Question

A 0.020-kg bullet traveling at a speed of 300 m/s embeds in a 1.0-kg wooden block resting on a horizontal surface. The block slides horizontally 4.0 m on a surface before stopping. What is the coefficient of friction between the block and the surface?

Answer 1

The coefficient of friction between the block and the surface is μk=0.441

Step-by-step explanation:

Let

mb = bullet mass = 0.02 kg

vb = bullet speed = 300 m/s

mw = mass of the wood block = 1 kg

d = distance covered by the block plus the bullet = 4 m

u = speed of the bullet plus the block

g = gravity = 9.8 m/s2

μk = coefficient of friction, variable unknown

We will use the following expression to calculate the coefficient of friction:

μk =
`(((mb*vb)/(mb+mw))^(2) )/(2*g*d)`

Replacing known values:

μk=
`((((0.02kg)*(300m/s))/(0.02kg+1kg))^(2) )/(2*9.8m/s^(2)*4m )=0.441`

The coefficient of friction is a dimensionless value