The speed of a pitched baseball is 46.0m/s. You want to know how fast is your school's star baseball pitcher could throw. You make a pendulum with a rope and a small box lined with a thick layer of soft clay, so that the baseball would stick to the inside of the box. The rope was 0.955m long, the box with the clay had a mass of 5.64kg and the baseball had a mass of 0.350kg. The angle was recorded as 20deg. How fast did your star pitcher pitch the ball.

Question

Ans: I am trying to use the conservation of energy and momentum separately, by first finding V' - sqrt(2gh) and substituting that into the conservation of momentum. Is that correct, I am not getting the required answer of 18.2m/s.

Answer 1

Inelastic collisions do no conserve energy, use conservation of momentum for the ball/clay impact.

m1u + m2(0) = (m1+m2)v
Solve for u when v is known (see below)

After the inelastic collision, conservation of energy would apply, once you have obtained the common velocity of the ball/clay mass, i.e. for the pendulum part of the question.

(1/2)(m1+m2)v² = (m1+m2)gR(1-cos(φ))

Solve for v.