SOLUTION: A 400 kg box and a 200 kg are to pushed across a horizontal table, the exact same distance with the exact force. Which box will have the most work done on it? Which box will get to

Question 1162487: A 400 kg box and a 200 kg are to pushed across a horizontal table, the exact same distance with the exact force. Which box will have the most work done on it? Which box will get to the end first? Explain both of your responses.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's say both boxes travel 10 meters, which is the displacement. Also, let's say that 1 newton of force was applied to each box. You could use any numbers you want here (as long as they are positive of course) to help see how everything works out.

work = force*displacement
work = 1*10
work = 10 joules
Each box has 10 joules of work applied to it. The work is the same because for each box the same amount of force and displacement happens.

For the 400 kg box, we can say,
force = 1 newton
force = mass*acceleration
1 = 400*acceleration
acceleration = 1/400 meters per second^2
acceleration = 0.0025 meters per second^2
Each second, the larger box's velocity is increasing by 0.0025 meters per second.

While the smaller box would have an acceleration of...
force = 1 newton
force = mass*acceleration
1 = 200*acceleration
acceleration = 1/200 meters per second^2
acceleration = 0.005 meters per second^2
Which is twice as much as the larger box.

Put simply: if the force applied is the same for the two boxes, then the smaller box will have larger acceleration. This is because more force is needed to push on the larger mass.

Because the smaller box has more acceleration, it will naturally travel faster compared to the larger box. Therefore, the smaller box reaches the goal line faster.

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Summary: Both boxes have the same amount of work applied to them. The smaller box will get to the end first.
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