Question

A 76 g , 35-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 15 g ball of clay traveling horizontally at 2.7 m/s hits and sticks to the very bottom tip of the rod.

To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?

Express your answer to two significant figures and include the appropriate units.

Answer 1

here,

mass of rod , m1 = 0.076 kg

l = 0.35 m

mass of ball , m2 = 0.015 kg

initial speed , u = 2.7 m/s

let the final angular speed be w

using conservation of angular momentum

m2 * u * l = ( m2 * l^2 + m1 * l^2 /3) * w

0.015 * 2.7 * 0.35 = ( 0.015 * 0.35^2 + 0.076 * 0.35^2 /3) * w

solving for w

w = 2.87 rad/s

let the maximum angle be theta

using conservation of energy

(m1 + m2) * g * l * ( 1 - cos(theta)) = 0.5 * I * w^2

(0.076 + 0.015) * 9.81 * ( 1 - cos(theta)) = 0.5 * ( 0.015 * 0.35^2 + 0.076 * 0.35^2 /3) * 2.87^2

solving for theta

theta = 12.2 degree

the maximum angle from the vertical is 12.2 degree