Question

The figure below shows a thin rod, of length L and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m is attached to the other end. The rod is pulled aside through an angle and released. 

(a) What is the speed of the ball at the lowest point if L = 1.30 m, θ = 32.0°, and m = 500 kg? 

(b) Does the speed increase, decrease, or remain the same if the mass is increased? 

• increase 

• decrease 

• remain the same

Answer 1

a) let the speed at the lowest point is v

using conservation of energy

0.50 * m * v^2 = m * g* L(1 - cos(theta))

0.50 * v^2 = 9.8 * 1.3 *(1 - cos(32))

v = 1.97 m/s

the speed of the ball at the lowest point is 1.97 m/s

b) the speed at the lowest point is independent of the mass of the pendulum

the speed at the lowest point remains the same