Question 1

A 7.0-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 1.2 kN/m). The block is initially at rest at its equilibrium position when a force of magnitude P acting parallel to the surface is applied to the block, as shown. When the block is 8.0 cm from the equilibrium position, it has a speed of 0.80 m/s. How much work is done on the block by the force P as the block moves the 8.0 cm?

Accepted Answer

A)  7.4 J 
B)  5.4 J 
C)  6.1 J 
D)  6.7 J 
E)  4.9 J

Question 2

Jane and Jake are looking at what happens to body 1 of mass m and body 2 of mass 2m, initially at rest, when equal forces are applied separately to the two bodies. Jake says that equal forces applied for equal times do equal amounts of work on the two bodies. Jane says that the two forces do equal amounts of work only if the two bodies move equal distances in the direction of the forces. Which one, if either, is correct?

Accepted Answer

A)  Jake, because the speed of body 1 is half the speed of body 2, but m1v1 = m2v2. 
B)  Jane, because work does not depend on mass, only on force times distance. 
C)  Jake, because all bodies travel equal distances when equal forces are applied for equal times. 
D)  Jane, because it takes the same time for all bodies to travel equal distances when equal forces are involved. 
E)  Neither, because we can't compare the amounts of work done on bodies of different mass.

Question 3

A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40° below the horizontal position. What is the tension in the string at the instant when the object passes through its lowest position?

Accepted Answer

A)  11 N 
B)  25 N 
C)  42 N 
D)  18 N 
E)  32 N

Question 4

The force a spring exerts on a body is a conservative force because

Accepted Answer

A)  a spring always exerts a force opposite to the displacement of the body. 
B)  a spring always exerts a force parallel to the displacement of the body. 
C)  the work a spring does on a body is equal for compressions and extensions of equal magnitude. 
D)  the work a spring does on a body is equal and opposite for compressions and extensions of equal magnitude. 
E)  the net work a spring does on a body is zero when the body returns to its initial position.

Question 5

A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s. What is the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent?

Accepted Answer

A)  −1.3 kJ 
B)  −1.5 kJ 
C)  −1.8 kJ 
D)  −2.0 kJ 
E)  −2.3 kJ

Question 6

A 2.0-kg block slides down a plane (inclined at 40° with the horizontal) at a constant speed of 5.0 m/s. At what rate is the gravitational force on the block doing work?

Accepted Answer

A)  +98 W 
B)  +63 W 
C)  zero 
D)  +75 W 
E)  −75 W

Question 7

A 3.50 kg block is pulled along a moving conveyor belt at a constant speed of 0.500 m/s relative to a stationary observer while the belt moves at a constant speed of 0.200 m/s in the same direction. If the coefficient of kinetic friction is 0.400, the magnitude of the mechanical energy dissipated, in J, caused by the force of friction on the block in 8.00 s is

Accepted Answer

A)  5.6. 
B)  22.0. 
C)  32.9. 
D)  54.8. 
E)  76.8.

Question 8

A rain cloud contains 2.66 × 10⁷ kg of water vapor. How long would it take for a 2.0 kW pump to lift the same amount of water to an altitude of 2 000 m?

Accepted Answer

The answer of A rain cloud contains 2.66 × 10⁷...

Question 9

Which of the following is a conservative force? (All refer to a car on a slope.)

Accepted Answer

A)  The force you exert on the car pushing it uphill. 
B)  The force exerted by rain drops falling on the car. 
C)  The frictional force of the road on the car. 
D)  The gravitational force acting on the car. 
E)  The force you exert on the car (pushing it uphill) after it starts to slide downhill.

Question 10

The solution to a problem is the equation below. Which description best fits this solution?

Accepted Answer

A)  A vertical spring compressed 0.120 m shoots a 2.00 kg mass 2.90 cm above the equilibrium position of the spring. 
B)  A vertical spring stretched 0.120 m shoots a 2.00 kg mass 9.10 cm above the equilibrium position of the spring. 
C)  A vertical spring compressed 0.120 m shoots a 2.00 kg mass 12.0 cm above the equilibrium position of the spring. 
D)  A vertical spring compressed 0.120 m shoots a 2.00 kg mass 14.9 cm above the equilibrium position of the spring. 
E)  A 2.00 kg mass has fallen 0.820 m and compressed the upper end of a vertical spring 12.0 cm below the equilibrium position.

Question 11

A 70-kg high jumper leaves the ground with a vertical velocity of 6.0 m/s. How high can he jump?

Accepted Answer

The answer of A 70-kg high jumper leaves the ground...

Question 12

Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is

Accepted Answer

A) 
 mgl. 
B)  3mgl. 
C) 
 mgl. 
D)  6mgl. 
E)  9mgl.

Question 13

A 2.0-kg mass swings at the end of a light string (length = 3.0 m). Its speed at the lowest point on its circular path is 6.0 m/s. What is its kinetic energy at an instant when the string makes an angle of 50° with the vertical?

Accepted Answer

A)  21 J 
B)  15 J 
C)  28 J 
D)  36 J 
E)  23 J

Question 14

A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. A 2.0-kg block that is initially 0.40 m above the upper end of the spring is dropped from rest onto the spring. What is the kinetic energy of the block at the instant it has fallen 0.50 m (compressing the spring 0.10 m)?

Accepted Answer

A)  5.3 J 
B)  6.8 J 
C)  6.3 J 
D)  5.8 J 
E)  6.5 J

Question 15

As an object moves from point A to point B only two forces act on it: one force is conservative and does −70 J of work, the other force is nonconservative and does +50 J of work. Between A and B,

Accepted Answer

A)  the kinetic energy of object increases, mechanical energy increases. 
B)  the kinetic energy of object decreases, mechanical energy increases. 
C)  the kinetic energy of object decreases, mechanical energy decreases. 
D)  the kinetic energy of object increases, mechanical energy decreases. 
E)  None of the above.

Question 16

Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen equal distances, we find that

Accepted Answer

A)  KB = KA. 
B)  KB = 2KA. 
C)  KB = 4KA. 
D)  KA = 2KB. 
E)  KA = 4KB.

Question 17

A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up?

Accepted Answer

A)  61° 
B)  54° 
C)  69° 
D)  77° 
E)  47°

Question 18

A 12-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.80 kN/m). The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N) acting parallel to the surface is applied to the block, as shown. What is the speed of the block when it is 13 cm from its equilibrium position?

Accepted Answer

A)  0.78 m/s 
B)  0.81 m/s 
C)  0.71 m/s 
D)  0.58 m/s 
E)  0.64 m/s

Question 19

A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed?

Accepted Answer

A)  2.2 m/s 
B)  2.5 m/s 
C)  1.9 m/s 
D)  1.5 m/s 
E)  3.6 m/s

Question 20

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would reach the summit in ____ seconds.

Accepted Answer

A)  1 
B)  460 
C)  500 
D)  1 000 
E)  35 000

Exam 8: Conservation of Energy

A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40° below the horizontal position. What is the tension in the string at the instant when the object passes through its lowest position?

The force a spring exerts on a body is a conservative force because

A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s. What is the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent?

A 2.0-kg block slides down a plane (inclined at 40° with the horizontal) at a constant speed of 5.0 m/s. At what rate is the gravitational force on the block doing work?

A rain cloud contains 2.66 × 10⁷ kg of water vapor. How long would it take for a 2.0 kW pump to lift the same amount of water to an altitude of 2 000 m?

Which of the following is a conservative force? (All refer to a car on a slope.)

The solution to a problem is the equation below. Which description best fits this solution?

A 70-kg high jumper leaves the ground with a vertical velocity of 6.0 m/s. How high can he jump?

Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is

A 2.0-kg mass swings at the end of a light string (length = 3.0 m) . Its speed at the lowest point on its circular path is 6.0 m/s. What is its kinetic energy at an instant when the string makes an angle of 50° with the vertical?

As an object moves from point A to point B only two forces act on it: one force is conservative and does −70 J of work, the other force is nonconservative and does +50 J of work. Between A and B,

Two masses, M_A and M_B, with M_B = 2M_A, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen equal distances, we find that

A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up?

A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed?

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would reach the summit in ____ seconds.

Exam 8: Conservation of Energy

A 2.5-kg object suspended from the ceiling by a string that has a length of 2.5 m is released from rest with the string 40° below the horizontal position. What is the tension in the string at the instant when the object passes through its lowest position?

The force a spring exerts on a body is a conservative force because

A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s. What is the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent?

A 2.0-kg block slides down a plane (inclined at 40° with the horizontal) at a constant speed of 5.0 m/s. At what rate is the gravitational force on the block doing work?

A rain cloud contains 2.66 × 107 kg of water vapor. How long would it take for a 2.0 kW pump to lift the same amount of water to an altitude of 2 000 m?

Which of the following is a conservative force? (All refer to a car on a slope.)

The solution to a problem is the equation below. Which description best fits this solution?

A 70-kg high jumper leaves the ground with a vertical velocity of 6.0 m/s. How high can he jump?

Cubical blocks of mass m and side l are piled up in a vertical column. The total gravitational potential energy of a column of three blocks is

A 2.0-kg mass swings at the end of a light string (length = 3.0 m) . Its speed at the lowest point on its circular path is 6.0 m/s. What is its kinetic energy at an instant when the string makes an angle of 50° with the vertical?

As an object moves from point A to point B only two forces act on it: one force is conservative and does −70 J of work, the other force is nonconservative and does +50 J of work. Between A and B,

Two masses, MA and MB, with MB = 2MA, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen equal distances, we find that

A 0.60-kg object is suspended from the ceiling at the end of a 2.0-m string. When pulled to the side and released, it has a speed of 4.0 m/s at the lowest point of its path. What maximum angle does the string make with the vertical as the object swings up?

A 20-kg mass is fastened to a light spring (k = 380 N/m) that passes over a pulley as shown. The pulley is frictionless, and the mass is released from rest when the spring is unstretched. After the mass has dropped 0.40 m, what is its speed?

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would reach the summit in ____ seconds.

A rain cloud contains 2.66 × 10⁷ kg of water vapor. How long would it take for a 2.0 kW pump to lift the same amount of water to an altitude of 2 000 m?

Two masses, M_A and M_B, with M_B = 2M_A, are released at the same time and allowed to fall straight down. Neglect air resistance. When we compare their kinetic energies after they have fallen equal distances, we find that