DSM Module 9: Conservation of Energy

Which of the following forces is considered a conservative force?

Gravity

A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. The block can be pushed in the negative x-direction to compress the spring or pulled in the positive x-direction to stretch the spring. Where along the x-axis does the block have to be for the spring to have zero potential energy?

The spring has zero potential energy when the block is at x = 0, where the spring is neither stretched nor compressed.

A weightlifter brings a 400-N barbell upward from his shoulders to a point 50 cm higher at a steady speed. During this process, what is the total work done on the barbell?

0 joules

A weightlifter exerts an upward force on a 1000-N barbell and holds it at a height of 1 meter for 2 seconds. Approximately how much power does the weightlifter exert on the barbell during this time?

0 watts

A weightlifter exerts an upward force on a 1000-N barbell and lifts the barbell 1 meter upward in 2 seconds. Approximately how much power does the weightlifter exert on the barbell during this time?

500 watts

In both figures, a particle of mass m is released from rest at a height, h. In figure (a), the particle is dropped straight downward and in figure (b) the particle is released from rest down a frictionless ramp. Which particle, the one in figure (a) or (b), will have more kinetic energy at the bottom? Figure (a) shows a particle of mass m on the edge of a vertical cliff of height h. Figure (b) shows a particle of mass m at the top of a straight, shallow slope of height h.

Both particles will have the same kinetic energy at the bottom.

A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction to compress the spring and then release the block, what happens to the energy in the system immediately after the block is released?

The elastic potential energy in the spring decreases while the kinetic energy of the block increases.

Which of the following forces is considered a conservative force?

The force due to a spring

When helping a friend move into a new home, you push a chair across the room. What do you know about the force of gravity applied to the chair?

The force of gravity applied to the chair does not change the energy of the system (the chair) and therefore does no work on the system.

When helping a friend move into a new home, you push a chair across the room. What do you know about the force that you exert on the chair?

The force you exert on the chair contributes to the overall change in kinetic energy of the system (the chair) with a positive amount and therefore does positive work on the system.

When helping a friend move into a new home, you push a chair across the room. What do you know about the force of friction applied to the chair by the floor?

The frictional force applied to the chair contributes to the overall change in kinetic energy of the system (the chair) with a negative amount and therefore does negative work on the system.

A block slides along a rough surface and comes to a stop. What can you conclude about the frictional force exerted on the block?

The frictional force does negative work on the block and decreases its kinetic energy.

In both figures, a particle of mass m, is released from rest at a height, h. In figure (a), the particle is dropped straight downward and in figure (b) the particle is released from rest and slides down a ramp with a rough surface. Which particle, the one in figure (a) or (b), will have more kinetic energy at the bottom? Figure (a) shows a particle of mass m on the edge of a vertical cliff of height h. Figure (b) shows a particle of mass m at the top of a straight, shallow slope of height h.

The particle in figure (a) will have more kinetic energy than the particle in figure (b) at the bottom.

In figure (b), a particle of mass m is released from rest at the top of a frictionless ramp of height h and in figure (c), a particle of mass 2m is released from rest at the top of the same frictionless ramp. Which particle, the one in figure (b) or (c), will have more kinetic energy at the bottom? Figure (b) shows a particle of mass m at the top of a straight, shallow slope of height h. Figure (c) shows a particle of mass 2m at the top of a straight, shallow slope of height h.

The particle in figure (c) will have more kinetic energy than the particle in figure (b) at the bottom.

A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction and compress the spring, what is true about the potential energy stored in the spring during this motion?

The potential energy in the spring increases because the spring does negative work on the block.

A block of mass m is attached to a horizontal spring and rests on a flat, smooth surface as seen in the figure. If you push on the block in the negative x-direction and compress the spring, what is true about the work done by the spring on the block during this motion?

The spring does negative work on the block because the spring force is in the opposite direction of the block's displacement.

What is true about the work done by a conservative force?

The work done by a conservative force is always path independent.

What is true about the work done by a non-conservative force?

The work done by a non-conservative force will always change the total mechanical energy of a system.

The graph shows the x-component of a force applied to an object versus the position of that object in the x-direction. How is the work done by this force determined from the data in this graph?

The work done by the force is equal to the area under the force versus position function.

When you lift a book upward off of a table, what is true about the work done on the book by the force of gravity?

The work done by the force of gravity is negative and proportional to the upward displacement of the book.

You observe two identical balls of putty heading directly toward each other at equal speeds. What can you say about their total kinetic energy?

They have twice the kinetic energy of either ball by itself.

In which of these processes is the total energy of the system conserved?

Two balls of putty (the system) collide in midair and stick together.

A variety of forces are applied to an object such that the net force does positive work on that object. What can you conclude about the speed of the object?

When the total work done on the object is positive, the object's speed will increase.

The mechanical energy of a system is conserved during a certain process only if __________.

non-conservative forces do zero total work on the system during that process

If Quantity X is conserved for a certain system and during a certain process, that means__________.

quantity X for that system does not change in any way during that process