Answer:
The potential energy stored in the spring when it is compressed by a distance of 16.0 cm can be calculated using the formula:
U = (1/2) k x^2
where U is the potential energy, k is the spring constant, and x is the displacement from equilibrium position.
Plugging in the given values, we get:
U = (1/2) * 60 N/m * (0.16 m)^2
U = 0.768 J
When the mass is released, the potential energy stored in the spring is converted to kinetic energy of the mass as it moves upward. At the highest point, all of the kinetic energy is converted back to potential energy. The total mechanical energy of the system (spring + block) is conserved, so we can equate the potential energy at the highest point to the initial potential energy stored in the spring:
mgh = U
where m is the mass of the block, g is the acceleration due to gravity (9.81 m/s^2), h is the maximum height reached by the block.
Plugging in the values, we get:
(0.250 kg) * (9.81 m/s^2) * h = 0.768 J
Solving for h, we get:
h = 0.768 J / (0.250 kg * 9.81 m/s^2) ≈ 0.312 m
Therefore, the block rises to a maximum height of approximately 0.312 m above its initial position.
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3. An 87 kg fullback moving east with a speed of 5.0 m/s is tackled by a 97 kg opponent running
west at 3.5 m/s, and collision is perfectly inelastic. Calculate the following:
Given:
Sketch the before and after collisions:
a.
The velocity of the players just after the tackle
b. The decrease in kinetic energy during the collision
The decrease in kinetic energy during the collision is 1187.62 J.
Steps
Before the collision, the fullback's momentum is:
p1 = m1v1 = (87 kg)(5.0 m/s) = 435 kg*m/s (to the east)
The opponent's momentum is:
p2 = m2v2 = (97 kg)(-3.5 m/s) = -339.5 kg*m/s (to the west)
The total momentum before the collision is:
p1 + p2 = (435 kgm/s) + (-339.5 kgm/s) = 95.5 kg*m/s (to the east)
After the collision, the two players move together as one mass. Let vf be their common final velocity. Then the total momentum after the collision is:
p = (m1 + m2)vf = (87 kg + 97 kg)vf = 184 kg*vf (to the east)
Since momentum is conserved, we can equate the total momentum before and after the collision:
p1 + p2 = p
95.5 kgm/s = 184 kgvf
vf = 0.52 m/s (to the east)
Therefore, the velocity of the players just after the tackle is 0.52 m/s to the east.
To find the decrease in kinetic energy during the collision, we first need to find the initial kinetic energy:
KEi = (1/2)m1v1^2 + (1/2)m2v2^2
KEi = (1/2)(87 kg)(5.0 m/s)^2 + (1/2)(97 kg)(-3.5 m/s)^2
KEi = 1211.75 J
Since the collision is perfectly inelastic, the final velocity is the same for both players, and their combined mass is 184 kg. Therefore, the final kinetic energy is:
KEf = (1/2)mvf^2
KEf = (1/2)(184 kg)(0.52 m/s)^2
KEf = 24.13 J
The decrease in kinetic energy during the collision is:
ΔKE = KEi - KEf
ΔKE = 1187.62 J
Therefore, the decrease in kinetic energy during the collision is 1187.62 J.
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thirty 6kg boxes lifted on to ashelf 1.5m height what is the total work
We must first determine the amount of force needed to lift the boxes against gravity. The weight of the boxes is calculated as follows: 30 boxes x 6 kg/box = 180 kg
Work = Force x Distance Work = 1765.8 N x 1.5 m Work = 2648.7 Joules Force = Weight x Gravitational Acceleration Force = 180 kg x 9.81 m/s2 Force = 1765.8 N
The total work required to raise thirty 6 kilogram boxes onto a 1.5 m high shelf is therefore 2648.7 Joules.
How can the gravitational pull of a planet be strengthened?Hence, the gravitational pull between two objects grows as their respective masses do as well. The force of gravity between two objects is equal to their respective masses multiplied by two. To put it another way, the gravitational potential energy directly relates to how high an item is above the earth. Consequently, an item needs be elevated higher in order to enhance its gravitational potential energy. The gravitational potential energy increases with height.
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Match each vocabulary word with the correct definition
Medium
Transverse Waves
1. the overlapping of 2 waves having equal amplitude and wavelength
a disturbance that travels through a medium transporting energy from one location to another location 2.
Surface Waves
3. a substance or material in which something exists or occurs
Crest
4. waves that require a medium in which to travel, involves a transfer of kinetic energy from one place to another in the material
Trough
5. waves in which the movement in the medium is perpendicular to the direction the wave is traveling
Interference
6. waves in which the movement in the medium is parallel to the direction the wave is traveling
Wave
7. a wave that travels on the surface of the water in both transverse and longitudinal motions
Amplitude
8. Height of a wave
Longitudinal Waves
9. Highest part of the wave
Mechanical Waves
10. Lowest part of the wave
Answer:
Medium - 3. a substance or material in which something exists or occurs
Transverse Waves - 5. waves in which the movement in the medium is perpendicular to the direction the wave is traveling
Surface Waves - 7. a wave that travels on the surface of the water in both transverse and longitudinal motions
Crest - 9. Highest part of the wave
Trough - 10. Lowest part of the wave
Interference - 1. the overlapping of 2 waves having equal amplitude and wavelength
Wave - 2. a disturbance that travels through a medium transporting energy from one location to another location
Amplitude - 8. Height of a wave
Longitudinal Waves - 6. waves in which the movement in the medium is parallel to the direction the wave is traveling
Mechanical Waves - 4. waves that require a medium in which to travel, involves a transfer of kinetic energy from one place to another in the material
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Hw2b. 8. Position from polar velocity a particle starts at time at the position the velocity of the particle is written in the polar basis associated with its current position, and is: what is the position of at ?
The particle's location vector at time t is given by: r(t) = t³ + t² + 1
As per the question, we have the velocity of the particle in polar coordinates, but we need to find the position of the particle at time t. To do this, we need to integrate the velocity vector to obtain the position vector.
Let's consider the given velocity vector:
v(t) = (3t² + 2t)i + (2t² + 3t)j
To integrate this velocity vector, we need to find the corresponding position vector. Since the velocity vector is given in polar coordinates, we can express it in terms of polar variables:
v(t) = r'(t) + r(t)θ'(t)
where r'(t) and θ'(t) are the radial and angular components of the velocity vector, respectively.
By comparing the given velocity vector with the above equation, we can write:
r'(t) = 3t² + 2t
θ'(t) = (2t²+ 3t)/r(t)
Integrating r'(t) with respect to t, we get:
r(t) = t³ + t² + C
where C is the constant of integration.
To determine the value of C, we need to use the initial condition given in the problem. The particle starts at the position r = 1 and θ = π/4 at time t = 0. This implies:
r(0) = 1
θ(0) = π/4
Substituting these values in the equation for r(t), we get:
1 = 0 + 0 + C
C = 1
Therefore, the position vector of the particle at time t is given by:
r(t) = t³ + t² + 1
To find the value of θ at time t, we integrate θ'(t) with respect to t:
θ(t) = ∫(2t² + 3t)/r(t) dt
= ∫(2t² + 3t)/(t³ + t² + 1) dt
This integral is not trivial to solve analytically. Therefore, the position of the particle at time t can be expressed as:
r(t) = (t³ + t² + 1)i + f(t)j
where f(t) is the solution of the above integral for θ(t).
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A hot tub holds 480kg of water. On a cold day, the initial temperature of the water is 4 degrees C. Before getting in, the hot tub needs to reach a temperature of 50 C.
A). how much heat is needed to warm up the hot tub water?
B). The hot tub is heated by a propane heater. When burned, propane releases 4.65x10⁷ joules of heat energy per kilogram of propane. How much propane has to be burned to heat the hot tub water?
How do i set this up??
The amοunt οf heat required tο increase the temperature οf 480 kg water tο increase the temperature frοm 4°C tο 50°C is 9.3 × 10⁷ J.
The amοunt οf prοpane burned is 2kg.
What is heat energy?Temperature is a numerical indicatοr οf hοw hοt οr cοld sοmething is. Atοms and mοlecules make up sοlids, liquids, and gases. The temperature οf that substance wοuld be lοw while these atοms and mοlecules are mοving slοwly. The temperature rises as the atοms and mοlecules mοve mοre quickly. The cοmbined energy οf these atοms and mοlecules in mοtiοn is knοwn as heat.
Cοnductiοn, cοnvectiοn and radiatiοn are the three methοds οf heat transfer.
Using the fοrmula:
H = m×s×ΔT
where,
H is the tοtal heat
m is the mass
and ΔT is the change in temperature.
substituting the values and sοlving fοr H,
H = 9.3× 10⁷ J
The amοunt οf prοpane required = H/h
where
H is the tοtal heat and,
h is the heat released by 1kg οf Prοpane.
Mass οf prοpane required= 2kg
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Answer the following questions
1- How to Calculate Power?
2- What is the units of Power?
3- Write a solved example?
Answer:
1- How to Calculate Power?
ans; power is defined as " work done per unit time"
therefore calculated by P= Work/time.
2- What is the units of Power?
Ans; It is watt denoted by "W"
3- Write a solved example?
Ans; Lets say we move a block from One place to another by using 10joules in 4 seconds.
so put values
P=work/time
P=10/4
P=2.5
Explanation:
What is the crossover point in miles between the hybrid vehicle and the alternative vehicle from a competing auto manufacturer? Hybrid Vehicle Vehicle Purchase Cost $18 comma 000 Vehicle Operating Cost per Mile $0. 14 Useful Life of Vehicle 14 years Miles per Year 16 comma 500 Miles per Gallon 33 Average Fuel Price per Gallon $3. 68 Alternative Vehicle Vehicle Purchase Cost $20 comma 000 Vehicle Operating Cost per Mile $0. 10 Useful Life of Vehicle 14 years Miles per Year 16 comma 500 Miles per Gallon 36 Average Fuel Price per Gallon $3. 68 The crossover point, M, is nothing miles (round your response to the nearest whole number)
The crossover point is 56,000 miles, rounded to the closest whole number. The total cost of owning the hybrid vehicle and the alternative vehicle is the same at this point.
The formula for the total cost is :
Total Cost = Vehicle Purchase Cost + (Operating Cost per Mile x Miles per Year x Useful Life of Vehicle)/Miles per Gallon x Average Fuel Price per Gallon
For the hybrid vehicle:
Total Cost = $18,000 + ($0.14 x 16,500 x 14)/33 x $3.68 = $47,672.03
For the alternative vehicle:
Total Cost = $20,000 + ($0.10 x 16,500 x 14)/36 x $3.68 = $47,672.22
Solving these two equations for M gives :
$18,000 + ($0.14 x 16,500 x 14)/33 x $3.68 = $20,000 + ($0.10 x 16,500 x 14)/36 x $3.68
M = 55998
If the vehicle's expected mileage exceeds 56,000 miles, the alternative vehicle becomes more cost-effective; if it falls below 56,000 miles, the hybrid vehicle becomes more cost-effective.
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For the flight of airplanes in the earth's atmosphere, the variation of acceleration of gravity with altitude is generally ignored. One of the highest-flying aircraft has been the lockheed u-2 (see fig. 2 5. 52) which was designed to cruise at 70,000ft. How much does the acceleration of gravity at this altitude differ from the value at sea level?
The Lockheed U-2 or other high-flying aircraft's performance is likely to be unaffected by this disparity.
At an altitude of 70,000ft, the acceleration of gravity is slightly lower than the value at sea level due to the decrease in distance from the center of the Earth. However, this difference is typically small and is often ignored for the flight of airplanes in the Earth's atmosphere. The difference in acceleration of gravity between sea level and 70,000ft is approximately 0.006 m/s^2 or 0.06% of the value at sea level.
Therefore, the effect of this difference on the flight of the Lockheed U-2 or other high-flying aircraft is likely to be negligible and can be safely ignored for practical purposes.
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Light passes from air (n=1) into another medium at 30.0 degrees to the normal. If the angle of refraction is 18.0 degrees, what is the index of refraction of the new medium?
The refractive index of the new medium is approximately 1.59.
Snell's law relates the angles of incidence and refraction of light passing through a boundary between two media with different refractive indices (n). The formula is:
n₁ sin θ₁ = n₂ sin θ₂
where n₁ is the refractive index of the first medium, θ₁ is the angle of incidence, n₂ is the refractive index of the second medium, and θ₂ is the angle of refraction.
In this problem, we know that the angle of incidence is 30.0 degrees and the angle of refraction is 18.0 degrees. We also know that the refractive index of air (n₁) is 1.00. Therefore, we can use Snell's law to solve for the refractive index of the new medium (n₂):
n₁ sin θ₁ = n₂ sin θ₂
1.00 sin 30.0° = n₂ sin 18.0°
n₂ = (1.00 sin 30.0°) / sin 18.0°
n₂ ≈ 1.59
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2. Convert the following to the specified units a). 56MΩ to Ω c). 60Kj to Joules d). 75µC to C
Answer:
c.) 60 000j
Explanation:
c.) 1kj=1000j
60kjx1000
=60 000joules
in one cycle of the engine, the net change in the entropy of both reservoirs (hot and cold together) is.
In one cycle of an engine, the net change in the entropy of both reservoirs (hot and cold together) is zero. This is because the entropy of each reservoir remains constant throughout the cycle.
Entropy is a measure of the randomness and disorder of a system, so the fact that the entropy of the two reservoirs remains constant throughout the cycle is a consequence of the law of conservation of energy. The engine cycle is designed so that the energy transfers between the two reservoirs cause the entropy of each reservoir to remain constant.
In an ideal cycle, the total amount of energy transferred from the hot reservoir to the cold reservoir is equal to the total amount of energy transferred from the cold reservoir to the hot reservoir. Thus, the net change in the entropy of both reservoirs is zero. This can be shown by examining the equation for the change in entropy of a system:
ΔS = Q/T, where Q is the energy transfer and T is the temperature.
The amount of energy transferred between the hot and cold reservoirs will be the same in both directions. Thus, the temperature ratio between the two reservoirs is the same. Since the energy transfer is the same, the change in entropy for both reservoirs is equal, and the net change in entropy is zero. This can be illustrated by the following equation:
ΔS = Q/T = Q/T + Q/T = 0.
In summary, the net change in the entropy is zero. This is due to the law of conservation of energy and the fact that the temperature ratio between the two reservoirs remains constant during the cycle.
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Find a center of mass of a thin plate of density delta equals 5 bounded by the lines y equals x and x equals 0 and the parabola y equals 20 minus x squared in the first quadrant
The center of mass of the thin plate is located at the point (16/3, 8/3) in the first quadrant.
To find the center of mass of a thin plate with a density of delta equals 5 bounded by the lines y equals x and x equals 0 and the parabola y equals 20 minus x squared in the first quadrant, we can use the following formula:
x = (1/M) ∫∫ x δ(x,y) dA
y = (1/M) ∫∫ y δ(x,y) dA
Now we can use this value of M to find the center of mass:
x = (1/M) ∫∫ x δ(x,y) dA
= (1/125) ∫₀²₀ ∫₀^x x 5 dy dx
= (1/125) ∫₀²₀ 5x²/2 dx
= 16/3
y = (1/M) ∫∫ y δ(x,y) dA
= (1/125) ∫₀²₀ ∫₀^x y 5 dy dx
= (1/125) ∫₀²₀ 5x(20-x²)/2 dx
= 8/3
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Find the magnitude of the electric force between the charges 0. 12 C and 0. 33 C at a separation of 2. 5 m. Is the force attractive or repulsive?
The magnitude of the electric force between the charges 0. 12 C and 0. 33 C at a separation of 2. 5 m is 4.987 N. If the charges are of the same sign, the force will be repulsive; if they are of opposite signs, the force will be attractive.
We can use Coulomb's law to find the magnitude of the electric force between two charges:
F = k * ([tex]q_{1}[/tex] * [tex]q_{2}[/tex]) / [tex]r^{2}[/tex]
where F is the magnitude of the force, k is Coulomb's constant (9 x [tex]10^{9}[/tex]10^9 N*[tex]m^{2}[/tex]/[tex]C^{2}[/tex]), [tex]q_{1}[/tex] and [tex]q_{2}[/tex] are the magnitudes of the charges, and r is the separation between the charges.
Plugging in the given values, we get:
F = (9 x [tex]10^{9}[/tex] N*[tex]m^{2}[/tex]/[tex]C^{2}[/tex]) * ((0.12 C) * (0.33 C)) / (2.5 m)^2
Simplifying:
F = 4.987 N
Therefore, the magnitude of the electric force between the charges is approximately 4.987 N.
To determine whether the force is attractive or repulsive, we need to know the signs of the charges.
Since the problem does not specify the signs of the charges, we cannot determine whether the force is attractive or repulsive.
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Directions: SHOW ALL WORK.
What net force is required to accelerate a car at a rate of 2 m/s² if the car has a mass
of 3.000 kg?
F=
m=
Hint: Gravity has an acceleration of 9.8m/s2
a=
Mass times the body's acceleration is how force is calculated. m * a = 3000 * 2 = 6000 Newton is the formula for force, which is defined as mass times acceleration.
What does force in science mean?The definition of "force" is obvious. At this level, the phrases "push" and "pull" are entirely suitable to describe forces. A force is not something that exists inside or within an object. A force acts on the first thing from another.
What differences do forces have?These types of forces are present when two objects interact physically and physically come into contact with one another. The various types of contact forces include frictional, tensile forces, normal, air pressure, applied, and spring forces.
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Gravity has an acceleration of 9.8m/s2. However, this does not apply to the question since the acceleration of the car is 2 m/s². The net force required to accelerate the car is 6.000 kg m/s².
What is acceleration?Acceleration is the rate of change of velocity. It is a vector quantity that is defined as the change in velocity divided by the change in time. Acceleration can be seen as the rate at which an object changes its speed or the rate at which its direction changes. Acceleration can occur in any direction, and can be either positive (speeding up) or negative (slowing down). In physics, acceleration can be caused by forces, such as gravity, friction, and air resistance, or by changes in the motion of an object, such as starting, stopping, turning, or changing speed.
F = ma
F = (3.000 kg)(2 m/s²)
F = 6.000 kg m/s²
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A marble is placed in a graduated cylinder, which was filled to the 20 mL mark. The level rises to 40 mL. What happens to the volume of the water?
Answer:
Below
Explanation:
The volume of water remains the same....the new measurement now includes the volume of the marble ( 20 ml)
A 60 kg rollerblader holds a 4 m long rope that is loosely tied around a metal pole. You push the rollerblader, exerting a 40 N force on her, which causes her to move increasingly fast in a counterclockwise circle around the pole. The surface of the skate is smooth, and the wheels of her rollerblades are well oiled. Determine the tangential and rotational acceleration of the rollerblader
The tangential acceleration of the rollerblader is [tex]0 m/s^2[/tex], and her centripetal acceleration is [tex]0.42 m/s^2.[/tex]
What is centripetal force?The force you exert on the rollerblader is causing her to move in a circular path around the metal pole. This means that there must be a centripetal force acting on her, which is provided by the tension in the rope.
[tex]a = v^2 / r[/tex]
where a is the centripetal acceleration, v is the speed of the rollerblader, and r is the radius of the circle.
To find the speed of the rollerblader, we can use the fact that the tension in the rope is equal to the force you exert on her, which is 40 N. Therefore:
Tension = Centripetal force = [tex]m * a = m * v^2 / r[/tex]
[tex]40 N = (60 kg) * v^2 / 4 m[/tex]
[tex]v^2 = (40 N * 4 m) / 60 kg = 2.67 m/s[/tex]
[tex]v = \sqrt(2.67 m/s) = 1.63 m/s[/tex]
Now we can calculate the centripetal acceleration:
[tex]a = v^2 / r = (1.63 m/s)^2 / 4 m = 0.42 m/s^2[/tex]
Since the rollerblader is moving at a constant speed, her tangential acceleration is zero.
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define the term amplitude
The largest displacement or distance a wave oscillates from its rest state is referred to as amplitude. It establishes the amount of energy a wave may carry by determining the strength or intensity of the wave.
How should amplitude be named?Depending on whether the sun is rising or sinking, the amplitude is designated by the same names as the declination: E or W. The identified and named compass mistake is as follows: It is the distinction between the correct bearing and the compass.
What does amplitude measure mean?The distance between a wave's peak or trough and the location of the medium at rest, also known as the equilibrium position, is often measured as the amplitude in transverse waves.
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Drivers should compensate for a lack of depth perception by..
Answer:
decreasing speed
Explanation:
so that way you have a faster reaction time
A body is displaced through a certain distance x by a force of 30n. if the work done is 100j and the displacement is in the direction of force, what is the value of x
The work done on an object by a constant force is given by the formula:
W = Fd cos(theta)
where:
W = work done (in joules)
F = applied force (in newtons)
d = displacement (in meters)
theta = angle between the force and displacement vectors (in degrees)
In this case, the force is in the same direction as the displacement, so the angle between them is 0 degrees. Therefore, we can simplify the formula to:
W = Fd
We are given that the work done is 100 J and the force is 30 N. Substituting these values into the formula, we get:
100 J = 30 N * d
Solving for d, we get:
d = 100 J / (30 N) = 3.33 meters
Therefore, the displacement is 3.33 meters.
Two identical conducting spheres having charges of opposite sign attract each other with a force of 0.108N when separated by 50.0cm. The spheres are suddenly connected by a thin conducting wire which is then removed and thereafter the spheres repels each other with a force of 0.0360 N. What were the initial charges on the spheres?
Answer:
3 μC, -1 μC or -3 μC, 1 μC
Explanation:
As you can see in the image, let initial charges on two identical spheres be Q and q respectively (we are not considering the sign of q to be negative, value of q will be negative after solving)
initially,
[tex]-0.108 = \frac{KQq}{r^2}[/tex] …. (1)
where r = 0.5 meter (given in question),
after connecting a thin wire, both spheres tend to achieve the same potential conserving the total charge as initial, so after connecting a thin wire potential of both spheres become equal.
let q1 be the final charge on sphere 1 and q2 be the final charge on sphere 2,
[tex]\dfrac{Kq_1}{r} = \dfrac{Kq_2}{r}\\\\q_1 = q_2\\[/tex]... (2)
also, charge is conserved so total charge remains the same,
[tex]Q + q = q1 + q2[/tex] … (3)
if you solve equation 2 and 3, you will get the the final charges,
[tex]q_1 = q_2 = \dfrac{Q + q}{2}[/tex]
now after connecting the spheres the force equation becomes,
[tex]0.0360 = \dfrac{K\left(\dfrac{Q + q}{2}\right)^2}{r^2}[/tex] … (4)
divide the equation 2 by 4, after some simplification we get the below quadratic equation
[tex]3Q^2 + 10Qq + 3q^2 = 0[/tex]
divide the whole equation by [tex]q^2[/tex],
[tex]3\left(\dfrac{Q}{q}\right)^2 + 10\dfrac{Q}{q} + 3 = 0[/tex]
now this is a quadratic equation, after solving we get
[tex]Q = -3q[/tex]
(other solution also works, considering magnitude of charge on Q is more)
now substitute [tex]Q = -3q[/tex] in equation 2 and solve for q
q = 1 μC
Q = -3 μC
(you may consider Q = 3 μC and q = -1 μC)
Hopefully this answer will help you figure out the solution
A student performing simple pendulum 1.2 sec, 1.23 sec, 4. 18. sec, 1. 25 sec, suspectuly time period. Tume Value Absolute error of Mean absolute ervar Percentage a cerror an experiment note the time period for
Answer:
Based on the data provided, it seems that the student is measuring the time period of a simple pendulum. The measured time periods are:
1.2 sec
1.23 sec
4.18 sec
1.25 sec
To find the mean time period, we add up all the measured values and divide by the total number of measurements:
Mean time period = (1.2 + 1.23 + 4.18 + 1.25) / 4 = 2.215 sec
To find the absolute error of each measurement, we subtract the mean time period from each measurement and take the absolute value:
Absolute error of 1st measurement = abs(1.2 - 2.215) = 1.015 sec
Absolute error of 2nd measurement = abs(1.23 - 2.215) = 0.985 sec
Absolute error of 3rd measurement = abs(4.18 - 2.215) = 1.965 sec
Absolute error of 4th measurement = abs(1.25 - 2.215) = 0.965 sec
To find the mean absolute error, we add up all the absolute errors and divide by the total number of measurements:
Mean absolute error = (1.015 + 0.985 + 1.965 + 0.965) / 4 = 1.23 sec
To find the percentage error of each measurement, we divide the absolute error of each measurement by the mean time period and multiply by 100:
Percentage error of 1st measurement = (1.015 / 2.215) * 100 = 45.9%
Percentage error of 2nd measurement = (0.985 / 2.215) * 100 = 44.4%
Percentage error of 3rd measurement = (1.965 / 2.215) * 100 = 88.8%
Percentage error of 4th measurement = (0.965 / 2.215) * 100 = 43.6%
Note that the third measurement has a significantly larger percentage error compared to the other measurements, which suggests that it may be an outlier or there may have been some systematic error in that particular measurement. It is important to carefully analyze such outliers and repeated experiments to ensure accurate results.
A baby mouse 1. 2 cm high is standing 4. 0 cm from a converging mirror having a focal length of 30 cm
The problem involves the image formation of a small object by a converging mirror.
According to the mirror equation, 1/f = 1/di + 1/do, where f is the focal length of the mirror, do is the object distance, and di is the image distance. In this case, the object is a baby mouse that is 1.2 cm high and located 4.0 cm away from the mirror. The mirror is a converging mirror with a focal length of 30 cm. To determine the image distance, we can use the mirror equation as follows: 1/30 = 1/di + 1/4. Solving for di, we get: di = 3.75 cm. This means that the image of the baby mouse is formed 3.75 cm behind the mirror. The size of the image can be determined using the magnification equation, M = -di/do, where M is the magnification. Substituting the values, we get: M = -(3.75 cm)/(4.0 cm) = -0.9375. The negative sign indicates that the image is inverted compared to the object. The magnification also tells us that the image is smaller than the object, with a height of: hi = Mho = (-0.9375)(1.2 cm) = -1.125 cm. Again, the negative sign indicates that the image is inverted. The absolute value of the height tells us that the image is smaller than the object, with a height of 1.125 cm.
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How do this ? I don’t know. I need help
Answer:
inductance and genorator
Explanation:
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the current, and follows any changes in current.
in which electrical wave changed into mechanical wave
A 0.20 kg k g puck is being pushed across a table with a horizontal force of 2.0 N N . It starts from rest and is pushed for 13 seconds, ending with a speed of 1 m/s m / s . Calculate the coefficient of friction μk μ k between the puck and the table.
Answer:
The coefficient of friction between the puck and the table is [tex]\sf 0.00784[/tex]
Explanation:
Here are some of the equations we will be using. Below are the equations for Work, Kinetic Energy, Potential Energy, Distance, and the Force due to Friction.
[tex]\sf W=fd[/tex]
[tex]\sf K_E=\sf \dfrac{1}{2}mv^2[/tex]
[tex]\sf U_E=mgh[/tex]
[tex]\sf d=\dfrac{tv_f}{2}+ \dfrac{tv_i}{2}[/tex]
[tex]\sf F_{Fr} =mg \mu_k[/tex]
Conservation of Energy
If there are frictional forces present, then the work done against the frictional forces is equal to the change in the total Mechanical Energy. The Mechanical Energy will decrease because of the work done against the frictional forces.
[tex]\sf W_{Fr}= \left(K_F+U_F\right)-\left(K_i+U_i\right)[/tex]
Lets put together some of these formulas now.
[tex]\sf -F_{Fr} d= \left(\sf \dfrac{1}{2}mv_f^2+mgh_f\right)-\left(\sf \dfrac{1}{2}mv_i^2+mgh_i\right)[/tex]
[tex]\sf -mg \mu_k\left(\sf \dfrac{tv_f}{2}+ \dfrac{tv_i}{2}\right)= \left(\sf \dfrac{1}{2}mv_f^2+mgh_f\right)-\left(\sf \dfrac{1}{2}mv_i^2+mgh_i\right)[/tex]
In this example our object is starting from rest and is on a flat surface, so we can cancel out any terms with [tex]\sf v_i[/tex] and [tex]\sf h[/tex].
[tex]\sf -mg \mu_k \left(\sf \dfrac{tv_f}{2}\right)= \left(\sf \dfrac{1}{2}mv_f^2\right)[/tex]
Lets solve for [tex]\sf \mu_k[/tex].
Combine [tex]\sf m[/tex] and [tex]\sf \frac{tv_f}{2}[/tex].
[tex]\sf -1\cdot g \cdot \mu_k \cdot \left(\sf \dfrac{m(tv_f)}{2}\right)= \left(\sf \dfrac{1}{2}mv_f^2\right)[/tex]
Combine [tex]\sf g[/tex] and [tex]\sf \frac{m(tv_f)}{2}[/tex].
[tex]\sf -1\cdot \mu_k \cdot\left(\sf \dfrac{g(m(tv_f))}{2}\right)= \left(\sf \dfrac{1}{2}mv_f^2\right)[/tex]
Combine [tex]\mu_k[/tex] and [tex]\sf \frac{g(m(tv_f))}{2}[/tex].
[tex]\sf -1\cdot\sf \dfrac{g(m(tv_f))\mu_k}{2}= \left(\sf \dfrac{1}{2}mv_f^2\right)[/tex]
Remove the parentheses.
[tex]\sf -1\cdot\sf \dfrac{gmtv_f\mu_k}{2}= \left(\sf \dfrac{1}{2}mv_f^2\right)[/tex]
Simplify the right side.
[tex]\sf -1\cdot\sf \dfrac{gmtv_f\mu_k}{2}= \sf \dfrac{mv_f^2}{2}[/tex]
Divide both sides of the equation by [tex]\sf -1[/tex].
[tex]\sf \sf \dfrac{gmtv_f\mu_k}{2}= -\sf \dfrac{mv_f^2}{2}[/tex]
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
[tex]\sf gmtv_f\mu_k= -\sf mv_f^2[/tex]
Divide both sides of the equation by [tex]\sf gmtv_f[/tex].
[tex]\sf \sf \dfrac{gmtv_f\mu_k}{\sf gmtv_f}= \sf \dfrac{-mv_f^2}{\sf gmtv_f}[/tex]
On the left side cancel the common factor of [tex]\sf gmtv_f[/tex].
[tex]\sf \mu_k= \sf \dfrac{-mv_f^2}{\sf gmtv_f}[/tex]
On the right side cancel the common factor of [tex]\sf m[/tex].
[tex]\sf \mu_k= \sf \dfrac{-v_f^2}{\sf gtv_f}[/tex]
On the right side cancel the common factor of [tex]\sf v_f[/tex]
Finally we have an equation to evaluate the coefficient of friction.
[tex]\boxed{\sf \mu_k= -\sf \dfrac{v_f}{\sf gt}}[/tex]
Numerical Evaluation
In this example we are given
[tex]\sf v_f=1\\g=-9.81\\t=13[/tex]
Substituting our given values into the equation yields
[tex]\boxed{\sf \mu_k= -\sf \dfrac{1}{\sf -9.81\cdot 13}}[/tex]
[tex]\boxed{\sf \mu_k=0.007841292245}[/tex]
Rounding to the hundred thousandth leaves us with
[tex]\boxed{\sf \mu_k=0.00784}[/tex]
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The coefficient of kinetic friction between the puck and the table is approximately 0.0079.
What is coefficient of friction?The coefficient of friction is a measure of the amount of frictional force that exists between two surfaces in contact. It is denoted by the symbol μ (mu) and is defined as the ratio of the force of friction between two objects to the normal force that is pressing them together. In other words, it is a value that indicates how difficult it is to slide one object over another.
To resolve this issue, we need to use the equation of motion:
v = u + at
where v is the final velocity (1 m/s), u is the initial velocity (0 m/s), a is the acceleration, and t is the time (13 seconds).
We can rearrange this equation to solve for the acceleration:
a = (v - u) / t
a = (1 m/s - 0 m/s) / 13 s
a = 0.077 m/s²
Next, we can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration:
Fnet = ma
where Fnet is the net force acting on the object, m is its mass (0.20 kg), and a is the acceleration we just calculated.
We know that the only horizontal force acting on the puck is the applied force of 2.0 N, so we can use that as the net force:
Fnet = 2.0 N
Setting Fnet equal to ma and solving for the coefficient of kinetic friction μk:
Fnet = ma
μkmg = ma
μk = a/g
μk = (0.077 m/s²) / 9.81 m/s²
μk = 0.0079
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A sealed, empty 1. 0 L plastic sports bottle is sitting on a porch
in the hot sunlight. The temperature of the air inside the bottle
is 39 °C (312 K). When the sun goes down, the air in the bottle
cools to 20. °C (293 K). Assuming that the bottle is completely
flexible, what is the volume of air at the cooler temperature?
The volume of air in the bottle at the cooler temperature is 1.064 L.
How to calculate volume of air at the cooler temperature?
To solve this problem, we can apply the Ideal Gas Law:
PV = nRT
where P is the gas's pressure, V is its volume, n is the number of moles in the gas, R is the ideal gas constant, and T is its absolute temperature.
Since the bottle is completely flexible, we can assume that the pressure inside the bottle remains constant throughout the process. Therefore, we can set the pressures of the gas at both temperatures equal to each other:
P1V1 = P2V2
where P1 and T1 are the pressure and temperature of the gas at the initial state (when it is hot) and P2 and T2 are the pressure and temperature of the gas at the final state (when it is cool).
We can rewrite this equation to find V2:
V2 = (P1/P2) * V1 * (T2/T1)
where V1 is the gas's initial volume.
Now, we can plug in the values:
V1 = 1.0 L
P1 = P2 (since the bottle is completely flexible)
T1 = 39 °C = 312 K
T2 = 20 °C = 293 K
The ideal gas constant R is 8.31 J/(mol*K), but we do not need to use it here since we are not given the number of moles of gas in the bottle.
Thus, we have:
V2 = (312/293) * 1.0 L = 1.064 L
Therefore, the volume of air in the bottle at the cooler temperature is 1.064 L.
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Categorize each scenario according to whether or not work is done on the object. Work is not done Work is done on the locked door that remains closed while you try to pull it open on the door as you push against it and open it pull a tablecloth out from under them and they remain in place on the dishes when you on boxes as you lift them and place them on the shelf on a shopping cart as you push it around the store on the piano when you drop it from the thind floor to the ground floor on the bowling ball that you are holding while waiting for your turn to bowl
Work is done on the boxes as we push it around the store and on the piano when we drop it from the third floor and work is not done on the locked door, on the dishes and on the bowling ball.
The work done is given by the dot product of the displacement and the force,
W = F.d
W = FdcosA, A is the angle at which the force is applied.
In the first scenario, the work is not done on the locked door that remains closed while we try to pull it open on the door as we push against it and open it, because there is no displacement.
Work in not done to pull a tablecloth out from under them and they remain in place on the dishes, because no displacement of the dishes.
Work is done on boxes as we lift them and place them on the shelf on a shopping cart as we push it around the store because displacement happened.
Work is done on the piano when we drop it from the third floor to the ground floor because A = 0 degrees.
Work is not done on the bowling ball that we are holding while waiting for our turn to bowl because A = 90 degrees.
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Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. B to C is a horizontal span 2.8 m long with a coefficient of kinetic friction μk = 0.20. The section CD under the spring is frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.15 m.
A) Determine the velocity of the block at point B.
B) Determine the thermal energy produced as the block slides from B to C.
C) Determine the velocity of the block at point C.
D) Determine the stiffness constant k for the spring.
An object experiences two forces acting on the same surface (i. E. They are additive): a force of 5. 0N acting at 60. ∘ to the horizontal and a force of 8. 0N acting 45∘ to the horizontal.
What is the magnitude of the resultant force on the object? Give your answer to the nearest newton, without units
The magnitude of the resultant force on the object is approximately 12 N.
For the 5.0 N force:
Horizontal component = 5.0 N * cos(60°) ≈ 2.5 N
Vertical component = 5.0 N * sin(60°) ≈ 4.3 N
For the 8.0 N force:
Horizontal component = 8.0 N * cos(45°) ≈ 5.7 N
Vertical component = 8.0 N * sin(45°) ≈ 5.7 N
Next, we can add the horizontal and vertical components separately:
Resultant horizontal component = 2.5 N + 5.7 N ≈ 8.2 N
Resultant vertical component = 4.3 N + 5.7 N ≈ 10 N
Finally, we can use the Pythagorean theorem to find the magnitude of the resultant force:
Resultant force = sqrt((8.2 N)^2 + (10 N)^2) ≈ 12 N
The resultant force is the net force that acts on an object. It is the vector sum of all the forces acting on the object. If an object is subjected to multiple forces, the resultant force determines the direction and magnitude of the object's motion. If the resultant force is zero, the object will remain at rest or continue moving at a constant velocity. If the resultant force is non-zero, the object will accelerate in the direction of the force.
The concept of the resultant force is particularly important in dynamics, the branch of mechanics that deals with the motion of objects under the influence of forces. The laws of motion developed by Sir Isaac Newton, which are the foundation of classical mechanics, are formulated in terms of resultant forces. The first law states that an object at rest will remain at rest or move at a constant velocity unless acted upon by a net external force, while the second law relates the acceleration of an object to the net force acting on it.
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a 22.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. what centripetal force must be exerted on her for her to remain at constant distance of 1.97 m from the merry-go-round's center
The centripetal force exerted on a 22.0 kg child riding a playground merry-go-round rotating at 40.0 rev/min, to remain at a constant distance of 1.97 m from the merry-go-round's center is 502.82 N.
Centripetal force is the force required to maintain an object in a circular motion with a constant speed. Its direction is towards the center of the circle in which the object is moving.
The formula for calculating the centripetal force is given as: Fc = mv2/r where,
Fc is the centripetal force, m is the mass of the object,
v is the velocity of the object,
r is the radius of the circle.
Substituting the given values,
Mass of the child, m = 22.0 kg
Velocity, v = 40.0 rev/min,
we know 1 rev = 2π rad2π rad/1 rev so 40.0 rev/min = 40.0 * 2π rad/min = 80π rad/min
Radius, r = 1.97 m
Now, converting the velocity units from radians per minute to meters per second,1 rad/min = (1/60) rad/s
Therefore, 80π rad/min = 80π/60 rad/s = (4/3)π rad/s
Velocity, v = rω where, ω is the angular velocity.
Substituting the given values,ω = v/rω = (4/3)π rad/s / 1.97 mω = 2.012 rad/s
Substituting the given values in the formula for centripetal force, we get
Fc = mv2/rFc = 22.0 kg × (2.012 m/s)2 / 1.97 mFc = 502.82 N
Thus, the centripetal force exerted on the child is 502.82 N.
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light travels a certain distance in 2000 years. is it possible that an astronaut, traveling slower than light, would go as far in 20 years of her life as light travels in 2000 years?
They will be unable to cover as much distance as light does.
The statement is: Light travels a certain distance in 2000 years. No, it is not possible for an astronaut, traveling slower than light, to go as far in 20 years of her life as light travels in 2000 years because the speed of light is constant and cannot be matched by anything with mass.
The speed of light in a vacuum is 299,792,458 meters per second (m/s), which is incredibly fast. On the other hand, the fastest spacecraft to ever leave Earth was NASA's New Horizons probe, which traveled at a speed of about 16.26 kilometers per second.
It would take this spacecraft 37,200 years to travel 2000 light-years. Astronauts cannot travel faster than the speed of light, and their velocity will always be lower than that of light. As a result, they will be unable to cover as much distance as light does.
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