Question

A block of wood (M_block = 6.1 kg) rests on a horizontal surface for which the coefficient of kinetic friction is 0.49. A bullet (m_bullet = 34 g) is shot along the horizontal direction and embeds in the block, displacing the block 81 cm.

What is the magnitude of the acceleration of the bullet and block from immediately after the impact until they come to a stop?

What is the magnitude of the velocity of the bullet and block immediately after the impact?

What was the magnitude of the initial velocity of the bullet immediately before the impact?

Please show all work and equations used :)

Answer 1

here,

the mass of block , M = 6.1 kg

mass of bullet , m = 34 g = 0.034 kg

distance traveled before stopping , s = 81 cm = 0.81 m

the magnitude of acceleration of the bullet and block after the impact before they come to stop , a = uk * g

a = 0.49 * 9.81 m/s^2 = 4.81 m/s^2

the magnitude of the velocity of the bullet and block immediately after the impact, v = sqrt(2 * a * s)

v = sqrt(2 * 4.81 * 0.81) m/s

v = 2.86 m/s

let the magnitude of the initial velocity of the bullet immediately before the impact be u

using conservation of momentum

m * u = (M + m) * v

0.034 * u = ( 6.1 + 0.034) * 2.86

solving for u

u = 516 m/s

the magnitude of the initial velocity of the bullet immediately before the impact is 516 m/s