Question

A block of mass m = 75 kg is hanging on a vertical rope of length L = 12 m. What work is done by the

gravitational force when the block swings to a position where the rope makes an angle θ = 40° with
the vertical?

Answer 1

2100 J

Step-by-step explanation:

Draw a picture. Notice that the rope forms a triangle, where the hypotenuse is L and the height is L cos θ. The height of the mass is h. The total height is L, so:

L = h + L cos θ

h = L − L cos θ

The work done by gravity is force times distance:

W = mgh

W = mg (L − L cos θ)

W = (75 kg) (9.8 m/s²) (12 m − 12 m cos 40°)

W = 2063 J

Rounding to two significant figures, the work done is 2100 J.