A blob of clay having mass m and speed v0 hits a stationary rod of length D and

Question

A blob of clay having mass m and speed v0 hits a stationary rod of length D and equal mass m a distance D/4 from one end, traveling perpendicular to the rod. The rod and clay slide on a horizontal frictionless surface, and the clay sticks to the end.

a) What is the linear speed of their center of mass after the collision?

b) What is the rod's angular speed after the collision?

c) What impulse does the clay deliver to the rod?

d) If the clay bounced off instead of sticking, would your answers to each of (a-c) increase, decrease, or stay the same? Justify each.

Explanation / Answer

m = mass of clay

vo = initial velocity of clay

m = mass of rod

Vi = initial velocity of rod = 0

V = final velocity of clay-rod combination

using conservation of linear momentum

mvo + m Vi = (m + m) V

V = vo/2

b)

I = moment of inertia of rod about one end = ML2/3

Wi = initial angular velocity of rod about one end = 0

Wf = final angular velocity of combination

using conservation of angular momentum

m vo (L/4) + I Wi = (I + m(L/4)2) Wf

m vo (L/4) + (mL2/3) Wi = ((mL2/3) + m(L/4)2) Wf

Wf = vo (L/4) /(19L2/48)

Wf =12 vo/(19L)

c)

Impulse = change in momentum of rod = m V -0 = m vo/2

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