Question

1. Sally and Bill are on identical swings:
   1. Assume they weight the same. If sally is pushed harder than Bills, who would come back sooner?
   2. Assume Bill is heavier than Sally. If both are pushed equally hard, who would come back sooner? Who has greater amplitude?

Answer 1

Since sally is pushed harder, that is initial velocity of sally is greater than that of Bill.

Suppose, initial velocity v is implied to the object.Here the sum of kinetic energy(K) and potential energy(U) would be constant.

Initial

  

k + U = ____________(1)

Let maximum height achieved be h.

at highest point

K = 0 U = m * g * h

K + U = mgh ______________(2)

equating equation 1 and 2

(please note that h is independent of mass)

a) Sally is imparted velocity which is greater than that of bill so Sally would traverse a longer a height and will take more time.

(h is maximum height traversed)

So, Bill will come sooner.

b) maximum height is independent of mass.So both of them will have same magnitude .Also, both of them will come back at the some time