How Do You Calculate the Momentum of a Particle Relative to the Center of Mass?

[bmoore509]

Homework Statement

A 3.64 g particle is moving at 2.58 m/s toward a stationary 10.2 g particle. With what speed does the heavier particle approach the center of mass of the two particles?
Answer in units of m/s.
Answer: 0.67855913 m/s

What is the magnitude of the momentum of the lighter particle, relative to the center of mass? Answer in units of Ns.

Homework Equations

momentum=mv

The Attempt at a Solution

Since its in Ns, I'd use 0.00364kg.
Momentum=0.00364*0.67855913
= 0.002469955

Which the online homework said wasn't right. So I tried using 3.64 and got 2.46995523 which isn't right either.

I don't understand what I'm doing wrong.

 

[bmoore509]

If p=m*vc then the total momentum I got to be 9.3912, the big particle 6.9212601 and the small particle 2.46.

Can someone please help me figure out how this isn't right?

 

[PhanthomJay]

Homework Statement

A 3.64 g particle is moving at 2.58 m/s toward a stationary 10.2 g particle. With what speed does the heavier particle approach the center of mass of the two particles?
Answer in units of m/s.
Answer: 0.67855913 m/s

What is the magnitude of the momentum of the lighter particle, relative to the center of mass? Answer in units of Ns.

Homework Equations

momentum=mv

The Attempt at a Solution

Since its in Ns, I'd use 0.00364kg.
Momentum=0.00364*0.67855913
= 0.002469955

Which the online homework said wasn't right. So I tried using 3.64 and got 2.46995523 which isn't right either.

I don't understand what I'm doing wrong.

The question asks for the magnitude of the momentum of the lighter particle, relative to the center of mass. The speed of the lighter particle with respect to the center of mass is not .678 m/s. That was the speed of the heavier particle with respect to the center of mass. The momentum of each particle with respect to the center of mass should be the same.

 

[bmoore509]

I eventually got it.

 

[rwisz]

There could be a few things that you may be doing wrong. Firstly, the momentum of the lighter particle should be calculated relative to the center of mass, which is not the same as the speed at which the heavier particle approaches the center of mass. The momentum of the lighter particle can be calculated using the equation P = m1v1 - m2v2, where m1 and v1 are the mass and velocity of the lighter particle, and m2 and v2 are the mass and velocity of the heavier particle.

Secondly, when using the equation P = mv, make sure that you are using the correct units. In this case, the mass should be in kilograms (kg) and the velocity should be in meters per second (m/s). So, for the lighter particle, the momentum would be calculated as P = 0.00364 kg * 2.58 m/s = 0.0093912 Ns.

Lastly, make sure that you are using the correct values for the masses and velocities given in the problem. The lighter particle has a mass of 3.64 grams, which is equal to 0.00364 kg. The velocity given is 2.58 m/s, so there is no need to use the conversion factor. Similarly, the heavier particle has a mass of 10.2 grams, which is equal to 0.0102 kg, and is stationary (so its velocity is 0 m/s).

I hope this helps clarify any misunderstandings and helps you arrive at the correct answer. Remember to always double check your units and make sure you are using the correct equations for the given situation. Good luck!