Ok so i got this assignment to return tomorrow:(adsbygoogle = window.adsbygoogle || []).push({});

"A particle P with mass m is fastened to the end of a string, that has the length L. The particle starts at rest in a position where the string is rigid, and the strings direction makes a 60° with the vertical axis. At it's lowest point of the pendulums swing, the particle P hits an object A, which is at rest on a frictionless horizontal table. The object A has a mass of n*m, where n is a positive number. The collision between P and A is completely elastic. Gravitational acceleration we call g and we ignore wind resistance. So the known variables are: n, m, l, and g.

1. Just before the collision, the particle P has the kinetic energy [tex]T_0[/tex], find [tex]T_0[/tex].

2. Find the velocity of the object A and the particle P right after the collision, and find out how big a part "q" of the kinetic energy [tex]T_0[/tex] has been transfered to A.

3. Investigate q for [tex]n -> \infty[/tex]. Give a short comment about the observed effect.

4. Find [tex]cos\theta_0[/tex], where [tex]cos\theta_0[/tex] is the angle between the string and the vertical axis, when the particle P is at it's highest point in the gravitational field.

5. Inveistigate the expresion for [tex]cos\theta_0[/tex] for [tex]n -> \infty[/tex], give a short comment on the observed effect"

Ok this was translated over to english so i just hope i got it written down right :)

So ok, i think i got 1 and 2, and the most of 3.

First we find the height of P and use conservation of energy to find it's velocity just before it hits A

[tex]h=L-(cos(\theta)*L)[/tex]

[tex]mgh=1/2*mv^2 => v=\sqrt{2g(L-(cos60°*L))}[/tex]

And cos60 being0.5 we get [tex]v=\sqrt{g*L}[/tex]

Then since it's totally elastic, no energy is lost and E before and E after is the same. That coupled with conservation of momentum i have two unknowns with two variables. It's rather tedious handworking but i got to

[tex]1/2mgl=1/2mu_1^2 + 1/2mnu_2^2[/tex]

[tex]mgl=mu_1 + mnu_2[/tex]

[tex]u_1=\sqrt{gl}*((n-1)/(n+1))[/tex]

[tex]u_2=2*\sqrt{gl}/(n+1)[/tex]

and the to find the fractional quantity of q transfered kinetic energy to A i just took the kinetic energy of the object A right after being hit, and divided it with the kinetic energy of the particle P just before the collision which should give me the % of energy transfered, and i got:

[tex]\frac{4n}{(n+1)^2}[/tex]

Now for #3, when n goes towards infinity. Obviously (n+1)^2 grows exponantually and much faster then 4n, so when n goes towards infinity, the whole shebang goes towards zero, which i can see mathematicly, but i'm not sure why physicly this is the case. I can also see that this must be correct looking at the formula for kinetic energy, since if V gets very small, then V^2 must be even smaller and the kinetic energy lessens, but i just don't feel like i have an understanding of it :/ Even though i could propably give an answer by simply quoting the formulas that would be satisfactory for this assignment. If i could get some better explenation that would be great too.

Now #4 i'm pretty lost on. First off of course i'll have a new v since it's an unknown variable, so [tex] v=\sqrt{2g(L-(cos\theta_0*L)}[/tex]. And i've tried playing a bit with that in the formulas, but i can't seem to get anything that makes good sense to me :/

If anyone could give me some tips on #4 and perhaps a better explenation of #3 (and of course if you see something wrong with 1 and 2) that'd be great :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Pendulum hitting static object

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**