# Physics Problem

• Nov 19th 2007, 08:27 AM
Linnus
Physics Problem
(a) If a particle that is moving has the same momentum and the same kinetic energy as another, must their masses and velocities be equal? If so, explain why, and if not, give a counterexample. (b) Describe the properties of two particles that have the same momentum, but different kinetic energies.

I got the answer to be the velocity and masses has to be equal, but apparently the answer is that they don't have to be equal. Can someone explain? Thanks
• Nov 19th 2007, 10:29 AM
relearning_calculus
Quote:

Originally Posted by Linnus
(a) If a particle that is moving has the same momentum and the same kinetic energy as another, must their masses and velocities be equal? If so, explain why, and if not, give a counterexample. (b) Describe the properties of two particles that have the same momentum, but different kinetic energies.

I got the answer to be the velocity and masses has to be equal, but apparently the answer is that they don't have to be equal. Can someone explain? Thanks

Hi Linnus,

The formula for momentum is [mass]*[velocity]. I once had an instructor call this the "Mickey Mouse" school of physics -- imagine that, if the formula equals a constant, that if one component grows large, what does the other have to do? Shrink. Sounds silly, but I'll use Mickey to this day.

Suppose momentum is 100 kg m/s:

\$\displaystyle 100 kg m/s = m * v\$, for \$\displaystyle m = 10 kg\$. What is \$\displaystyle v\$? \$\displaystyle 10 m/s\$.

Can you have the same momentum, for say 5 kg? Sure, but since \$\displaystyle m\$ has decreased, \$\displaystyle v\$ must correspondingly increase, to \$\displaystyle 20 m/s\$. The momentum remains the same, though.

The only time when the velocity has to be the same, for two objects of the same momentum, is when the masses are the same as well. They do not vary independently.

Make sense? Or did I misunderstand the question?
• Nov 19th 2007, 10:38 AM
Linnus
hmm, I think you kinda misunderstood the question...and partly right...because you also have to take the KE into account
• Nov 19th 2007, 10:48 AM
relearning_calculus
Quote:

Originally Posted by Linnus
(a) If a particle that is moving has the same momentum and the same kinetic energy as another, must their masses and velocities be equal? If so, explain why, and if not, give a counterexample. (b) Describe the properties of two particles that have the same momentum, but different kinetic energies.

I got the answer to be the velocity and masses has to be equal, but apparently the answer is that they don't have to be equal. Can someone explain? Thanks

Duh!!! I missed that part.

Okay, here's what I can come up with. Velocity is a vector. Velocity squared loses all sense of direction, and is a scalar. You could say that the momentum in *one component direction* -- say in the x-direction -- is the same in both particles, but the overall velocity is skewed more or less y-ward in one of them -- but skewed in such a way that the v^2 is the same.

If the answer is simpler/crazier than that, I don't know.