Comparing momentum and kinetic energy for two trucks

[Frank_Horrigan]

Hello I'm stuck on two momentum concept problems and can't figure them out, I was hoping someone could provide help.


1.A small truck and a large truck have the same kinetic energies, which truck has the greater momentum? Justify your answer.

Well i know Ek=.5mv^2 and that momentum p=mv I've tried rearranging these into each other and can't find a clear answer. I think it is the large truck but at the same time the small one will have a greater velocity so I don't know what one will have more momentum.


2. Can an object have kinetic energy but not momentum? Can an object have momentum but no kinetic energy? explain.

I said no to both because if you have kinetic energy you have a velocity, and if you have momentum then you have a veolocity therefore kinetic energy. I want to make sure I'm right here though.

 

[Fermat]

For 1), if they have the same KE then what is the ratio of their velocities ?
Use that ratio to compare their momenta.

Part 2) is correct.

 

[Galileo]

1. Strictly speaking, size isn't the relevant quantity but mass is. It's ofcourse meant that the larger truck has a greater mass.
Since you know $E=\frac{1}{2}mv^2$ and $p=mv$ the idea is to write the energy in terms of the momentum and mass, since those are the quantities that are 'given'. Write the kinetic energy by eliminating the velocity v in favor of the momentum p. Now what does it tell you?

2. That's correct.

 

[Frank_Horrigan]

Ok I am trying to figure out what you mean by writing the equations in terms of m and v. After playing around with the algebra for a while i got that P1=(P2V2)/V1 But i can't figure out what use this is. (2 is the larger truck 1 is the smaller one, I assume when it says smaller it references mass). I know since the kinetic energies are the same that V1 must be greater then V2. but in this equation i have 3 unknows so I don't know where to go.

Another thing I tried is E=.5PV so P=2E/V. I THINK this is what I am supposed to find. So this means that the smaller truck will have less momentum since it has a greater velocity. Am i correct?

 

[Fermat]

You have a big truck and a small truck. So m2 > m1, say.

KE1 = KE2
========
(1/2)m1.v1² = (1/2)m2.v2²
m2/m1 = (v1/v2)²
=============

Momentum
========
P1 = m1.v1
P2 = m2.v2

P1/P2 = ?

Can you finish it off now ?

 

[Frank_Horrigan]

k... So my other one was wrong then. I did this and got (p1/p2)=v2/v1 and since v2 will be less then v1 this means that p2 is larger right? Bah I am getting so confused by such a small question, I did fine with all the ones with actual data but this one is confusing me.

 

[Galileo]

Ok I am trying to figure out what you mean by writing the equations in terms of m and v.

I said writing the kinetic energy in terms of the momentum p by eliminating v. You 'll get $\frac{1}{2}mv^2=p^2/2m$.
Let's call the mass of the small truck m and the mass of the big truck M. Since you know the energies are equal, you know that:
$$\frac{p_s^2}{2m}=\frac{p_l^2}{2M}$$
the subscript s and l stand for small and large respectively. Now what does it tell you?