# Homework Help: Collision of bullet with mass hung from tree

1. Aug 22, 2008

### devanlevin

a wooden tree trunk with A mass M=9.98kg is hung from a tree by a cord who's mass is irrelevant, it is hit by a bullet with a mass of m=0.02kg and is travelling at v1=500m/s. the bullet hits the trunk and immediately gets stuck in it, what is the maximum height that the trunk and the bullet in it will get to?

mv1=(M+m)u
u=1m/s

u being their velocity after the collision

from here using conservation of energy

0.5(M+m)u^2=(M+m)gh

h=(u^2)/(2g)

h=0.05m(using g=10m/s2)

now how do i find out how long it took the trunk to get to the height?

2. Aug 22, 2008

### Defennder

Re: collision

Are you required by the question to do so? Secondly, you didn't provide the length of the cord, which I believe is needed for some circular motion calculations.

3. Aug 22, 2008

### devanlevin

Re: collision

the question does ask, it also says the length is irrelevant in relation to the mass of the trunk, whatever that means,

a

4. Aug 22, 2008

### tiny-tim

Re: collision

Hi devanlevin!

(You don't need t or length.)

You must split the problem into two separate parts: the instantaneous collision, and the swing up.

For the collision, find u by using conservation of momentum.

Then find h by using conservation of energy.

5. Aug 22, 2008

### devanlevin

Re: collision

i found both u and h, as stated in my question, but i need to find how much time it took to reach the height of h?? how do i do this?

6. Aug 22, 2008

### tiny-tim

pendulum …

Well … this is now an ordinary pendulum problem, with maximum speed u.

Do you know any equations for the period of a pendulum?

7. Aug 22, 2008

### Defennder

Re: collision

Hi tim, I'm not sure what you're on to here. The angle theta through which the cord swings might not necessarily be small, especially since we aren't given the length of the cord and it is apparent that the shorter the cord, the larger angle through which the cord swings in order to reach the same maximum height for a longer cord in a similar setup.

However if one uses the exact large amplitude mathematical model, the problem becomes horrendously complicated:
http://en.wikipedia.org/wiki/Pendulum_(mathematics)#Arbitrary-amplitude_period

Last edited by a moderator: Aug 22, 2008
8. Aug 22, 2008

### Redbelly98

Staff Emeritus
Re: collision

Can you quote the exact wording from the question where it asks for this?

9. Aug 23, 2008

### devanlevin

Re: collision

cant quote it exactly because its in hebrew and i translated it, but it asks to find the velocity after the collision and the maximum height, which i did without too much of a problem. then it asks how long it will take, after the collision to reach the height, it also says that the length of the cord is not relevant so i think it might have something to do with that, ie using simple kinematics to solve it saying treating it like an inclined slope, problem is i dont know the angle because i dont know how much of the circumference the arc it goes on is,,, any ideas?

10. Aug 23, 2008

### devanlevin

Re: collision

just looked at it again, the length of the cord is 2m, now how do i find the time it took

11. Aug 23, 2008

### Redbelly98

Staff Emeritus
Re: pendulum …

Use tiny-tim's hint: