Question

Three identical clay balls collide as in the diagram below. Two of the clay balls come in at equal angles of 35 degrees and equal (unknown) speeds, and strike the third (stationary) ball simultaneously. All three stick together and move off together without rotating. There are no forces on the balls of clay other than those that they exert on each other. Find the fraction of the original energy of the system that becomes thermal?

Answer 1

Step-by-step explanation:

Let the initial velocity of the two moving balls be u

Let the mass of one ball be m

Let the velocity after collision be v

Initial kinetic energy is

2(½mu²) = mu²

Assuming the 35° is measured above and below a common axis,

conservation on momentum.

the vertical portion of that velocity and momentum will be equal and will cancel out.

the horizontal momentum will be

m(ucos35) + m(ucos-35) + m(0) = 3mv

v = (2/3)ucos35 = 0.5461u

final kinetic energy is

½(3m)(0.5461u²) = 0.44734mu²

so the fraction of kinetic energy converted to heat energy is

(mu² - 0.44734mu²) / mu² = 0.5526599... = 0.55