Question 1

Which of the following are necessary for a point of stable equilibrium?

Accepted Answer

A) a local minimum in potential energy 
B) kinetic energy equal to zero 
C) potential energy equal to zero 
D) All are correct. 
E) A and C only are correct. 
A) a local minimum in potential energy 
B) kinetic energy equal to zero 
C) potential energy equal to zero 
D) All are correct. 
E) A and C only are correct.

Question 2

A child slides down a slippery slide (neglect friction)of length 3.0 m and angle of inclination 32S1U1P1$\circ$S1S1P0 above the horizontal.How fast is she going when she leaves the end of the slide?

Accepted Answer

A) 3.9 m/s 
B) 5.0 m/s 
C) 5.6 m/s 
D) 7.1 m/s 
A) 3.9 m/s 
B) 5.0 m/s 
C) 5.6 m/s 
D) 7.1 m/s

Question 3

Find the gravitational potential energy of a 1.88-m tall person whose weight is 670 N when he is standing on a high dive platform 3.00 m above the water (take the surface of the water as zero potential).

Accepted Answer

A) 2640 J 
B) 3270 J 
C) 25,900 J 
D) 32,000 J 
A) 2640 J 
B) 3270 J 
C) 25,900 J 
D) 32,000 J

Question 4

A block of mass M is sliding with velocity v along a horizontal surface with coefficient of friction   .How much heat produced in bringing the block to rest?

Accepted Answer

A) 1/2 Mv2 
B)    Mv 
C) 1/2   Mv2 
D)    v 
E) zero 
A) 1/2 Mv2 
B)    Mv 
C) 1/2   Mv2 
D)    v 
E) zero

Question 5

A spring is fixed vertically to the floor.A 10.0-kg box is then pressed down such that the spring is compressed 0.5 m beyond its equilibrium length.The box is then released and it travels vertically upward to a maximum height of 2.40 m above its release point.Assuming the work done against drag (air resistance)is 120 J,what is the spring constant of the spring?

Accepted Answer

A) 2500 N/m 
B) 3750 N/m 
C) 1880 N/m 
D) 3600 N/m 
E) 2840 N/m 
A) 2500 N/m 
B) 3750 N/m 
C) 1880 N/m 
D) 3600 N/m 
E) 2840 N/m

Question 6

A ball with mass m is thrown off a building of height h above the ground with a speed vo at an angle   above the horizontal as shown.The angle   is greater than 0S1U1P1$\circ$S1S1P0 and less than 90˚.Neglect friction for this problem.Which one of the following statements is true?

Accepted Answer

A) The speed at which the ball strikes the ground depends on   . 
B) The speed at which ball strikes the ground does not depend on the height of the building. 
C) The speed at which the ball strikes the ground depends on vo. 
D) The distance the ball strikes the ground from the building does not depend on   . 
E) The speed at which the ball strikes the ground depends on the mass of the ball. 
A) The speed at which the ball strikes the ground depends on   . 
B) The speed at which ball strikes the ground does not depend on the height of the building. 
C) The speed at which the ball strikes the ground depends on vo. 
D) The distance the ball strikes the ground from the building does not depend on   . 
E) The speed at which the ball strikes the ground depends on the mass of the ball.

Question 7

A 25-kg child starts from rest at the top of a slide inclined at 27S1U1P1$\circ$S1S1P0 relative to the horizontal.The slide is 6.0 m long.The coefficient of the kinetic friction of the slide is 0.25.When reaching the bottom of the slide,the child's speed is:

Accepted Answer

A) 5.2 m/s 
B) 4.0 m/s 
C) 7.3 m/s 
D) 6.5 m/s 
A) 5.2 m/s 
B) 4.0 m/s 
C) 7.3 m/s 
D) 6.5 m/s

Question 8

An arrow of mass 0.100 kg is launched directly upward with a bow of spring constant 1962 N/m.If the bow was stretched 10.0 cm and then released,how high above the bow did the arrow go before coming to rest temporarily?

Accepted Answer

A) 10.0 m 
B) 20.0 m 
C) 100 m 
D) 200 m 
A) 10.0 m 
B) 20.0 m 
C) 100 m 
D) 200 m

Question 9

A cannon is shot downward from a 195-m high cliff at an angle of 34S1U1P1$\circ$S1S1P0 with respect to the horizontal.The initial speed is 40.0 m/s.What is its speed when it hits the ground in m/s?

Accepted Answer

A) 41. 
B) 48.3 
C) 59.2 
D) 73.7 
E) 98.1 
A) 41. 
B) 48.3 
C) 59.2 
D) 73.7 
E) 98.1

Question 10

A 25-kg child starts from rest and attains a speed of 4 m/s at the bottom of a 27S1U1P1$\circ$S1S1P0slide of length 6 m.The coefficient of the kinetic friction of the slide is

Accepted Answer

A) 0.08. 
B) 0.19. 
C) 0.22. 
D) 0.36. 
A) 0.08. 
B) 0.19. 
C) 0.22. 
D) 0.36.

Question 11

The gravitational potential energy of a 35.0-kg rock is 690.0 J relative to the ground.The rock is at a height ______ above the ground.

Accepted Answer

A) 1.27 m 
B) 1.75 m 
C) 2.01 m 
D) 2.87 m 
E) 3.56 m 
A) 1.27 m 
B) 1.75 m 
C) 2.01 m 
D) 2.87 m 
E) 3.56 m

Question 12

A skier starts up a slope with a speed of 20.0 m/s.The slope makes an angle of 25.0S1U1P1$\circ$S1S1P0 with respect to the horizontal.The coefficient of kinetic friction between her skis and the snow is 0.0300.How far in meters does the skier travel before she stops?

Accepted Answer

A) 45.3 
B) 66.2 
C) 76.3 
D) 88.9 
E) 109 
A) 45.3 
B) 66.2 
C) 76.3 
D) 88.9 
E) 109

Question 13

A frustrated student drops his physics book of 2-kg out of the window that is 100 m from the ground.The kinetic energy of the book at 25 m from the ground is

Accepted Answer

A) 5000 J. 
B) 1472 J. 
C) 490 J. 
D) 250 J. 
A) 5000 J. 
B) 1472 J. 
C) 490 J. 
D) 250 J.

Question 14

Four balls are thrown off the top of a building 27 m high.All balls are thrown with identical speeds,but at different angles.Ball 1 is thrown straight upward.Ball 2 is thrown +30S1U1P1$\circ$S1S1P0 relative to the horizontal.Ball 3 is thrown at an angle of +45F1F1F1S1F1F1F10 relative to the horizontal.And Ball 4 is thrown at an angle of -45S1U1P1$\circ$S1S1P0 relative to the horizontal.Which ball has the greatest kinetic energy at the top of their respective paths?

Accepted Answer

A) ball 1 
B) ball 2 
C) ball 3 
D) ball 4 
E) All have the same kinetic energy 
A) ball 1 
B) ball 2 
C) ball 3 
D) ball 4 
E) All have the same kinetic energy

Question 15

Find the magnitude of the force acting on a 3.0-kg mass located at x=2.0 m inside a potential of   (assume all units in MKS).

Accepted Answer

A) 10 N 
B) 12 N 
C) 28 N 
D) 83 N 
A) 10 N 
B) 12 N 
C) 28 N 
D) 83 N

Question 16

A 200 N force pushes a 50-kg oak table a distance of 2.0 m across an oak floor.Friction resists this motion with a force of 157 N.The work done by the friction is

Accepted Answer

A) -128 J 
B) -86 J 
C) -400 J 
D) -314 J 
E) -714 J 
A) -128 J 
B) -86 J 
C) -400 J 
D) -314 J 
E) -714 J

Question 17

A particle of mass m moving in the x-y plane is confined by a two-dimensional potential.The net force on the mass is   .What is the potential?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

A pendulum of length 0.471 m,with a bob of mass 0.593 kg is moved out to an angle and released from rest.The speed of the bob at the bottom of the pendulum oscillation is 1.20 m/s.What is the angle from which the pendulum is released? (in degrees)

Accepted Answer

A) 32.4 
B) 37.9 
C) 44.4 
D) 51.9 
E) 60.7 
A) 32.4 
B) 37.9 
C) 44.4 
D) 51.9 
E) 60.7

Question 19

A 2-kg mass is dropped 2.0 m above a spring with a spring constant 40.0 N/m.How much does the spring compress? Use g=10 m/s2.

Accepted Answer

A) 1.4 m 
B) 2.0 m 
C) 1.0 m 
D) 1.5 m 
E) 2.5 m 
A) 1.4 m 
B) 2.0 m 
C) 1.0 m 
D) 1.5 m 
E) 2.5 m

Question 20

A 1210-kg car travels up an incline at constant velocity.The incline is 15S1U1P1$\circ$S1S1P0 measured with respect to the horizontal.The change in the car's potential energy is 1.92 MJ.What is the length of the incline?

Accepted Answer

A) 0.55 km 
B) 0.34 km 
C) 0.48 km 
D) 0.75 km 
E) 0.62 km 
A) 0.55 km 
B) 0.34 km 
C) 0.48 km 
D) 0.75 km 
E) 0.62 km

Exam 6: Potential Energy and Energy Conservation

Which of the following are necessary for a point of stable equilibrium?

A child slides down a slippery slide (neglect friction)of length 3.0 m and angle of inclination 32 ∘\circ∘ above the horizontal.How fast is she going when she leaves the end of the slide?

Find the gravitational potential energy of a 1.88-m tall person whose weight is 670 N when he is standing on a high dive platform 3.00 m above the water (take the surface of the water as zero potential).

A block of mass M is sliding with velocity v along a horizontal surface with coefficient of friction .How much heat produced in bringing the block to rest?

A ball with mass m is thrown off a building of height h above the ground with a speed vo at an angle above the horizontal as shown.The angle is greater than 0 ∘\circ∘ and less than 90˚.Neglect friction for this problem.Which one of the following statements is true?

A 25-kg child starts from rest at the top of a slide inclined at 27 ∘\circ∘ relative to the horizontal.The slide is 6.0 m long.The coefficient of the kinetic friction of the slide is 0.25.When reaching the bottom of the slide,the child's speed is:

An arrow of mass 0.100 kg is launched directly upward with a bow of spring constant 1962 N/m.If the bow was stretched 10.0 cm and then released,how high above the bow did the arrow go before coming to rest temporarily?

A cannon is shot downward from a 195-m high cliff at an angle of 34 ∘\circ∘ with respect to the horizontal.The initial speed is 40.0 m/s.What is its speed when it hits the ground in m/s?

A 25-kg child starts from rest and attains a speed of 4 m/s at the bottom of a 27 ∘\circ∘ slide of length 6 m.The coefficient of the kinetic friction of the slide is

The gravitational potential energy of a 35.0-kg rock is 690.0 J relative to the ground.The rock is at a height ______ above the ground.

A skier starts up a slope with a speed of 20.0 m/s.The slope makes an angle of 25.0 ∘\circ∘ with respect to the horizontal.The coefficient of kinetic friction between her skis and the snow is 0.0300.How far in meters does the skier travel before she stops?

A frustrated student drops his physics book of 2-kg out of the window that is 100 m from the ground.The kinetic energy of the book at 25 m from the ground is

Find the magnitude of the force acting on a 3.0-kg mass located at x=2.0 m inside a potential of (assume all units in MKS).

A 200 N force pushes a 50-kg oak table a distance of 2.0 m across an oak floor.Friction resists this motion with a force of 157 N.The work done by the friction is

A particle of mass m moving in the x-y plane is confined by a two-dimensional potential.The net force on the mass is .What is the potential?

A pendulum of length 0.471 m,with a bob of mass 0.593 kg is moved out to an angle and released from rest.The speed of the bob at the bottom of the pendulum oscillation is 1.20 m/s.What is the angle from which the pendulum is released? (in degrees)

A 2-kg mass is dropped 2.0 m above a spring with a spring constant 40.0 N/m.How much does the spring compress? Use g=10 m/s2.

A 1210-kg car travels up an incline at constant velocity.The incline is 15 ∘\circ∘ measured with respect to the horizontal.The change in the car's potential energy is 1.92 MJ.What is the length of the incline?

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A child slides down a slippery slide (neglect friction)of length 3.0 m and angle of inclination 32^$\circ$ above the horizontal.How fast is she going when she leaves the end of the slide?

A 25-kg child starts from rest at the top of a slide inclined at 27^$\circ$ relative to the horizontal.The slide is 6.0 m long.The coefficient of the kinetic friction of the slide is 0.25.When reaching the bottom of the slide,the child's speed is:

A cannon is shot downward from a 195-m high cliff at an angle of 34^$\circ$ with respect to the horizontal.The initial speed is 40.0 m/s.What is its speed when it hits the ground in m/s?

A 25-kg child starts from rest and attains a speed of 4 m/s at the bottom of a 27^$\circ$slide of length 6 m.The coefficient of the kinetic friction of the slide is

A 2-kg mass is dropped 2.0 m above a spring with a spring constant 40.0 N/m.How much does the spring compress? Use g=10 m/s².

A 1210-kg car travels up an incline at constant velocity.The incline is 15^$\circ$ measured with respect to the horizontal.The change in the car's potential energy is 1.92 MJ.What is the length of the incline?