mechanical energy problem?

Anonymous @Anonymous

May 2021 3 19 Report

mechanical energy problem?

A high jumper with a mass of 65kg just clears a height of 2.13m and drops onto a 0.3m thick landing mat.

What average net force does the landing mat exert on the high jumper if it is compressed by 0.18m during the landing?

This annoys me greatly because i THOUGHT i could do it but i get the answer wrong. :/

I get around 7500 N, whereas the book says the answer is 6500 N

Any help with this (showing steps please) is appreciated :)

Science & Mathematics / Physics

oldprof

Verified answer

I have no clue how you worked this. But I do see some issues. A high jumper has a not inconsiderable vx = V cos(theta) X direction velocity when jumping. And your problem gives no info to calculate vx. vx would add to the impact kinetic energy when landing on that mat.

1/2 mvy^2 = mgh; vy^2 = 2gh, where vy is the vertical velocity vector due to falling h = 2.13 - .3 m straight down to the mat's surface which is .3 m above ground level.

Without vx, we must assume vx = 0, which is not very realistic. In any case, the mat absorbs the kinetic energy KE = 1/2 mvy^2 = 1/2 m(2gh); where m = 65 kg, g = 9.81 m/sec^2, and h = 2.13 - .3 = 1.83 m

The mat does the following work to absorb KE, WE = 1/2 kdX^2 = 1/2 mvy^2 = 1/2 m2gh = KE, from the coservation of energy. (Note, I had to assume the mat acts like a spring when compressing. But, again, that is not very realistic. Since the mat's compression characteristics were not given, the spring model is a WAG.)

Solve for k, the compression constant for the mat. k = 2mg/dX^2. Then the average force F/2 = kdX/2 = mgh/dX = 65*9.81*(2.13-.3)/.18 = 6482.775 Newtons.

Given the assumptions, I agree with the textbook answer. However, the problem discounts a lot of horizontal energy/velocity that really should not be discounted in a realistic problem.