# Bullet shot into a block

## Homework Statement

A bullet with a mass of 7.00g is fired horizontally with a speed of 450m/s , into a wooden block with mass of 0.810kg , initially at rest on a level surface. The bullet passes through the block and emerges with its speed reduced to 140m/s . The block slides a distance of 50.0cm along the surface from its initial position.

a) What is the coefficient of friction between the block and the surface?

b) What is the kinetic energy of the block the instant after the bullet passes through it?

c) What fraction of the initial kinetic energy was "lost" ( converted to other forms of energy) in this inelastic collision?

## Homework Equations

u=F/N
M1U1+M2U2=M1V1+M2V2

## The Attempt at a Solution

Im not sure how to get part a) since I dont have a force to find the coefficient of friction and I dont know how to find the velocity of the block after the bullet passes though it to determine the kinetic energy of the block. Part C should be easy but seems a little confusing. is that talking about the kinetic energy loss of the bullet or the block? ... I guess it would make more sense for that to be talking about the entire system since that takes both into account.

For part a) use conservation of linear momentum. You know the initial momentum of the bullet, the final momentum of the bullet and the mass of the block. Solve for the speed of the block.

Then you know the initial speed of the block, the final speed of the block, and the displacement of the block so use kinematics to solve for the acceleration of the block. Use Newton's laws to find the force on the block and set that equal to the frictional force and solve for the coefficient of friction.

b) Use the speed of the block you found in a) to find the kinetic energy of the block

c) Find the initial kinetic energy of the bullet, the final kinetic energy of the bullet and use your answer to b) to calculate the fraction of kinetic energy lost.

a) M1U1+M2U2=M1V1+M2V2 gives you everything you need. You know the initial velocity, how far it traveled, and the final velocity. That gives deceleration, and deceleration gives coefficient of friction.

b)K=.5mv^2

c)K2/K1=?