# Homework Help: A bullet through a pendulum.

1. Mar 31, 2012

1. The problem statement, all variables and given/known data

A 10g bullet moving at 300.m/s hits and passes through a 2.20kg pendulum target. After the impact, the 1.20m long pendulum rises up to an angle of 15 degree, find the final speed of the bullet.

2. Relevant equations
Ek= 1/2MV^2
Ep= MGH
Momentum = MV

3. The attempt at a solution

I assumed all energy before and after the question will be = because the collision is inelastic, both masses dont stay together. I found the height the pendulum rises by doing 1.2-(1.2Cos15). Then I put everything i knew in EK= Ep + EK

(300^2)*(0.01)*(0.5) = (2.20)(9.8)(0.04) + (0.5)(0.01)(v')^2

When I solve for velocity I get the answer wrong. What am I doing wrong, am I wrong that energy is conserved ?

2. Mar 31, 2012

### issacnewton

why are you using 300^2 ? use conservation of linear momentum to get the relationship between the initial and final velocities of the bullet.

3. Mar 31, 2012

I tried solving via energy.

4. Mar 31, 2012

Though when I try solving momentum i get. 300(0.01)=2.2(v)+0.01(v) 2 variables.

5. Mar 31, 2012

### issacnewton

well you need BOTH energy and momentum to solve this... since bullet gets stuck inside the pendulum, this is an inelastic collision and kinetic energy is not conserved.....

6. Mar 31, 2012

Though the bullet leaves the pendulum, do we still consider this inelastic ?

7. Mar 31, 2012

### issacnewton

oh sorry. didn't read the question properly. let me think

8. Mar 31, 2012

### Staff: Mentor

Conservation of momentum works regardless of the nature of the collision. The trick here is to figure out how much momentum ended up in the pendulum bob...

9. Mar 31, 2012

### issacnewton

well. the collision is still inelastic. use the conservation of energy to get the velocity of the
pendulum immediately after the collision. then use conservation of linear momentum to connect all three velocities

10. Mar 31, 2012

this doesn't work.

11. Mar 31, 2012

And if the collision is still inelastic you cant "use the conservation of energy to get the velocity of the pendulum immediately after the collision" because in a inelastic collision EK is not conserved.

12. Mar 31, 2012

### Staff: Mentor

You were given other information about the pendulum involving its energy...

13. Mar 31, 2012

Thats why I tried solving by.... Ek(bullet) = Ep(pendulum) + EK(bullet)
Why doesnt that work ?

14. Mar 31, 2012

### issacnewton

well, lets say that velocity of the pendulum immediately after the collision is $v_2$. Now since the gravitational force is conservative, here, the total energy is
conserved and you can use conservation of energy to connect angle with this velocity and find $v_2$. since the bullet is momentarily inside the pendulum, the KE of the bullet is NOT conserved. but if we take system as bullet + pendulum, then there are no
external forces in x direction. so we can still use conservation of linear momentum.

15. Mar 31, 2012

Yes I tried that 300(0.01) = 2.21(v'). But what do I do with that velocity.
I tried Ek(pendulum+bullet) = Ek + Ep yet got the wrong answer.

16. Mar 31, 2012

Is there something wrong with this ?

17. Mar 31, 2012

### Staff: Mentor

Because energy is not conserved over the collision. Before and after the collision it is, for both objects separately.

Momentum, on the other hand, is always conserved. What do you need to know about the pendulum in order to calculate its momentum immediately after the collision? What information do you have on hand that could tell you?

18. Mar 31, 2012

### Staff: Mentor

The bullet does not remain in the pendulum, and energy is not conserved over an inelastic collsion. Even so, there is other information available that will allow you to calculate the KE of the pendulum bob immediately after the collision. If you have its KE, what else can you find?

19. Mar 31, 2012