Two masses collide elastically...

[GIASAL]

A body of mass m1 = 2 kg with a velocity v1 = 12 m/s collides elastically with a second body initially at rest. The first body continues to move in the same direction as the initial one but with a velocity equal to one-quarter of its initial velocity. Find the mass of the second body in kg.

Thanks

 

[renormalize]

Find the mass of the second body in kg.

Is this homework? Can you show your work where you attempt to solve it?

 

[GIASAL]

From the general expression for the total kinetic energy before the collision, I tried to derive m2, but I couldn't:

Ec = 1/2 m1 v1^2 + 1/2 m2 v2^2

I can't extrapolate m2

 

[Ibix]

What law related to energy should you be using? What other kinematic quantity has a similar law?

 

[kuruman]

In this problem, energy conservation allows you to find a number for the kinetic energy of the target particle. You need to use another equation that will separate how much of that number is $\frac{1}{2}v^2$ and how much is $m$.

 

[wrobel]

Suppose two particles of masses $m_1$ and $m_2$ moving along a line collide perfectly elastically. By definition, this means that if the velocities of the particles before the collision were $\boldsymbol v_1^-,\boldsymbol v_2^-$, then their velocities after the collision $\boldsymbol v_1^+,\boldsymbol v_2^+$ are determined from the system of equations:
$$m_1\boldsymbol v_1^-+m_2\boldsymbol v_2^- =
m_1\boldsymbol v_1^++m_2\boldsymbol v_2^+;$$
(conservation of momentum )
$$\frac{m_1|\boldsymbol v_1^-|^2}{2}+\frac{m_2|\boldsymbol v_2^-|^2}{2}= \frac{m_1|\boldsymbol v_1^+|^2}{2}+\frac{m_2|\boldsymbol v_2^+|^2}{2}$$
(conservation of energy)

 

[DEvens]

When you are doing collisions, the easy way is almost always to go to the centre of momentum (COM) frame. This frame has total momentum zero. And this is true after the collision. So when it's an elastic collision the momentum (in the COM frame) of each mass simply changes to the negative of the original value. So in this case you don't need to worry about kinetic energy. This converts the problem to a really easy to solve system of two equations in two unknowns. You have one equation for the velocity of M2 in the COM frame. And another that gives total momentum in the COM frame being zero. You should be able to get both of those, and to solve for M2.