Quick Conservation of Energy Question

Question

A wrecking ball, with a mass of 315 kg, hangs from a crane on 10.0 m of cable. The crane swings the wrecking ball so that the angle that the cable makes with the vertical is 30.0°. What will be the speed of the wrecking ball when it falls back to the vertical position?

Answer 1

The energy added to the system by the crane's swing is the gravitational potential energy gained by the change in the wrecking ball's height. We'll need to use trigonometry to determine the height based on the cable length and angle, calculate the potential energy gained, and convert it to kinetic energy.

P ≡ potential energy

K ≡ kinetic energy

m ≡ mass of object

h ≡ height

g ≡ acceleration due to gravity (constant)

l ≡ cable length

θ ≡ swing angle

P = m*h*g

h = sin(θ)*l

K = 1/2*m*v^2

P = K

Solve the above system of equations for v.

v = sqrt(2*K/m)

v = sqrt(2*m*h*g/m)

v = sqrt(2*h*g)

v = sqrt(2*sin(θ)*l*g)