Momentum of pendulum after hitting it with bullet

In summary: Actually, you don't need to solve for the KE at point C. You can just compare the total mechanical energy at point C to the total mechanical energy at point B.
  • #1
princesspriya
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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.
 
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  • #2
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?)
 
  • #3
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.
 
  • #4
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 isn't since it would be a inelastic collision because they stick together.
 
  • #5
princesspriya said:
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 isn't 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.
 
  • #6
but i thought momentum is always conserved before and after the inelastic collision?
 
  • #7
princesspriya said:
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.
 
  • #8
i see but back to the question now i feel so lost... no clue on how to solve it.
 
  • #9
Hint: Work backwards. Start by finding the KE of the "pendulum + bullet" immediately after the collision.
 
  • #10
you cannot because you don't have the final velocity of the pendulum.
 
  • #11
princesspriya said:
you cannot because you don't 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?
 
  • #12
i thought it would be zero but than that would make the KE=0 which would not make sense
 
  • #13
Why would that not make sense?
 
  • #14
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
 
  • #15
princesspriya said:
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.
 
  • #16
its not at the top o f its swing its at the lowest point so it will keep going.
 
  • #17
princesspriya said:
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.)
 
  • #18
actually i figured it out. i was making a really stupid mistake... thanks for the help!
 

1. What is the equation for calculating the momentum of a pendulum after hitting it with a bullet?

The equation for calculating the momentum of a pendulum after hitting it with a bullet is p = m * v, where p is momentum, m is mass, and v is velocity.

2. How does the mass of the bullet affect the momentum of the pendulum?

The mass of the bullet has a direct impact on the momentum of the pendulum. A heavier bullet will have a greater momentum, resulting in a larger swing of the pendulum.

3. Does the velocity of the bullet also affect the momentum of the pendulum?

Yes, the velocity of the bullet also plays a role in the momentum of the pendulum. A faster moving bullet will have a greater momentum, causing a larger swing of the pendulum.

4. Can the momentum of the pendulum be calculated after the bullet has hit it?

Yes, the momentum of the pendulum can be calculated after the bullet has hit it by measuring the mass and velocity of the bullet and using the equation p = m * v.

5. How does the angle at which the bullet hits the pendulum affect the momentum?

The angle at which the bullet hits the pendulum can affect the direction and magnitude of the momentum. A direct hit on the pendulum's center of mass will result in a larger momentum, while hitting at an angle may cause the momentum to be directed in a different direction.

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