Calculating Impact Force of Man Falling onto Cushion

AI Thread Summary
To calculate the impact force of a man falling onto a cushion, one must first determine his velocity just before impact by using the equations of motion, considering the height of the fall and gravitational acceleration. The change in momentum is then calculated using this velocity and the man's mass. The impact force is derived from the change in momentum over the time taken to come to rest, factoring in the net forces acting on the man, including his weight. The initial calculations presented were incorrect due to a misunderstanding of the change in momentum. Properly applying these principles will yield the correct impact force, which is expected to be greater than the man's weight.
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Homework Statement


the question goes like this
a man of mass 70kg falls onto a rescue cushion from a height of 7 m he comes to rest 0.2s after he reaches the cushion the cushion is 2m high when inflated
a)find the impact force acting on him (take the weight of the man into account)
b)by how many times is the impact force greater than his weight?


Homework Equations





The Attempt at a Solution


a) For a, I first calculated the change of momentum of the man, which is 700kgms-1, then the impact force will be the change of momentum over time, which gives an answer of 3500N, which is a wrong answers since the answer in the book is 4200, I don't get it...
 
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eureka_beyond said:
then the impact force will be the change of momentum over time,
No, the change in momentum over time gives the net force on the man. The impact force (the force of the cushion on the man) is only one of the forces acting on him. What's the other?
 
Your calculation for the change in momentum is wrong. Or rather, the answer you give is wrong. How did u calculate this?

It seems you have taken the change of momentum as his weight. That is, multiplied his mass 70kg with gravity ~10. However this is NOT the change in momentum.

You need to consider the change in his potential energy to calculate his velocity.
 
You first need to find the velocity (V)of the man just before he strikes the cushion.
(Use the familiar equations of motion for falling through a height of 7m onto cushion 2m thick with acceleration due to gravity.)
Use this velocity, combined with his mass to find his momentum just before he strikes the cushion.
Then use your impulse formula to find the impact force. (eta. noting the point in the question about his weight)
 
Last edited:
H_man said:
Your calculation for the change in momentum is wrong. Or rather, the answer you give is wrong. How did u calculate this?

It seems you have taken the change of momentum as his weight. That is, multiplied his mass 70kg with gravity ~10. However this is NOT the change in momentum.

You need to consider the change in his potential energy to calculate his velocity.
FYI: There's nothing wrong with the OP's calculation for the change in momentum. That's not the problem.
 

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