A few years back it was fashionable to sit on a big bouncy exercise ball at your

Question

A few years back it was fashionable to sit on a big bouncy exercise ball at your desk so you would keep moving and get some exercise while at work. A friend of mine discovered that I order to do the minimum amount of work it was best to bounce at the resonant frequency of the ball .My friend had a mass of 80kg, and the resonant frequency was 2 bounces/s.a(a)what is the spring constant of the ball.(b)we thought it might be interesting to use the ball as a pendulum bob for a giant pendulum hung from the first floor balcony rail(about 4.5m above the ground level) So we tied some string around it and set it swinging from an angle of 10degrees to the vertical. What was its period of oscillation.(c)Whhen we had played with the pendulum for while we thought it might be interesting to investigate how much energy was lost by the (1.5kg) ball as it collided with the ground floor after being dropped from the first floor balcony. The ball only returned to two thirds of its original height. How much was lost in the collision? (D) if no energy was lost to air resistance or in the collisions with the floor(assuming answer to part "c" is zero) What was the maximum amount that the ball squashed up while it was contact with the floor?

Explanation / Answer

(a) we know that w = sqrt(k/m)

w = 2*3.14*2 =12.56

k = 12.562* 80 =12620.3 N/m..........Ans.

(b) Period of oscillation T = 1/f = 1/2 = 0.5 sec.

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