Question

A 20.0 kg wood ball hangs from a 2.10 m-long wire. The maximum tension the wire can withstand without breaking is 400 N. A 0.900 kg projectile traveling horizontally hits and embeds itself in the wood ball.

What is the largest speed this projectile can have without causing the cable to break?

Answer 1

Given

Mass of the wood, M = 20 kg

Mass of the projectile, m = 0.9 kg

Length of the wire, l = 2.10 m

Maximum tension in the string, T = 400 N

Net force on the string is

F = T - (M+m)g

(M+m)v^2/l = 400 N -20.9 kg *9.8 m/s^2

v = 4.42 m/s

Let the initial velocity of the projectile be vi

By law of conservation of momentum principle, we have

mvi = (M+m) v

0.9 kg *vi = 20.9 kg *4.42 m/s^2

vi =102.64 m/s

so, the largest speed, the projectile can have is 102.64 m/s