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A 20
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?
Expert Solution
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
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