Module 9: Conservation of Energy

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. Since the barbell is not moving, the weightlifter is not doing work on the barbell. Therefore, if the work done is zero, then the power is also zero.

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.

Which of the following forces is considered a conservative force?

gravity

Total mechanical energy of a system

which includes kinetic and potential energies, is never changed by a conservative force.

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. Power is the rate at which work is done, or W/change of time. If we assume the weightlifter applies a F that is almost equal to the weight of the barbell, then he does 1000 J of work, which comes from multiplying the F he exerts on the barbell and the barbell's displacement. The power is determined by dividing the work by the time interval in which the work was done.

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?

Both particles will have the same kinetic energy at the bottom. Since there are no non-conservative forces doing work to change the mechanical energy of the system in either figure, the ME is conserved. This means that the gravitational PE that each particle starts with will convert completely into KE at the bottom. Both particles start at the same height so they the same amount of GPE. Therefore, they will gain the same amount of KE upon reaching the bottom of the motion.

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

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

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 KE of the block increases.

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

The frictional force does negative work on the block and decreases its KE. The frictional force acting on the block points in the opposite direction to the displacement of the clock, so by definition the work is negative. A negative change in KE means that the KE decreases.

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

The work done by a conservative force is always path independent. The work done by a conservative F acting on an object as the object moves from point A to point B will be the same, no matter what path the object follows to get from point A to point B.

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 ME of a system. Work-energy theorem: W= change in KE

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

They have twice the KE of either ball by itself.

Kinetic Energy

is a scale quantity that depends on the mass, which is always positive, and the squared magnitude of the velocity, which is always positive, so the KE cannot be negative and it is not possible to have a total KE of zero.

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

non-conservative forces do zero total work on the stem during that process. mechanical energy is the sum of kinetic and potential energy of the system.