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Question
(a) Calculate the force the woman in Figure 7.45 exerts to do a push-up at constant speed, taking all data to be known to three digits. (b) How much work does she do if her center of mass rises 0.240 m? (c) What is her useful power output if she does 25 push-ups in 1 min? (Should work done lowering her body be included? See the discussion of useful work in Work, Energy, and Power in Humans.
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<b>Figure 7.45</b> Forces involved in doing push-ups. The woman's weight acts as a force exerted downward on her center of gravity.
Figure 7.45 Forces involved in doing push-ups. The woman's weight acts as a force exerted downward on her center of gravity.
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Final Answer
  1. $490 \textrm{ N}$
  2. $118 \textrm{ J}$
  3. $98 \textrm{ W}$
Solution Video

OpenStax College Physics Solution, Chapter 7, Problem 60 (Problems & Exercises) (1:58)

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Video Transcript

This is College Physics Answers with Shaun Dychko. The force exerted by this woman to raise her body in one push up is equal to the gravitational force downwards because the question tells us that she's moving at constant speed so that means the force upwards must balance the force downwards. So the force she applies on the floor is gonna be the force that the floor in turn applies on her and so it's good enough to say this floor force is the same as the force she applies. So the force then is the 50 kilogram mass times 9.8 newtons per kilogram which is 490 newtons. The work that she does in raising her body once is that force multiplied by the distance she goes up and we are told that she rises 0.240 meters so we multiply that by 490 newtons giving us 118 joules of work done. The power output is gonna be the total work output divided by time. So we are told that she does 25 push ups per minute so that's 117.6 joules for a single direction of the push up, so up for example, multiplied by two directions per push up. Now this might be a little controversial but what I'm saying is that she does work going down as well as work on the way up. The work going down will be the same because since the question tells us she's moving at constant speed that means she must be exerting a force upwards to balance gravity whether she's going down or up. So both times both cases, she's exerting the same force in order to maintain the constant speed by having a force that balances gravity. So each push up has two directions with the same work being done in each then we multiply this by 25 push ups and divide by the time of 60 seconds so that is 98 watts is her power output.