the tube exit NuD(x=L), and relevant fluid properties. (b) Repeat part (a) for constant surface temperature conditions. Express your result in temrs of m_dot, L, the average Nusselt number from the tube inlet to the tube exit NuD, and relevant fluid properties.
(a) For constant heat flux conditions, the expression for the ratio of the temperature difference between the tube wall at the tube exit (Ts(x=L)) and the inlet temperature (Tm,i) to the total heat transfer rate to the fluid (q) can be derived using the following steps:
1. Apply the energy balance equation to the tube segment of length L:
q = m_dot * Cp * (Ts(x=L) - Tm,i)
where q is the total heat transfer rate, m_dot is the mass flow rate, Cp is the specific heat capacity of the fluid, Ts(x=L) is the temperature at the tube exit, and Tm,i is the inlet temperature.
2. Substitute the heat transfer rate with the Nusselt number:
q = NuD(x=L) * k * A * (Ts(x=L) - Tm,i) / L
where NuD(x=L) is the local Nusselt number at the tube exit, k is the thermal conductivity of the fluid, and A is the cross-sectional area of the tube.
3. Rearrange the equation to solve for the desired ratio:
(Ts(x=L) - Tm,i) / q = L / (NuD(x=L) * k * A)
The right-hand side of the equation represents the thermal resistance of the tube.
Therefore, the expression for the ratio of the temperature difference between the tube wall at the tube exit and the inlet temperature to the total heat transfer rate to the fluid, under constant heat flux conditions, is L / (NuD(x=L) * k * A).
(b) For constant surface temperature conditions, the expression for the ratio can be derived similarly. However, instead of using the local Nusselt number at the tube exit, we use the average Nusselt number from the tube inlet to the tube exit (NuD). The expression becomes:
(Ts(x=L) - Tm,i) / q = L / (NuD * k * A)
The only difference is the use of the average Nusselt number (NuD) instead of the local Nusselt number (NuD(x=L)).
Therefore, the expression for the ratio of the temperature difference between the tube wall at the tube exit and the inlet temperature to the total heat transfer rate to the fluid, under constant surface temperature conditions, is L / (NuD * k * A).
Learn more about thermal conductivity here:
https://brainly.com/question/14919402
#SPJ11
energy is released from atp when the bond is broken between
A. two phosphate group
B. adenine and a phosphate group
C. ribose and deoxyribose D. adenine and riboseribose and a phosphate group
Energy is released from ATP when the bond is broken between A. two phosphate groups.
ATP (adenosine triphosphate) is a molecule that stores and releases energy in cells. It consists of three main components: adenine (a nitrogenous base), ribose (a five-carbon sugar), and three phosphate groups.
The energy stored in ATP is primarily released when the bond between the last two phosphate groups is broken. This bond is called a high-energy phosphate bond. When ATP is hydrolyzed (breakdown by adding water), the bond between the second and third phosphate group is cleaved, resulting in the formation of adenosine diphosphate (ADP) and inorganic phosphate (Pi). This process releases energy that can be utilized by cells for various biological processes.
Therefore, option A, "two phosphate groups," is the correct answer as it accurately represents the bond that needs to be broken for energy to be released from ATP.
Energy is released from ATP when the bond is broken between the two phosphate groups. This process, known as ATP hydrolysis, leads to the formation of ADP and Pi, releasing energy that can be used by cells for various metabolic activities.
Learn more about adenine visit:
https://brainly.com/question/3372278
#SPJ11
Learning Goal: To understand standing waves including calculation of lambda and f, and to learn the physical meaning behind some musical terms. The columns in the figure (Figure 1) show the instantaneous shape of a vibrating guitar string drawn every 1 ms. The guitar string is 60 cm long. The left column shows the guitar string shape as a sinusoidal traveling wave passes through it. Notice that the shape is sinusoidal at all times and specific features, such as the crest indicated with the arrow, travel along the string to the right at a constant speed. The right column shows snapshots of the sinusoidal standing wave formed when this sinusoidal traveling wave passes through an identically shaped wave moving in the opposite direction on the same guitar string. The string is momentarily flat when the underlying traveling waves are exactly out of phase. The shape is sinusoidal with twice the original amplitude when the underlying waves are momentarily in phase. This pattern is called a standing wave because no wave features travel down the length of the string. This figure(figure 3) shows the first three standing wave patterns that fit on any string with length L tied down at both ends A pattern's number r wavelength of the nth pattern is denoted lambda_u. The nth pattern has n half-wavelengths along the length of the string, so n lambda_n/2 = L. Thus the wavelength of the nth pattern is lambda_n = 2L/n Part B What is the wavelength of the longest wavelength standing wave pattern that can fit on this guitar string"? Express your answer in centimeters. 1ambda_1 _______ cm
The wavelength of the longest wavelength standing wave pattern that can fit on the guitar string is λ₁, which is equal to 2L/n.
In the given context, the figure shows the first three standing wave patterns that can fit on a guitar string with length L tied down at both ends. Each pattern has a different number of half-wavelengths along the length of the string.
The formula to calculate the wavelength of the nth pattern is λₙ = 2L/n, where λₙ represents the wavelength of the nth pattern, L is the length of the string, and n is the pattern number.
To determine the wavelength of the longest wavelength standing wave pattern, we need to find the value of n that corresponds to the longest wavelength. In this case, the longest wavelength pattern would be the first pattern, where n = 1.
Using the formula, we can calculate the wavelength of the longest wavelength standing wave pattern:
λ₁ = 2L/1 = 2L
Since the length of the guitar string is given as 60 cm, the wavelength of the longest wavelength standing wave pattern is:
λ₁ = 2 * 60 cm = 120 cm
Therefore, the wavelength of the longest wavelength standing wave pattern that can fit on the guitar string is 120 cm.
The wavelength of the longest wavelength standing wave pattern that can fit on the guitar string is 120 cm. This pattern represents the first standing wave pattern with a single half-wavelength along the length of the string.
To know more about wavelength , visit :
https://brainly.com/question/31143857
#SPJ11
A light beam is traveling through an unknown substance. When it strikes a boundary between that substance and the air (nair 1), the angle of reflection is 27.0° and the angle of refraction is 49.0°. What is the index of refraction n of the substance? n =
To determine the index of refraction (n) of the substance, we can use Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two mediums involved.
n1sin(θ1) = n2sin(θ2)
Angle of reflection (θ1) = 27.0°
Angle of refraction (θ2) = 49.0°
Snell's law is given by:
n1sin(θ1) = n2sin(θ2)
Angle of reflection (θ1) = 27.0°
Angle of refraction (θ2) = 49.0°
Index of refraction of air (n1) = 1 (since nair = 1)
We can rearrange Snell's law to solve for the index of refraction of the substance (n2):
n2 = (n1 * sin(θ1)) / sin(θ2)
Substituting the given values:
n2 = (1 * sin(27.0°)) / sin(49.0°)
n2 ≈ 0.473
Therefore, the index of refraction (n) of the unknown substance is approximately 0.473.
Learn more about refraction here
https://brainly.com/question/27932095
#SPJ11
A 2-kg mass is attached to a spring whose constant is 18 N/m, and it arrives at the position
of balance. From
t = 0, an external force equal to
f(t)=2sin2t.
Find the resulting equation of motion.
The resulting equation of motion for the system is given by m × x''(t) + k × x(t) = f(t), which is 2 × x''(t) + 18 * x(t) = 2 * sin(2t).
What is equation of motion?
The equations of motion are a set of mathematical relationships that describe the motion of objects under the influence of forces. There are different sets of equations of motion, depending on the specific scenario and the type of motion being considered (linear motion, projectile motion, circular motion, etc.). The equations of motion for linear motion, also known as the equations of uniformly accelerated motion.
To find the equation of motion for the system, we start with Newton's second law of motion, which states that the sum of forces acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the object is the 2-kg mass attached to the spring.
The force exerted by the spring is proportional to the displacement of the mass from its equilibrium position, and it can be expressed as F_spring = -k× x(t), where k is the spring constant and x(t) is the displacement of the mass at time t.
In addition to the force exerted by the spring, there is an external force f(t) = 2 ×sin(2t) acting on the mass.
Applying Newton's second law, we have the equation of motion: m ×x''(t) + k ×x(t) = f(t).
Substituting the given values, m = 2 kg and k = 18 N/m, we obtain 2 ×x''(t) + 18 × x(t) = 2 ×sin(2t).
Therefore, the resulting equation of motion for the system is 2 × x''(t) + 18 × x(t) = 2 × sin(2t).
To know more about equation of motion, refer here:
https://brainly.com/question/29278163#
#SPJ4