A 7.80-g bullet moving at 630 m/s penetrates a tree trunk to a depth of 6.40 cm.

Question

A 7.80-g bullet moving at 630 m/s penetrates a tree trunk to a depth of 6.40 cm.

(a) Use work and energy considerations to find the average frictional force that stops the bullet.
(b) Assuming the frictional force is constant, determine how much time elapses between the moment the bullet enters the tree and the moment it stops moving.

Explanation / Answer

(a) By work energy theorem:- =>W = delta KE =>Ff x s = 1/2mv^2 =>Ff = mv^2/2s =>Ff = [7.8 x 10^-3 x (530)^2]/[2 x 5.2 x 10^-2] =>Ff = 21067.50 N (b) By v^2 = u^2 - 2as =>0 = (530)^2 - 2 x a x 5.2 x 10^-2 =>a = 5401923.08 m/s^2 By v = u - at =>0 = 530 - 5401923.08 x t =>t = 9.8 x 10^-5 sec

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