Collision of bullet with mass hung from tree

[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 traveling 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?

 

[Defennder]

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.

 

[devanlevin]

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

a

 

[tiny-tim]

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.

 

[devanlevin]

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?

 

[tiny-tim]

pendulum …

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?

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

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

 

[Defennder]

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

 

[Redbelly98]

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

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

 

[devanlevin]

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 don't know the angle because i don't know how much of the circumference the arc it goes on is,,, any ideas?

 

[devanlevin]

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

 

[Redbelly98]

Use tiny-tim's hint:

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