Physics help needed?

Question

A 25kg child on a 2.0 m long swing is released from rest when the swing supports make an angle of 30.0 degrees with the vertical.

A) What is the maximum potential energy associated with the child?

B) Disregarding friction, find the child's speed at the lowest position.

C) What is the child's total mechanical engery?

D) If the speed of the child at the lowest position is 2.00 m/s, what is the change in mechanical energy due to friction?

*I would like to see how it is worked and what equations are used. Thanks

Answer 1

We'll put the origin at the lowest point that the child reaches. The height of the child above that point at the point of release is

h = ( 2.0 m ) sin 30.0 degrees

So the total energy of the child at this instant is all potential energy;

E = m g h.

After the child is released, the energy at the lowest point is all kinetic:

E = 1/2 m v^2

Set these two expressions equal to one another and solve for the only unknown, the velocity v.

However, we see that v is actually only 2.00 m/s. Compute the kinetic energy; the difference between what you now have and what you started with is the lost energy.