To make his grand entrance, a professional wrestler of mass M = 100kg stands on

Question

To make his grand entrance, a professional wrestler of mass M = 100kg stands on a spring-loaded platform below the surface of the stage. When his music hits, the wrestler is launched into the air and greeted by the roar of the crowd. Assume that the wrestler has only elastic (or spring) potential energy before he is launched. That is, choose his prelaunch point to be the point where we take his gravitational potential energy to be zero. If the spring on the launcher has a spring constant of k = 1600 N/m and the spring has been compressed by 2 m while the wrestler is standing on it. Ignore any effects of friction or air resistance.
a.) Find the elastic (or spring) potential energy the wrestler has before he is launched.
b.) Find the gravitational potential energy the wrestler has just as he leaves the platform. That is, when he is 2 m above his initial position.
c.) How much kinetic energy does he have at this point?
d.) How fast is he traveling at this point?
e.) What maximum height above his initial position does he reach?
f.) How would the wrestler’s kinetic energy and maximum height change if we did not ignore friction in the spring and air resistance?

Explanation / Answer

given

mass of the wrestler = M = 100kg

spring constant k = 1600N/m

compressed distance x = 2m

a) spring potential energy = 1/2 * kx^2 = 3200N

b) gravitationalpotential energy = mgh = 100 * 9.8 * 2m = 1960m

c) kinetic enrgy = K = 1/2 * kx^2 - mgh = 1240 J

d) kinetic energy = 1/2 *Mv^2 = 1240J

                               v = 4.97m/s

e) 1/2 * kx^2 = mgH

   H = 3200N/100 * 9.8m/s^2 =
      = 32.65m

f) if air resistance is considered both kinetic energy , maxium height changes.

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