Question

A 30-g riffle bullet traveling 250 m/s buries itself in a 4 kg pendulum hanging on a 3 m long string, which makes the pendulum swing upward in an arc. Ignoring friction and air resistance, what angle will the pendulum make with the vertical at the peak of its swing?

Answer 1

first need to calculate the speed at just after bullet buries itself in pendulum for it apply momentum conservation

Pi = Pf

Pbullet + Pendulam = P ( bullet +pendulum)

30*10^-3 *250 + 0 = ( 30*10^-3 +4) *v

v = 1.86 m/s

now apply energy conservation suppose it make maximu theta angle with vertical

so

Kinetic energy of  bullet +pendulum = converted into potential energy of  bullet +pendulum

1/2* Mtotal *1.86^2 = Mg*L( 1-cos )

0.5 *1.86^2 = g*L*( 1-cos)

( 1-cos) = 0.5 *1.86^2 / 9.8*3

cos = 1- 0.5 *1.86^2 / (9.8*3) = 0.94116

=Acos(0.94116 ) = 19.75 degree answer

see diagrma for better undestanding

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