Question

a 25 kg child sits in a swing that is attached to ropes 1.5 m long. It is 0.5m above the ground. Find the potential energy of the child relative to his lowest position when the ropes are (a) horizontal, (b) vertical ; (c) make 30 degrees with the horizontal.

Answer 1

Explanations & Calculations

• When the child is sitting on the swing at rest above the ground is when he experiences the lowest potential energy.
• Any swing back and forth increases the potential energy.
• When potential energy is measured relative to the child's lowest position, the net distance from that level need to be considered.

a)

• When the ropes are horizontal, the vertical distance between the two locations is $\small 1.5m.$
• Then the relative potential energy is

$\qquad\qquad \begin{aligned} \small E_1&=\small mg\Delta h\\ &=\small 25kg\times9.8\times1.5m\\ &=\small 367.5\,J \end{aligned}$

b)

• the relative potential energy is 0.

c)

• The hight difference at this location is

$\qquad\qquad \begin{aligned} \small \Delta h&=\small 1.5(1-\sin30)=0.75m\\ \end{aligned}$

• Therefore, the relative potential energy is

$\qquad\qquad \begin{aligned} \small E_2&=\small 2.5\times9.8\times0.75\\ &=\small 18.4J \end{aligned}$