# Momentum of pendulum after hitting it with bullet

princesspriya

## Homework Statement

An 9 g bullet is fired into a 2.5 kg pendulum bob which is initially at rest and becomes embedded in the bob. The pendulum then rises a vertical distance of 6cm.
What was the initial speed of the bullet? What will be the kinetic energy of the pendulum when the pendulum swings back to its lowest point?

## Homework Equations

M1Vi+M2Vi=M1Vf+M2Vf

## The Attempt at a Solution

For the first part how would i be able to find the final speed of the pendulum because to use vf^2=vi^2+2ax i would need to know the acceleration which is not given.

For the second part wouldn't the KE be zero since the pendulum stops at it lowest point??

thanx for the help.

Mentor
To find the initial speed of the bullet, treat this problem as having two parts:
(1) The collision of bullet and pendulum. (What's conserved here?)
(2) The swinging of pendulum+bullet after the collision. (What's conserved here?)

lzkelley
Note that in problems like this, using the acceleration to find velocities (etc) is impossible because we don't know enough about the situation (i.e. the material characteristics) - and we don't need to.

princesspriya
in the first one the total momentum's conserved but i would need to find the vf in order to use the equation and in the second one only total momentum is conserved the kinetic energy isnt since it would be a inelastic collision because they stick together.

Mentor
in the first one the total momentum's conserved but i would need to find the vf in order to use the equation and in the second one only total momentum is conserved the kinetic energy isnt since it would be a inelastic collision because they stick together.
During the collision, momentum is conserved but mechanical energy is not. (As you correctly point out, the collision is inelastic.)

After the collision, mechanical energy (but not momentum) is conserved.

princesspriya
but i thought momentum is always conserved before and after the inelastic collision?

Mentor
but i thought momentum is always conserved before and after the inelastic collision?
Momentum is conserved during any collision, which means the momentum before and immediately after the collision will be the same. But the pendulum is suspended. As it swings, an external force (the tension in the string) acts and thus momentum is no longer conserved.

princesspriya
i see but back to the question now i feel so lost... no clue on how to solve it.

Mentor
Hint: Work backwards. Start by finding the KE of the "pendulum + bullet" immediately after the collision.

princesspriya
you cannot because you dont have the final velocity of the pendulum.

Mentor
you cannot because you dont have the final velocity of the pendulum.
What do you mean by "final"? After the pendulum rises, what must its speed be at the top of its swing?

princesspriya
i thought it would be zero but than that would make the KE=0 which would not make sense

Mentor
Why would that not make sense?

princesspriya
well idk but my teacher said its 1.5 J.. and since its like swinging back it would be that velocity not the velocity at its lowest point.. i think

Mentor
well idk but my teacher said its 1.5 J.. and since its like swinging back it would be that velocity not the velocity at its lowest point.. i think
Not sure why you think it will have a non-zero speed at the top of its swing. If it had a non-zero speed it wouldn't be at the top--it would keep going higher! (It's like tossing a ball straight up in the air. What's the speed of the ball at the highest point? Zero of course.)

Compare the total mechanical energy of the "pendulum + bullet" immediately after the collision to its total energy at the highest point of its swing.

princesspriya
its not at the top o f its swing its at the lowest point so it will keep going.

Mentor
its not at the top o f its swing its at the lowest point so it will keep going.
We seem to be talking in circles a bit. Distinguish three points in the life of the pendulum bob:

(A) Before the bullet hits it.
(B) Immediately after the bullet hits it. (At the lowest point of its swing.)
(C) At the top of its swing.

Point C is where the KE is zero. (Of course it's also zero before the bullet hits it, but who cares about that.)

How much total energy does the pendulum have at point C? (Compared to point B.)

princesspriya
actually i figured it out. i was making a really stupid mistake... thanx for the help!