4

A pendulum of mass 200 g is pulled horizontally sideways by 30 cm. The length of

the pendulum string is 50 cm.

a Calculate the potential energy of the pendulum in this position. Assume g =

9.8 N/kg

? cm

50 cm

30 cm

marks)

0.2 J

Explanation:

The pendulum forms a right triangle, with hypotenuse of 50 cm and base of 30 cm. The height of this triangle can be found with Pythagorean theorem:

c² = a² + b²

(50 cm) ² = a² + (30 cm) ²

a = 40 cm

The height of the triangle is 40 cm. The height of the pendulum when it is at the bottom is 50 cm. So the end of the pendulum is lifted by 10 cm. Assuming the mass is concentrated at the end of the pendulum, the potential energy is:

PE = mgh

PE = (0.200 kg) (9.8 N/kg) (0.10 m)

PE = 0.196 J

Rounding to one significant figure, the potential energy is 0.2 J.