Collision problem cant figure it out

[jjf5122]

Question: A ball of mass m is suspended from a string of length l. A lump of clay of mass 3m is thrown horizontally at the ball w/ a speed of v0 making a direct hit and sticking to it. Find the speed of the combined object right after the collision, and how high it rises.

Answer: 3/4vo 9/32(v0*v0/g)

the answer is given but i need to know how this problem is actually solved. Any help would be greatly appreciated.

 

[neutrino]

Have you tried to solve using conservation laws?

 

[jjf5122]

the book i was given for this class shows barely anything at all in it. I don't really know where to begin. The only equation given in this entire chapter relating to a inelastic equation (which I am assuming this collision is) would be>>>>>> m1v1+m2v2=(m1+m2)v' however...where does a distance come into this ie. lenth of the height? And how woud i actually utalize this equation when almost no information is given?

 

[neutrino]

First, use that equation (which is a special case of the law of conservation of momentum) to find the velocity the combined mass would be having immediately after collision. Once you have figured out the velocity, use the law of conservation of energy to find the height.

 

[jjf5122]

hmm...how do i do that if no actual masses or velocities are given?

v'= m1v1+m2v2/ total mass...but i have no numbers, am i missing something?

 

[neutrino]

Not every problem comes with numbers involved with every quantity. As you can see from the answer, it is a multiple of v0. You know one mass is 3 times the other, and the ball was at rest, initially. Substitute these details into the equation.

 

[jjf5122]

awesome i see what u mean. The momentum of the first object is 0 because its at rest. the total mass is obviously 4m therefore: 3m vo/ 4m... the ms cancel leaving 3/4 vo. Ok i get that now. However... what is the conservation of energy formula that i need to solve for the distance?

 

[neutrino]

Have you come across the terms 'kinetic energy' and 'potential energy' before?

 

[jjf5122]

Yes but I am confused as to how to actually set this up to work...how do i use the velocity that i got, or do i need to. Am i suppossed to use, delta K + delta Ug(ptoential gravitational force) = 0? And if so...how would i actually set this up?

also... K= mgh
U = -mgh

 

[neutrino]

Am i suppossed to use, delta K + delta Ug(ptoential gravitational force) = 0?

Exactly.

And if so...how would i actually set this up?
also... K= mgh
U = -mgh

Kinetic energy is (1/2)mv²! and U = mgh.

Delta {something} refers to change in the something, usually at two different times. You know what the velocity of the combined mass is after colission. Consider the point to be at the 'zero' height. Now can you solve for the height to which the mass will go to?

 

[jjf5122]

Sry this is frustrating for me...wouldnt the velocity i solved for actually be the initial velocity, right after the collosion occurred, and the final velocity be 0(because it will come to a stop briefly when it reaches its max height)? So I am still confused as to how this is actually set up.

1/2mv2'-1/2mv2 + mgh'-mgh = 0
0 - 1/2m(3/4vo)2 + mgh' - mg(0)= 0
-1/2m(3/4vo)2 + mgh'
-1/2m(3/4vo)2/mg = -h



this doesn't seem right...do u have any suggestions as to how to set the equation up?

 

[neutrino]

wouldnt the velocity i solved for actually be the initial velocity, right after the collosion occurred, and the final velocity be 0(because it will come to a stop briefly when it reaches its max height)?

That is correct.

So I am still confused as to how this is actually set up.

1/2mv2'-1/2mv2 + mgh'-mgh = 0
0 - 1/2m(3/4vo)2 + mgh' - mg(0)= 0
-1/2m(3/4vo)2 + mgh'
-1/2m(3/4vo)2/mg = -h
this doesn't seem right...do u have any suggestions as to how to set the equation up?

Why doesn't it seem right? It's perfect*. You just have to simplify it to get it to look like it is given in your book. *-1/2m(3/4vo)2/mg = -h (If that 2 in bold means "squared," then it's correct). It is customary to denote powers by ^. Example: (3/4vo)^2

 

[jjf5122]

2m(9/16)/mg( this is where I am confused...g would be 9.8m/s^2?) if i multiply 4m(9.8) i get 39.2 m^2s^2

none of this seems to reduce down to the answer in my book of 9/32 v0^2/g

 

[neutrino]

$$\frac{\frac{1}{2}m\left(\frac{9v_{o}^{2}}{16}\right)}{mg}$$

Does that make more sense?

 

[jjf5122]

hmm...so i don't actually have to plug a mass(inthe denominator) or 9.8 m/s^2 into the formula?