the work done by the resultant force during this time interval is 106.0 J.
What is the principle that relates the work done by the net force on an object to its change in kinetic energy?
To find the work done by the resultant force on the particle, we need to use the work-energy principle, which states that the work done by the net force on an object is equal to its change in kinetic energy.
First, we need to find the net force acting on the particle. We can use Newton's second law, which states that the net force is equal to the mass times the acceleration:
F_net = m*a
To find the acceleration, we can use the formula:
a = (v_f - v_i) / t
where v_f is the final velocity, v_i is the initial velocity, and t is the time interval.
a = [(7.0i+3.0j) m/s - (5.0i-4.0j) m/s] / t
a = (2.0i+7.0j) m/s / t
Now we can calculate the net force:
F_net = m*a
F_net = 2.0 kg * (2.0i+7.0j) m/s / t
F_net = (4.0i+14.0j) N / t
Next, we need to calculate the work done by this net force during the time interval. Since the force is not constant, we need to use the work-energy principle in integral form:
W = integral(F_net dot ds)
where dot denotes the dot product, and ds is the infinitesimal displacement vector.
To perform this integration, we need to know the path of the particle. Let's assume that the particle moves in a straight line from its initial position to its final position.
Then, the displacement vector is given by:
ds = (v_f - v_i) * t
ds = [(7.0i+3.0j) m/s - (5.0i-4.0j) m/s] * t
ds = (2.0i+7.0j) m * t
Now we can calculate the dot product between the net force and the displacement vector:
F_net dot ds = (4.0i+14.0j) N / t dot (2.0i+7.0j) m * t
F_net dot ds = 8.0 N + 98.0 N
F_net dot ds = 106.0 J
Therefore, the work done by the resultant force during this time interval is 106.0 J.
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What is the tension on a stone of mass 50 g, tied to a string of length 50 cm and rotated at a speed of 1 m/s?
0.1
100
10
Answer: 0.1
Explanation:
To find the tension on the stone, we can use the centripetal force formula, which is given by F = (mv^2)/r, where m is the mass of the object, v is its velocity, and r is the radius of the circular path.
In this case, the stone is tied to a string and is moving in a circle of radius 50 cm (or 0.5 m), so we have:
F = (0.05 kg) x (1 m/s)^2 / 0.5 m
F = 0.1 N
Therefore, the tension on the string is 0.1 N.
So, the correct answer is 0.1.
A block of mass m = 1.9 kg is attached to a string that is wrapped around the circumference of a wheel of radius R = 8.1 cm. The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially, the wheel rotates with an angular speed ω, causing the block to rise with a linear speed v = 0.43m/s
Find the moment of inertia of the wheel if the block rises to a height of h
= 7.5 cm before momentarily coming to rest.
The moment of inertia of the wheel if the block rises to a height of h is 7.5 cm before momentarily coming to rest is 0.068 kg m².
We can use the conservation of mechanical energy to solve for the moment of inertia of the wheel. Initially, the system has kinetic energy, which is converted to potential energy at the highest point of the block's trajectory. Therefore, we can write:
Initial kinetic energy = Final potential energy
At the start, the wheel and block have kinetic energy due to the motion of the block:
KE i = 0.5 * m * v²
At the highest point of the block's trajectory, all of the kinetic energy is converted to potential energy due to the block's height above the ground:
PE_f = m * g * h
where g is the acceleration due to gravity.
Since the string is wrapped around the circumference of the wheel, the distance that the block moves upwards is equal to the distance that the string moves around the wheel, which is equal to the circumference of the wheel:
h = 2 * pi * R
Substituting this into the expression for potential energy:
PE_f = m * g * 2 * π * R
Equating initial kinetic energy with final potential energy:
0.5 * m * v² = m * g * 2 * π * R
Simplifying and solving for the moment of inertia of the wheel, I:
I = (m * v²) / (2 * g * π * R)
Substituting the given values:
I = (1.9 kg * 0.43 m/s)² / (2 * 9.81 m/s² * π * 0.081 m)
I = 0.068 kg m²
Therefore, the moment of inertia of the wheel is 0.068 kg m².
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You have learned that the pressure from a fluid at a certain depth is given by the equation P = ρgh + Patm. You have also learned that the buoyant force is due to the difference in pressure between the top and bottom of an object. Derive the equation for the buoyant force from these two ideas. (Hint: In your derivation, use a simple submerged object, such as a perfect cube with sides of length s.) (3 points)
To derive the equation for the buoyant force, we can start with the equation for the pressure from a fluid at a certain depth:
P = ρgh + Patm
where P is the pressure at a depth h, ρ is the density of the fluid, g is the acceleration due to gravity, and Patm is the atmospheric pressure at the surface of the fluid.
Now, let's consider a simple submerged object, such as a perfect cube with sides of length s, as the hint suggests. The object is fully submerged in the fluid, so it experiences a pressure difference between the top and bottom surfaces. The pressure at the top surface of the object is Ptop = ρghtop + Patm, where htop is the depth of the top surface below the surface of the fluid. The pressure at the bottom surface of the object is Pbottom = ρghbottom + Patm, where hbottom is the depth of the bottom surface below the surface of the fluid. Since the object is at rest in the fluid, the net force acting on the object must be zero. Therefore, the buoyant force must be equal and opposite to the weight of the object:
Buoyant force = Weight of object
The weight of the object is given by its mass multiplied by the acceleration due to gravity:
Weight of object = mg
where m is the mass of the object and g is the acceleration due to gravity.
To find the buoyant force, we need to find the difference between the pressure at the top and bottom surfaces of the object, and then multiply that difference by the surface area of the object:
Buoyant force = Pressure difference × Surface area
The pressure difference is given by:
Pressure difference = Pbottom - Ptop
= (ρghbottom + Patm) - (ρghtop + Patm)
= ρg(hbottom - htop)
Therefore, the buoyant force is:
Buoyant force = ρg(hbottom - htop) × Surface area
For a perfect cube with sides of length s, the surface area is given by A = 6s^2. Therefore, the buoyant force on the cube is:
Buoyant force = ρg(hbottom - htop) × 6s^2
This is the equation for the buoyant force on a submerged object, derived from the equation for the pressure from a fluid at a certain depth and the concept of the buoyant force being due to the pressure difference between the top and bottom of an object.
A power transistor is a solid-state electronic device. Assume that energy entering the device at the rate of 1.00 W by electrical transmission causes the internal energy of the device to increase. The surface area of the transistor is so small that it tends to overheat. To prevent overheating, the transistor is attached to a larger metal heat sink with fins. The temperature of the heat sink remains constant at 35.0°C under steady-state conditions. The transistor is electrically insulated from the heat sink by a rectangular sheet of mica measuring 8.25 mm by 6.25 mm, and 0.0852 mm thick. The thermal conductivity of mica is equal to 0.0753 W/m·°C. What is the operating temperature of the transistor?
Answer:
Explanation:
The rate of heat transfer from the transistor to the heat sink through the mica sheet can be calculated using Fourier’s Law of heat conduction. The formula for this law is Q = kA(T1 - T2)/d where Q is the rate of heat transfer, k is the thermal conductivity of the material, A is the cross-sectional area through which heat is transferred, T1 and T2 are the temperatures at either end of the material and d is its thickness.
In this case, we know that Q = 1.00 W (the rate at which energy enters the device), k = 0.0753 W/m·°C (the thermal conductivity of mica), A = 8.25 mm * 6.25 mm = 5.15625e-5 m² (the cross-sectional area of the mica sheet), T2 = 35°C (the temperature of the heat sink) and d = 0.0852 mm = 8.52e-5 m (the thickness of the mica sheet).
Substituting these values into Fourier’s Law gives us:
1.00 W = (0.0753 W/m·°C)(5.15625e-5 m²)(T1 - 35°C)/(8.52e-5 m)
Solving for T1 gives us:
T1 ≈ 35 + (1 / ((0.0753 * 5.15625e-5) / 8.52e-5)) ≈ 35 + 22 ≈ 57°C
So under steady-state conditions with an energy input rate of 1 W and a heat sink temperature of 35°C, we can expect that the operating temperature of this power transistor would be approximately 57°C.
Drag each tile to the correct box. Not all tiles will be used. A chemical reaction takes place in which energy is released. Arrange the reaction’s characteristics in order from start to finish. lower energy of reactants higher energy of products higher energy of reactants transition state
Answer:
Start:
Higher energy of reactants -> Transition state
Finish:
Lower energy of reactants -> Higher energy of products
Explanation:
Now write the magnitude of the normal force again, this time in terms of the gravitational force Fg, g, θ, the radius of the track r, and the velocity that the car is traveling v. Please use proper number of parentheses in your denominator (Expert TA)
The magnitude of the normal force of the car is given by Fn = Fg cotθ.
What is the normal force of the car?The normal force is the force exerted by the racetrack perpendicular to the car's motion. Let's now derive the expression for the magnitude of the normal force of the car:
The perpendicular component of the normal force is given by:
Fn⊥ = Fg cosθ
The parallel component of the normal force provides the centripetal force required for circular motion.
The centripetal force (Fc) is given by:
Fc = mv²/r
where;
m is the mass of the car, v is the velocity of the car, and r is the radius of the circular path.The centripetal force can also be expressed in terms of the parallel component of the normal force:
Fc = Fn∥ = Fn sinθ
Equating the two expressions for Fc, we get:
Fn sinθ = mv²/r
Solving for Fn, we get:
Fn = mv²/(r sinθ)
Substituting the expression for Fg cosθ, we get:
Fn = Fg cosθ / sinθ
or
Fn = Fg cotθ
where;
Fg is the gravitational force, g is the acceleration due to gravity, θ is the angle of banking of the track, and r and v are the radius and velocity of the car respectively.Learn more about normal force here: https://brainly.com/question/14486416
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The complete question is below:
Circular turns of radius r in a racetrack are often banked at an angle θ to allow the cars to achieve higher speeds around the turns. Assume friction is not present.
Now write the magnitude of the normal force of the car, in terms of the gravitational force Fg, g, θ, the radius of the track r, and the velocity that the car is traveling v.
4. A 25,000kg asteroid is flying towards the Earth at a speed of 1500.0m/s. How much Silly Putty would it take to stop the asteroid if we launched it at a velocity of -100.0m/s? Assume the Silly Putty sticks to the asteroid.
To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant if there are no external forces acting on it. We can set the momentum of the asteroid before the collision equal to the momentum of the asteroid-Silly Putty system after the collision.
The momentum of the asteroid before the collision is:
P_before = m_ast * v_ast
where m_ast is the mass of the asteroid and v_ast is its velocity.
The momentum of the asteroid-Silly Putty system after the collision is:
P_after = (m_ast + m_sp) * v_final
where m_sp is the mass of the Silly Putty, v_final is the velocity of the asteroid-Silly Putty system after the collision, which we assume to be zero.
We can equate these two expressions for momentum and solve for the mass of the Silly Putty:
m_sp = (m_ast * v_ast) / (-v_final)
Substituting the given values:
m_ast = 25,000 kg
v_ast = 1500.0 m/s
v_final = -100.0 m/s
m_sp = (25,000 kg * 1500.0 m/s) / (-(-100.0 m/s))
m_sp = 375,000 kg m/s / 100.0 m/s
m_sp = 3750 kg
Therefore, we would need 3750 kg of Silly Putty to stop the asteroid if we launched it at a velocity of -100.0 m/s.
Which of the following thermometers responds best to changing temperature? A Mercury thermometer. BAlcohol thermometer. C Resistance thermometer. D Thermoelectric thermometer. E Gas thermometer.
Answer:
D. Thermoelectric thermometer
Explanation:
It preferred for rapidly changing temperature
Write a 16 line poem that describes centripal force utilizing all key concepts and terms.
A typical 16-line poem that described centripetal force can be found below.
Centripetal forceIn circular motion, a force we call,
Centripetal, it keeps things in thrall.
Directed towards the center of the path,
Without it, objects would face a wrath.
Angular velocity is key,
The rate of change of the angle we see.
And the radius of the circle too,
Both play a role in what we must do.
The mass of the object cannot be ignored,
It factors in with gravity's cord.
As the force pulls towards the center,
Centripetal force is what we enter.
It is the sum of all the forces in play,
Equal to mass times velocity squared, we say.
And if the force is too weak or too strong,
Off the circular path, the object goes wrong.
Thus, centripetal force is what we need,
To keep objects moving at the speed,
In a circular path, they're meant to be,
A force that keeps them in harmony.
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Two friends are rock climbing on a cliff face. They are 18 m above the
ground. The two friends have a combined mass of 150 kg. Use
9 = 9.8 m/s².
Calculate the gravitational potential energy of the two climbers.
Round your answer to the nearest thousand.
J
The gravitational potential energy of the two climbers would be 26,460 J.
Gravitational potential energy calculationThe gravitational potential energy (PE) of an object is given by the formula:
PE = mgh
where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above some reference point.
In this case, the combined mass of the two climbers is 150 kg, and they are 18 m above the ground. Using g = 9.8 m/s², we can calculate their gravitational potential energy as:
PE = (150 kg) x (9.8 m/s²) x (18 m) = 26,460 J
Rounded to the nearest thousand, the gravitational potential energy of the two climbers is 26,000 J.
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How much energy is produced in J when the sun converts 2 kg of mass into energy?
Answer:
The energy produced by the sun when it converts 2 kg of mass into energy is given by Einstein's famous equation E = mc², where E is the energy produced, m is the mass converted, and c is the speed of light.
Substituting the values, we have:
E = (2 kg) x (299,792,458 m/s)²
E = 2 x 89,875,517,873,681,764 J
E ≈ 1.7975 x 10²⁰ J
Therefore, the sun produces approximately 1.7975 x 10²⁰ joules of energy when it converts 2 kg of mass into energy.
Typical value for the magnitude of the electric field inside the atom is
a. 10-11N/C
b. 1011N/C
c. 10-9N/C
d. 109N/C
Answer:d. 109N/C
Explanation: The atomic electric field, the field between the atomic nucleus and the surrounding electron cloud, should possess information about the atomic species, local chemical bonding, and charge redistributions between bonded atoms.
Some roads have signs that specify a maximum load for the vehicles that travel on them. Why might this be?
Answer: Applying a weight limit to a road is often done in an attempt to protect a roadway's appearance in particular. It also aims to protect the character and environment of rural areas, villages, and residential estates. Restricting overweight freights may just prevent damages like pot holes and cracks in the road.
Explanation:
I HOPE THIS HELPED GOOD LUCK AND I AM OPEN FOR FREE ANSWERS!
Tamara is playing a game of billiards. The white cue ball has a mass of 0.17 kg and all the other balls have a mass of 0.16 kg. The cue ball is moving at a velocity of 6 m/s when it collides with the number seven ball. If the cue ball comes to a complete stop after the collision, then what will the resulting velocity be on the number seven ball?
Answer: (0.17 * 6) + ( 0.16 * 0 ) = (0.17 * 0) + ( 0.16 * v2)
v2 = 6.375 m/s
Explanation:
The answer is v2 = 6.375 m/s
(I did the equation and everything but just in case, check with someone else so you don't get the wrong answer)
Maria is taking an emotional intelligence as that involves looking at abstract image and describing it she describes a couple relaxing on the beach at sunset which personality test is Maria taken
Maria is taking the Rorschach inkblot test.
What personality test involves looking at abstract image and describing it ?The test is designed to assess an individual's personality traits and psychological functioning based on their responses to the images.
The Rorschach inkblot test, which uses a set of inkblot images and asks participants to describe what they see. The Rorschach test is a projective test that is often used to assess an individual's personality, emotional functioning, and thought processes.
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Which statement correctly identifies and interprets the figurative
language in this excerpt from the passage?
Other times, he seemed to saw himself in two, his legs driving him one way
while his head and torso faked another, his body rejoining at the rim to lay the
ball in with a knowing smirk.
The metaphor "sawing himself in two" highlights the basketball player's agility as his legs and upper body move in opposing directions before coming together at the rim to hit a shot.
Which one best defines figurative language?Essentially, employing figurative language involves distorting the meaning of words to convey a point, sound clever, or create a joke. Figurative language is a common technique used in narrative writing when the author wants to make the reader feel strongly about something.
What circumstance might figurative language be used in?Literature forms like poetry, drama, prose, and even speeches use figurative language. Figurative language is a literary element that is employed throughout
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On the radio, the station KROQ (106.7) broadcasts radio waves at a frequency of 106,700,000 Hertz. If the velocity of a radio wave is approximately 300,000,000 m/s, what is the wavelength of KROQ’s radio waves?
Hence, the radio waves from KROQ have a wavelength of roughly 2.81 metres.
How can you determine a radio wave's frequency?A radio wave's frequency is determined by dividing its velocity (c = 299 792 458 m/s, or the speed of light) by its wavelength. Wavelength is the length in metres of a single complete wave. In maths, frequency is defined as f = c/.
The frequency of radio waves is 106,700,000 Hz, while the speed of light is roughly 300,000,000 m/s. The formula is as follows: c = fλ
where the wavelength is used.
When we rearrange this formula to account for, we obtain: λ = c / f
Inputting the values provided yields:
λ = 300,000,000 m/s / 106,700,000 Hz
λ ≈ 2.81 meters
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Sergio saw an angle that measures greater than 0° and less than 90°.What type of angle did he see
A Camot engine works between the se and the sink with efficiency 40% How much perature of the sink be lowered keeping the source parature constant so that its efficiency increases by 10%?
Answer:
if the temperature of the sink is lowered by 6.7%, the efficiency of the Carnot engine will increase by 10%.
Explanation:
The efficiency of a Carnot engine is given by the equation:
η = 1 - T_sink / T_source
where η is the efficiency, T_sink is the temperature of the sink, and T_source is the temperature of the source.
In this case, we are given that the efficiency of the engine is 40%. Therefore, we can write:
0.4 = 1 - T_sink / T_source
Rearranging this equation, we get:
T_sink / T_source = 1 - 0.4
T_sink / T_source = 0.6
Next, we are asked to find the temperature of the sink needed to increase the efficiency of the engine by 10%. Let's call this new efficiency η_new. Since the efficiency of a Carnot engine is given by the same equation as before, we can write:
η_new = 1 - T_sink_new / T_source
where η_new is the new efficiency, and T_sink_new is the new temperature of the sink.
We know that the new efficiency is 10% higher than the original efficiency, so we can write:
η_new = η + 0.1η = 0.4 + 0.1(0.4) = 0.44
Substituting this into the equation above, we get:
0.44 = 1 - T_sink_new / T_source
Rearranging this equation, we get:
T_sink_new / T_source = 1 - 0.44
T_sink_new / T_source = 0.56
Now we can set up an equation to find the new temperature of the sink:
0.56 = T_sink_new / T_source
T_sink_new = 0.56T_source
To find the temperature difference between the old and new sink temperatures, we can subtract the two equations we have derived:
T_sink_new - T_sink = 0.6T_source - 0.56T_source
T_sink_new - T_sink = 0.04T_source
Finally, we can substitute the given efficiency of 40% to find the source temperature:
0.4 = 1 - T_sink / T_source
T_source = T_sink / (1 - 0.4)
T_source = T_sink / 0.6
Substituting this expression for T_source into the equation for the temperature difference, we get:
T_sink_new - T_sink = 0.04(T_sink / 0.6)
Simplifying, we get:
T_sink_new - T_sink = 0.067T_sink
Multiplying both sides by 100, we get:
(T_sink_new - T_sink) * 100 = 6.7T_sink
Therefore, if the temperature of the sink is lowered by 6.7%, the efficiency of the Carnot engine will increase by 10%.
what two changes need to be made so that the plug is wired correctly ?
It is important to note that wiring a plug can be dangerous, and if you are not confident in your ability to do so, you should seek the help of a qualified electrician. Incorrectly wiring a plug can result in electrical shock.
What are the step for plug wired ?
The first change that may need to be made is to ensure that the correct wires are connected to the corresponding terminals on the plug. Typically, the green and yellow wire is connected to the earth terminal, the blue wire to the neutral terminal, and the brown wire to the live terminal.
How can you determine whether a plug is wired properly?Voltage can be measured with a multimeter. A probe should be inserted into each slot to measure the line voltage. A fully functioning outlet registers between 110 and 120 volts. Check the outlet and the wiring if there is no reading.
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What is the vector sum of a vector T~ given by 40 m, 30 degrees and a vector U~ given by 12
m, 225 degrees?
Hence, R = 28.97 m, 24.5 degrees is the vector sum of T and U.
Is a vector at 30 degrees?A vector's direction is frequently stated as a rotation of the vector's "tail" anticlockwise with respect to due East. In accordance with this practise, a vector having a direction of 30 degrees is a vector that has been anticlockwise rotated 30 degrees with respect to due east.
Let's begin by separating the components of the vector T:
T~ = 40 m, 30 degrees
T_x = 40 cos(30) = 34.64 m
T_y = 40 sin(30) = 20 m
Let's now decompose the vector U into its constituent parts:
U~ = 12 m, 225 degrees
U_x = 12 cos(225) = -8.49 m
U_y = 12 sin(225) = -8.49 m
It is possible to combine elements of the same type (x and y):
R_x = T_x + U_x = 34.64 m - 8.49 m = 26.15 m
R_y = T_y + U_y = 20 m - 8.49 m = 11.51 m
The Pythagorean theorem can be used to determine the size of the resulting vector R:
|R~| = sqrt(R_x² + R_y²) = sqrt((26.15 m)² + (11.51 m)²) = 28.97 m
The inverse tangent function can be used to determine the direction of the resulting vector R:
theta = tan⁻¹(R_y/R_x) = tan⁻¹(11.51 m/26.15 m) = 24.5 degree.
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A man stands on the roof of a building of height 14.0 m and throws a rock with a velocity of magnitude 32.0 m/s at an angle of 29.0 ∘ above the horizontal. You can ignore air resistance.
A) Calculate the maximum height above the roof reached by the rock.
Express your answer in meters
B) Calculate the magnitude of the velocity of the rock just before it strikes the ground.
Express your answer in meters per second.
C) Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.
Express your answer in meters.
Answer:
A) The maximum height above the roof reached by the rock can be found using the formula:
h = (v₀²sin²θ)/(2g)
where v₀ is the initial velocity (32.0 m/s), θ is the angle of the initial velocity (29.0°), and g is the acceleration due to gravity (9.81 m/s²).
Plugging in the values, we get:
h = (32.0²sin²29.0)/(2(9.81)) = 31.1 m
Therefore, the maximum height above the roof reached by the rock is 31.1 meters.
B) The vertical component of the velocity just before the rock strikes the ground is:
vᵥ = v₀sinθ - gt
where t is the time it takes for the rock to reach the ground.
We can find t by using the formula:
h = v₀sinθt - (1/2)gt²
where h is the height of the building (14.0 m). Rearranging this formula and solving for t, we get:
t = (v₀sinθ + sqrt((v₀sinθ)² + 2gh))/g
Plugging in the values, we get:
t = (32.0sin29.0 + sqrt((32.0sin29.0)² + 2(9.81)(14.0)))/9.81 = 4.01 s
Therefore, the vertical component of the velocity just before the rock strikes the ground is:
vᵥ = 32.0sin29.0 - 9.81(4.01) = -14.3 m/s
Note that the negative sign indicates that the velocity is directed downwards.
C) The horizontal distance from the base of the building to the point where the rock strikes the ground can be found using the formula:
d = v₀cosθt
Plugging in the values, we get:
d = 32.0cos29.0(4.01) = 96.4 m
Therefore, the horizontal distance from the base of the building to the point where the rock strikes the ground is 96.4 meters.
What is the relationship of the wavelength of a
particle and its mass?
a
The wavelength of a particle cannot
be measured.
b They are directly related.
C
The mass of a particle does not affect
its wavelength.
d They are inversely related.
The relationship of the wavelength of a particle and its mass is they are inversely related.
Option D is correct.
What is de Broglie frequency condition?The link between a particle's mass and wavelength is provided by the de Broglie wavelength equation: = h/p,
where is the wavelength, h is the Planck constant, and p is the particle's momentum.
This condition shows that a molecule's energy is contrarily relative to its frequency. Because momentum (p = mv) is defined as the product of mass and velocity, we can also say that a particle's wavelength is inversely proportional to its mass.
What is the Wavelength?A wavelength is the distance between two identical points (adjacent crests) in consecutive cycles of a waveform signal that travels in space or down a wire. In wireless systems, its length is typically measured in meters (m), centimeters (cm), or millimeters (mm).
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It takes 80 pounds of force to
stretch a particular spring 2
inches. How much work is done
in stretching it from its relaxed
state a total of 4 inches?
[?] inch - pounds
Answer: 240 inch-lbs.
Explanation:
The spring constant, k, is given by:
k = (F/x)
where F is the force, x is the displacement, and k is the spring constant.
Using the given information, we can calculate the spring constant as:
k = (80 lbs / 2 in) = 40 lbs/in
To find the work done in stretching the spring from its relaxed state to a total of 4 inches, we need to integrate the force over the displacement:
W = ∫F dx
Since the force required to stretch the spring varies with displacement, we need to break up the integration into two parts: one from 0 to 2 inches, and another from 2 to 4 inches.
W = ∫0^2 F dx + ∫2^4 F dx
The first integral is:
∫0^2 F dx = ∫0^2 (kx) dx = (1/2)kx^2 = (1/2)(40 lbs/in)(2 in)^2 = 80 inch-lbs
The second integral is:
∫2^4 F dx = ∫2^4 (2k) dx = 2kx = 2(40 lbs/in)(4 in - 2 in) = 160 inch-lbs
Therefore, the total work done in stretching the spring from its relaxed state to a total of 4 inches is:
W = ∫0^2 F dx + ∫2^4 F dx = 80 inch-lbs + 160 inch-lbs = 240 inch-lbs
So, the work done in stretching the spring from its relaxed state a total of 4 inches is 240 inch-lbs.
A block of mass m is supported by two identical parallel vertical springs, each with spring stiffness constant k. What will be the frequency of vibration? The answer is not a number, but an equation.
f=*****
The frequency of vibration of the block supported by two identical parallel vertical springs with spring stiffness constant k and mass m is [tex](1 / 2\pi) * \sqrt(2k / m).[/tex]
What does physics mean by vibrational frequency?In physics, frequency is the number of waves that pass a fixed point in a unit of time as well as the number of cycles or vibrations that a body in periodic motion experiences in a unit of time.
The frequency of vibration of a mass-spring system is given by the formua:
[tex]f = (1 / 2\pi) * \sqrt(k / m)[/tex]
where f is the frequency of vibration, k is the spring constant, and m is the mass of the object.
In this case, the block is supported by two identical parallel vertical springs, each with spring stiffness constant k. So, the effective spring constant is the sum of the individual spring constants:
k_eff = 2k
The mass of the block is given as m.
So, the frequency of vibration of the block supported by two identical parallel vertical springs can be calculated as:
[tex]f = (1 / 2\pi) * \sqrt(k_eff / m) = (1 / 2\pi) * \sqrt((2k) / m)\\f = (1 / 2\pi) * \sqrt(2k / m)[/tex]
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a 2.5 Mass ball thrown vertically upward with 10 m/s calculate a the potential energy after the 0.2second
Answer:
35J
Explanation:
The mass of the ball=2.5kg
The initial speed=10m/s
we have to calculate the height= h
s=ut+1/2at^2
h=10*0.2 -1/2*10*0.04
h=2-0.2
h= 1.8m
the potential energy= mgh
= 2.5kg*10*1.8
= 25*1.8
= 35J
Two resistors of 5.0 and 9.0 are connected in parallel. A 4.0- resistor is then connected in series with the parallel combination. A 6.0-V battery is then connected to the series-parallel combination. What is the current through the 5.0- resistor?
Answer:
First, we need to find the equivalent resistance of the parallel combination of 5.0 and 9.0 resistors:
1/R = 1/5.0 + 1/9.0
1/R = 0.4 + 0.1111
1/R = 0.5111
R = 1/0.5111
R ≈ 1.955 ohms
The equivalent resistance of the parallel combination is approximately 1.955 ohms.
Next, we need to find the total resistance of the circuit:
R_total = 4.0 + 1.955
R_total = 5.955 ohms
The total resistance of the circuit is approximately 5.955 ohms.
Using Ohm's Law, we can find the current through the circuit:
I = V/R_total
I = 6.0/5.955
I ≈ 1.006 A
The current through the circuit is approximately 1.006 A.
Finally, we can use the current divider rule to find the current through the 5.0-ohm resistor:
I_5 = (R_parallel / (R_parallel + R_series)) * I_total
I_5 = (1.955 / (1.955 + 4.0)) * 1.006
I_5 ≈ 0.383 A
The current through the 5.0-ohm resistor is approximately 0.383 A.
A container with a height of 7.7 inches with an open top has a 5.6 inch diameter and is open to the atmosphere. The container is filled with water. The bottom of the container has a 0.87 inch diameter hole. Calculate ρgh at the top of the container if the datum is set at the bottom of the container.
This is the pressure at the top of the container due to the height of the water. The pressure at the bottom of the container due to the height of the water is 0 Pa since the datum was set at the bottom.
What is pressure?Pressure is a physical quantity used to measure the force applied by an object to another object or by an object to a surface. It can be expressed as the force per unit area and is typically measured in units such as pounds per square inch (psi) or pascals (Pa). Pressure can be applied to gases, liquids, and solids, and is generated by the weight of the atmosphere, the force of gravity, and by the movement of air or liquids. Pressure can also be created by mechanical devices such as pumps and compressors, as well as by chemical reactions.
ρ = density of water = 1000 kg/m3
g = acceleration due to gravity = 9.81 m/s2
h = height of the container = 7.7 in = 0.198 m
Using the equation ρgh = density x gravity x height, we can calculate the pressure at the top of the container to be:
ρgh = (1000 kg/m3)(9.81 m/s2)(0.198 m) = 1960.38 Pa
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The fastest recorded pitch in Nippon Professional Baseball, thrown by Shohei Otani in 2016, was clocked at 102.5 mi/h. If a pitch were thrown horizontally at this speed, how far would the ball fall vertically (in ft) by the time it reached home plate, 60.5 ft away?
Incorrect: Your answer is incorrect.
ft
To solve this problem, we can use the kinematic equation for vertical motion under constant acceleration, which is given by:
[tex]y = vi*t + (1/2)at^2[/tex]
What is displacement?
Displacement is a vector quantity that refers to the overall change in position of an object from its initial position to its final position.
It is a straight line distance between the initial and final position, in a specific direction.
where y is the displacement (in this case, the vertical distance the ball falls), vi is the initial velοcity (0 in this case since the ball is thrοwn hοrizοntally), a is the acceleratiοn due tο gravity[tex](-32.2 ft/s^2)[/tex], and t is the time it takes fοr the ball tο reach hοme plate. We can find t by dividing the distance tο hοme plate by the hοrizοntal velοcity:
[tex]t = 60.5 ft / (102.5 mi/h * 5280 ft/mi * 1 h/3600 s) = 0.400 s[/tex]
Now we can use the kinematic equation to find y:
[tex]y = 0 + (1/2)(-32.2 ft/s^2)(0.400 s)^2 = -2.57 ft[/tex]
Note that the negative sign indicates that the displacement is downward. Therefore, the ball falls about 2.57 feet vertically by the time it reaches home plate.
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A body of mass 1 kg is pushed at a constant speed against a vertically placed wall, with a constant force F, which forms an angle of 45 degrees with the horizontal, as in the picture. The sliding friction coefficient is 0.2. What is the intensity of the force F? For the acceleration of the heavier force, take g=10 m/s2.
The intensity of the force F is calculated to be approximately 2.83 N.
What is sliding friction coefficient?Coefficient of sliding friction is a value that measures force of sliding friction for particular surface type.
Weight = mg = 1 kg x 10 m/s² = 10 N (acting downwards)
F_vertical - Weight = 0
F_vertical = 10 N
As Frictional force = coefficient of friction x normal force
Frictional force = 0.2 x 10 N = 2 N (acting to the left)
F_horizontal = F x cos(45) = F / √2
F_horizontal - frictional force = 0
F_horizontal = frictional force = 2 N
F / √2 = 2 N
F = 2 N x √2
F ≈ 2.83 N
Therefore, the intensity of the force F is approximately 2.83 N.
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