Question

A 19.0-kg child on a 4.00-m-long swing is released from rest when the ropes of the swing make an angle of 35.0° with the vertical.

(a) Neglecting friction, find the child's speed at the lowest position.
m/s

(b) If the actual speed of the child at the lowest position is 3.30 m/s, what is the mechanical energy lost due to friction?
J

Answer 1

PART A:

The situation can be visualized as

Let us take the point B as the reference energy for the potential energy (i.e the potential energy at point B is zero).

Now from the figure

That gives us

So, the total energy at point A is

And the total energy at point B is

The conservation of energy gives us

So, the child's speed at the lowest position is 3.76 m/s.

PART B:

The actual speed of the child at the lowest point is 3.30 m/s.

That gives us the actual kinetic energy at the lowest point is

So, the mechanical energy lost is

So, the energy lost due to friction is 31.24 J.