Question

Two small identical clay balls of mass m are suspended from the same point by strings of length L. One of them is pulled sideways and up such that its string makes an angle ? as shown. After being released from rest, it collides with the other ball, and they remain stuck together after the collision. How high h will the two balls rise after the collision? Enter your symbolic answer as a function of m, L, g, and theta (you'll have to type the whole word since you don't have a ? key on your keyboard), plus physical constants such as 1.0 or 0.5.

Answer 1

PE of single ball when lift up = mgL(1-cos[theta])

its velocity just before hitting the other ball:

0.5mv^2=mgL(1-cos[theta]) => v = sqrt(2gL(1-cos[theta]))

Conservation of momentum

mv=2m*u => u = v/2

Now both balls will start to move with a velocity of v/2

KE = 0.5*2m*u^2 = PE at top most point 2mgh

h = v^2/8g = 0.25*L(1-cos[theta])