Question

1. The following questions relate to the following scenario.

A student is listing possible factors that determine the change in the kinetic energy of objects. She has collected data in the following experimental setup:

Two blocks with different masses are free to slide on a very, very smooth table between two parallel lines. An air blower pushes each block horizontally, exerting the same constant force. Both blocks start from rest and cover the same distance on their track under the action of the air blower. The experimental data collected by the groups support the claim that the final kinetic energies of the two blocks are equal.

Of the following explanations, which is the most correct and complete causal account of the kinetic energies of the two blocks being equal?

Group of answer choices

-The two blocks have equal final kinetic energies because when there is negligible friction, mechanical energy stays constant.

-The two blocks have equal final kinetic energies because the blower transfers to each of them equal amounts of energy per meter.

-The two blocks have equal final kinetic energies because the blower transfers to each of them equal amounts of energy per second.

-The two blocks have equal final kinetic energies because the higher final speed of the lighter block compensates for its smaller mass.

Answer 1

This problem can be solved using work energy theorem ,

W net = change in kinetic energy

F × displacement = final kinetic energy - initial kinetic energy

Since initially both of them were at rest , therefore initial kinetic energy is 0 for both of them.

The above expression reduces to

Force × displacement = (1/2) mv^2

Now , since force and displacement is same for both of them , therefore both of them will have equal kinetic energy.

Now ,final kinetic energy which is equal for both of them = (1/2)mv^2.

It means , velocity is inversely proportional to the square root of mass .

Thus , the lighter mass will have a larger velocity at the end and larger mass will have a smaller velocity at the end.

Thus , final answer " The two blocks have equal final kinetic energies because the higher final speed of the lighter block compensates for its smaller mass".

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