Question

A physics student hurls a 315-gram baseball directly into a 3.54-kg box which is at rest on a table top. The baseball strikes the box with a pre-impact speed of 54.1 m/s. The box is filled with towels to help absorb the blow and effectively catch the ball. The coefficient of friction between the box and the table is 0.714. Determine the distance which the ball and box slide across the table after the collision.

Answer 1

here,

the mass of ball , m1 = 315 g = 0.315 kg

the mass of box , m2 = 3.54 kg

initial speed of ball , u = 54.1 m/s

let the velocity of system after the collison be v

using conservation of momnetum

m1 * u = ( m1 + m2) * v

0.315 * 54.1 = (0.315 + 3.54) * v

v = 4.42 m/s

magnitude of acceleration due to friction , a = uk * g

a = 0.714 * 9.81 m/s^2

a = 7 m/s^2

the distance which the ball and box slide across the table after the collision , s = v^2 /(2a)

s = 4.42^2 /(2*7) m

s = 2.8 m