Question

A 45 g bullet strikes and becomes embedded in a 1.55 kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.28, and the impact drives the block a distance of 13.0 m before it comes to rest, what was the muzzle speed of the bullet in meters/second?

Answer 1

299.51 m/s

Step-by-step explanation:

m = mass of the bullet = 45 g = 0.045 kg

M = mass of the block = 1.55 kg

v = muzzle speed of the bullet

V = speed of bullet-block combination after the collision

μ = Coefficient of friction between the block and the surface = 0.28

d = distance traveled by the block = 13 m

V' = final speed of the bullet-block combination = 0 m/s

acceleration of the bullet-block combination due to frictional force is given as

a = - μg

using the kinematics equation

V'² = V² + 2 a d

0² = V² + 2 (- μg) d

0 = V² - 2 (μg) d

0 = V² - 2 (0.28) (9.8) (13)

V = 8.45 m/s

Using conservation of momentum for collision between bullet and block

mv = (M + m) V

(0.045) v = (1.55 + 0.045) (8.45)

v = 299.51 m/s