Question 1

When a Hooke's law spring is stretched a distance 3x,how much is the increase in energy stored in it from when it was stretched a distance x? Give your answer in terms of a multiple of the energy stored in the spring when it is stretched a distance x.
A) It is 3 times as much.
B) It is 8 times as much.
C) It is 4 times as much.
D) It is 9 times as much.

Accepted Answer

The potential energy stored in a spring is proportional to the square of its displacement from its equilibrium position. Therefore, when the spring is stretched three times as far, the displacement is $(3x)^2 = 9x^2$ times as much as when it is stretched only $x$. Therefore, the increase in potential energy is $(9x^2-x^2) = 8x^2$ times as much as the potential energy stored when the spring is stretched only $x$.

Question 2

An 80,000-kg airliner is flying at 900 km/h at a height of 8.00 km.What is its total energy (kinetic + potential)if the total was 0 when the airliner was at rest on the ground?
A) 250 MJ
B) 478 MJ
C) 8770 MJ
D) 10,300 MJ

Accepted Answer

The total energy of the airliner can be calculated as the sum of its kinetic and potential energy.

Kinetic energy = 1/2 * m * v^2 = 1/2 * 80000 kg * (250 m/s)^2 = 2,500,000,000 J

Potential energy = m * g * h = 80000 kg * 9.81 m/s^2 * 8000 m = 6,278,400,000 J

Total energy = Kinetic energy + Potential energy = 8,778,400,000 J

Converting J to MJ: 8,778,400,000 J = 8,778.4 MJ

Therefore, the best choice is C with a total energy of 8770 MJ.

Question 3

A pole-vaulter clears 5.00 m.With what speed does he strike the mat in the landing area?
A) 2.70 m/s
B) 9.90 m/s
C) 10.8 m/s
D) 21.6 m/s

Accepted Answer

The answer of A pole-vaulter clears 5.00 m.With what speed...

Question 4

A simple pendulum,2.0 m in length,is released by a push when the support string is at an angle of 25° from the vertical.If the initial speed of the suspended mass is 3.0 m/s when at the release point,to what maximum angle will it move in the second half of its swing?
A) 36°
B) 30°
C) 19°
D) 47°

Accepted Answer

The answer of A simple pendulum,2.0 m in length,is released...

Question 5

Old Faithful geyser in Yellowstone Park shoots water hourly to a height of 30 m.With what velocity does the water leave the ground?
A) 7.0 m/s
B) 14 m/s
C) 24 m/s
D) 28 m/s

Accepted Answer

We can use the equation for projectile motion: 
y = vi*t + (1/2)*a*t^2

Where y = 30 m (maximum height reached by the water), vi is the initial velocity, t is the time it takes for the water to reach its maximum height (0.0 seconds since the water starts at the ground), and a is the acceleration due to gravity (-9.8 m/s^2 or -g).

Thus, we can solve for vi:

30 m = vi*(0.0 s) + (1/2)*(-g)*(0.0 s)^2

vi = sqrt((2*g*y)/1)

Plugging in values, we get:

vi = sqrt((2*9.8 m/s^2 * 30 m)/1) 
vi = sqrt(588) 
vi = 24.2 m/s

Thus, to two significant figures, the water from Old Faithful geyser leaves the ground with a velocity of 24 m/s.

Question 6

An amount of work equal to 3.0 J is required to compress the spring in a spring-gun.What is the "launch speed" of a 15 g marble?
A) 14 m/s
B) 15 m/s
C) 18 m/s
D) 20 m/s

Accepted Answer

The answer of An amount of work equal to 3.0...

Question 7

A Hooke's law spring is compressed 12.0 cm from equilibrium and the potential energy stored is 36.0 J.What is the spring constant in this case?
A) 10,000 N/m
B) 5000 N/m
C) 1200 N/m
D) The correct answer is not given.

Accepted Answer

The potential energy stored in a spring is given by $ PE = \frac{1}{2} k x^2 $. Solving for $ k $, we have $ k = \frac{2 \times PE}{x^2} $. Substituting $ PE = 36.0 \, \text{J} $ and $ x = 0.12 \, \text{m} $, we get $ k = \frac{2 \times 36.0}{0.12^2} = 5000 \, \text{N/m} $.

Question 8

A 50-N crate is pulled up a 5.0-m inclined plane by a worker at constant velocity.If the plane is inclined at an angle of 37° to the horizontal and there exists a constant frictional force of 20 N between the crate and the surface,what is the force applied by the worker?
A) zero
B) 50 N
C) 30 N
D) 40 N

Accepted Answer

The answer of A 50-N crate is pulled up a...

Question 9

Which of the following is not true about potential energy?
A) Potential energy is stored energy.
B) Potential energy is related to position.
C) Potential energy is a scalar quantity.
D) Potential energy has direction.

Accepted Answer

Potential energy is a scalar quantity, meaning it only has magnitude and not direction. It is related to position and is stored energy.

Question 10

By how much is the energy stored in a Hooke's law spring increased when its stretch is increased from 4.00 cm to 8.00 cm?
A) 100%
B) 200%
C) 300 %
D) The correct answer is not given.

Accepted Answer

The energy stored in a Hooke's law spring is given by the formula E = (1/2) kx^2, where k is the spring constant and x is the displacement from the equilibrium position. When the stretch is increased from 4.00 cm to 8.00 cm, the displacement (x) increases by a factor of 2. Therefore, the energy stored increases by a factor of (2)^2 = 4. This is equivalent to a percentage increase of 300% (i.e., the energy stored is quadrupled). Thus, the correct answer is C.

Question 11

A 2000-kg ore car rolls 50.0 m down a frictionless 10.0° incline.If there is a horizontal spring at the end of the incline,what spring constant is required to stop the ore car in a distance of 2.00 m?
A) 340 kN/m
B) 68.1 kN/m
C) 1700 kN/m
D) 85.1 kN/m

Accepted Answer

The answer of A 2000-kg ore car rolls 50.0 m...

Question 12

A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 30 m/s and initial angle of 30°.What is the kinetic energy of the baseball at the highest point of the trajectory? Ignore air friction.
A) zero
B) 51 J
C) 92 J
D) 120 J

Accepted Answer

At the highest point of the trajectory, the vertical component of the velocity is zero, but the horizontal component remains unchanged. The initial horizontal velocity is 30 m/s * cos(30°) = 25.98 m/s. The kinetic energy at the highest point is (1/2) * 0.15 kg * (25.98 m/s)^2 = 51 J.

Question 13

A bobsled makes a run down an ice track starting at 66 m vertical distance up the hill.If there is no friction,what is the velocity at the bottom of the hill?
A) 27 m/s
B) 36 m/s
C) 44 m/s
D) 54 m/s

Accepted Answer

The potential energy at the top is converted to kinetic energy at the bottom. Using the equation mgh = 0.5mv^2, where g = 9.8 m/s^2 and h = 66 m, we solve for v: v = sqrt(2gh) = sqrt(2*9.8*66) = 36 m/s.

Question 14

A spring with spring constant k is used to launch a mass m up a frictionless inclined plane having angle of elevation θ.What is the maximum height reached above the starting elevation of the mass during the motion of the mass if the spring is compressed a distance d before launch?
A)

B)

C)

D)

Accepted Answer

The answer of A spring with spring constant k is...

Question 15

A hill is 200 m long and makes an angle of 12° with the horizontal.As a 50-kg jogger runs up the hill,how much work does gravity do on the jogger?
A) 98,000 J
B) −20,000 J
C) 20,000 J
D) zero

Accepted Answer

The work done by gravity is calculated as the negative of the gravitational force component along the hill's incline. The vertical height (h) can be found using h = 200 m * sin(12°). The work done by gravity is then W = -mgh = -(50 kg)(9.8 m/s²)(200 m * sin(12°)) ≈ -20,000 J.

Question 16

A worker pushes a sled with a force of 40 N over a level distance of 6.0 m.If a frictional force of 16 N acts on the wheelbarrow in a direction opposite to that of the worker,what total work is done on the wheelbarrow?
A) 240 J
B) 216 J
C) 144 J
D) 96 J

Accepted Answer

The total work done on the wheelbarrow is the net force multiplied by the distance. The net force is the applied force minus the frictional force: 40 N - 16 N = 24 N. Therefore, the work done is 24 N * 6.0 m = 144 J.

Question 17

A simple pendulum,2.0 m in length,is released with a push when the support string is at an angle of 25° from the vertical.If the initial speed of the suspended mass is 2.0 m/s when at the release point,what is its speed at the bottom of the swing? (g = 9.8 m/s²) A) 2.3 m/s B) 2.6 m/s C) 2.8 m/s D) 0.5 m/s

Accepted Answer

The answer of A simple pendulum,2.0 m in length,is released...

Question 18

A Hooke's law spring is compressed 12.0 cm from equilibrium,and the potential energy stored is 36.0 J.What compression (as measured from equilibrium)would result in 100 J being stored in this case?
A) 20.0 cm
B) 14.1 cm
C) 13.6 cm
D) The correct answer is not given.

Accepted Answer

The potential energy stored in a spring is given by:$$U = \frac{1}{2}kx^2$$where:* U is the potential energy stored in the spring (in joules)* k is the spring constant (in newtons per meter)* x is the displacement of the spring from its equilibrium position (in meters)In this case, we are given that the potential energy stored in the spring is 36.0 J when the spring is compressed 12.0 cm from equilibrium. We can use this information to find the spring constant:$$36.0 J = \frac{1}{2}k(0.12 m)^2$$$$k = \frac{2(36.0 J)}{(0.12 m)^2} = 2000 N/m$$Now, we can use the spring constant to find the compression that would result in 100 J being stored in the spring:$$100 J = \frac{1}{2}(2000 N/m)x^2$$$$x = \sqrt{\frac{2(100 J)}{2000 N/m}} = 0.2 m = 20.0 cm$$Therefore, the correct answer is A) 20.0 cm.

Question 19

A pendulum consists of a mass m suspended from a string of length L.When the pendulum is swinging,how much greater is the mass's potential energy when the string is displaced from the vertical by the angle θ than when the mass is at the lowest position?
A) mgL​sinθ
B) mgL​cosθ
C) mgL(1 - sinθ)
D) mgL(1 - cosθ)

Accepted Answer

When the mass is at the lowest position, all the potential energy is converted into kinetic energy. At maximum displacement, the potential energy is maximum and kinetic energy is zero. Therefore, the difference in potential energy is equal to the maximum potential energy.
The maximum potential energy is given by:
Ep = mgh
h = L(1 - cosθ)
Ep = mgL(1-cosθ)
Therefore, the answer is D.

Question 20

A 2.00-kg ball has zero potential and kinetic energy.Maria drops the ball into a 20.0-m deep well.After the ball comes to a stop in the mud,the sum of its potential and kinetic energy is:
A) 392 J.
B) −392 J.
C) 784 J.
D) zero.

Accepted Answer

The total energy of the ball is conserved, so the sum of its potential and kinetic energy is the same before and after it is dropped. Before it is dropped, the ball has zero potential and kinetic energy. After it comes to a stop in the mud, it has only potential energy, which is equal to its weight times the height of the well. Therefore, the sum of its potential and kinetic energy is:PE = mgh = (2.00 kg)(9.8 m/s^2)(20.0 m) = 392 JThe negative sign indicates that the energy is potential energy.

Quiz 6: Momentum and Collisions: Part A

When a Hooke's law spring is stretched a distance 3x,how much is the increase in energy stored in it from when it was stretched a distance x? Give your answer in terms of a multiple of the energy stored in the spring when it is stretched a distance x.

An 80,000-kg airliner is flying at 900 km/h at a height of 8.00 km.What is its total energy (kinetic + potential) if the total was 0 when the airliner was at rest on the ground?

A pole-vaulter clears 5.00 m.With what speed does he strike the mat in the landing area?

A simple pendulum,2.0 m in length,is released by a push when the support string is at an angle of 25° from the vertical.If the initial speed of the suspended mass is 3.0 m/s when at the release point,to what maximum angle will it move in the second half of its swing?

Old Faithful geyser in Yellowstone Park shoots water hourly to a height of 30 m.With what velocity does the water leave the ground?

An amount of work equal to 3.0 J is required to compress the spring in a spring-gun.What is the "launch speed" of a 15 g marble?

A Hooke's law spring is compressed 12.0 cm from equilibrium and the potential energy stored is 36.0 J.What is the spring constant in this case?

A 50-N crate is pulled up a 5.0-m inclined plane by a worker at constant velocity.If the plane is inclined at an angle of 37° to the horizontal and there exists a constant frictional force of 20 N between the crate and the surface,what is the force applied by the worker?

Which of the following is not true about potential energy?

By how much is the energy stored in a Hooke's law spring increased when its stretch is increased from 4.00 cm to 8.00 cm?

A 2000-kg ore car rolls 50.0 m down a frictionless 10.0° incline.If there is a horizontal spring at the end of the incline,what spring constant is required to stop the ore car in a distance of 2.00 m?

A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 30 m/s and initial angle of 30°.What is the kinetic energy of the baseball at the highest point of the trajectory? Ignore air friction.

A bobsled makes a run down an ice track starting at 66 m vertical distance up the hill.If there is no friction,what is the velocity at the bottom of the hill?

A spring with spring constant k is used to launch a mass m up a frictionless inclined plane having angle of elevation θ.What is the maximum height reached above the starting elevation of the mass during the motion of the mass if the spring is compressed a distance d before launch?

A hill is 200 m long and makes an angle of 12° with the horizontal.As a 50-kg jogger runs up the hill,how much work does gravity do on the jogger?

A worker pushes a sled with a force of 40 N over a level distance of 6.0 m.If a frictional force of 16 N acts on the wheelbarrow in a direction opposite to that of the worker,what total work is done on the wheelbarrow?

A simple pendulum,2.0 m in length,is released with a push when the support string is at an angle of 25° from the vertical.If the initial speed of the suspended mass is 2.0 m/s when at the release point,what is its speed at the bottom of the swing? (g = 9.8 m/s²)

A Hooke's law spring is compressed 12.0 cm from equilibrium,and the potential energy stored is 36.0 J.What compression (as measured from equilibrium) would result in 100 J being stored in this case?

A pendulum consists of a mass m suspended from a string of length L.When the pendulum is swinging,how much greater is the mass's potential energy when the string is displaced from the vertical by the angle θ than when the mass is at the lowest position?

A 2.00-kg ball has zero potential and kinetic energy.Maria drops the ball into a 20.0-m deep well.After the ball comes to a stop in the mud,the sum of its potential and kinetic energy is: