# Conservation of Momentum Question

• Silverbird
In summary, you are trying to solve a conservation of linear momentum problem in which there are two unknowns. After solving the momentum equation for v1', you plugged this into the conservation of kinetic energy equation. However, you are getting hung up in the algebra somewhere and cannot get the correct answer.
Silverbird
PLEASE, please help! I have been working on this problem for two days and am about to pull my hair out. This is a distance course, so I have no one to ask for help.

I am trying to solve a conservation of linear momentum problem in which there are two unknowns. Object 1 (0.5 kg), going 7.0 m/s strikes Object 2 (1.0 kg) which is at rest. I need to determine the velocities of each object after the collision.

I know that it is necessary to use both the conservation of momentum and conservation of kinetic energy equations to solve the problem. I solved the momentum equation for v1' and plugged this into the KE equation. Cancelling the 1/2 and m1, I ended up with this:

v1^2 = [v1-(m2/m1)v2']^2 + (m2/m1)v2'^2

I am certain this is right up to this point. However, I am getting hung up in the algebra somewhere, because no matter what I do, I cannot get the correct answer (This is a study problem for which I have been given the answer, but not the means of solving.)

Could someone PLEASE go through the algebra STEP by STEP starting with the equation above and solving for v2'? Or, if this is not possible could you direct me to a resource where I can find this specific information?

I would be most grateful for any help, since there is a similar problem in my homework assignment and I am sure I will need to be able to do this for the test and for future problems. THANK YOU SO MUCH!

I'm sorry.But this is algebra and you're not solving an algebra problem,but a physics one.It's a prerequisite.U can't plunge into simple physics problems without knowledge of elementary algebra,geometry & trigonometry...

Conservation of linear momentum

$$m_{1}\vec{v}_{1}+m_{2}\vec{0}=m_{1}\vec{v'}_{1}+m_{2}\vec{v'}_{2}$$

For this one,u can make the assumption that the collision is 1 dimensional.

Assuming there's an ideal colllision,then KE is conserved,too.

$$m_{1}\frac{v_{1}^{2}}{2}+m_{2}\frac{0^{2}}{2}=m_{1}\frac{v'_{1}^{2}}{2}+m_{2}\frac{v'_{2}^{2}}{2}$$

Daniel.

I'm sorry if my question seems like it was too elementary. I am an adult student returning for a second degree, and I have completed multiple advanced courses in chemistry and biology. This is my second semester of physics, and I am doing very well in it. Though I do not remember everything that I learned in my last algebra class (15 years ago), I do remember most of it. I would not have gotten this far if I didn't. There is something in the algebra of this problem that is messing me up, but I DO GET the physics concept. Can you help me?

Eh, you can't understand the physics without understanding the mathematics so...

If you can tell us, exactly, your problem with the algebra involved, we may be able to help.

Thank you, I found all the help I needed on very knowledgeable, HELPFUL website.

Your problem involved solving a quadratic algebraic equation.I think that's taught in first year of high-school...

Daniel.

## 1. What is the conservation of momentum?

The conservation of momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time. This means that in the absence of external forces, the total momentum of a system before and after a collision or interaction will be the same.

## 2. Why is the conservation of momentum important?

The conservation of momentum is important because it helps us understand and predict the motion of objects in various scenarios, such as collisions and explosions. It also plays a crucial role in the laws of thermodynamics and the study of fluid dynamics.

## 3. How is momentum conserved in a closed system?

In a closed system, the total momentum is conserved because there are no external forces acting on the system. This means that the total momentum before an interaction or collision is equal to the total momentum after the interaction or collision.

## 4. Can momentum be lost?

No, momentum cannot be lost in a closed system. It can only be transferred between objects within the system. This is known as the law of conservation of momentum.

## 5. How does the conservation of momentum relate to Newton's laws of motion?

The conservation of momentum is a direct consequence of Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This means that when two objects interact, the total momentum of the system is conserved.

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