## anonymous one year ago Sphere A has mass m and is moving with velocity v. It makes a head-on elastic collision with a stationary sphere B of mass 2m. After the collision their speeds (vA and vB) are:

1. anonymous

@michele_laino

2. anonymous

@irishboy123

3. anonymous

Conserve momentum and also energy. Initial total momentum and energy would be mv and 0.5mv^2 Final total momentum and energy would be mvA + 2mvB and 0.5mvA^2+ 0.5(2m)vB^2

4. Abhisar

Hint: $$\sf V_B = \Large \frac{2M_1V}{M_1+M_2}$$

5. anonymous

@mashy and @abhisar it would be very kind of you to lead me to the conclusion and get me the final answer....

6. IrishBoy123

step 1 formally write out the equation for conservation of momentum as it applies here do that and we can go to step 2

7. Michele_Laino

since we have an elastic collision, and such collision happen along a horizontal line, then we have to apply the conservation of momentum (our mechanical system is isolated) and the conservation of kinetic energy ( there is no potential energy of interaction), so we can write this: $\large \left\{ \begin{gathered} mv = m{u_1} + \left( {2m} \right){u_2}\quad \left( {{\text{conservation of momentum}}} \right) \hfill \\ \hfill \\ \frac{{m{v^2}}}{2} = \frac{{mu_1^2}}{2} + \frac{{\left( {2m} \right)u_2^2}}{2}\quad \left( {{\text{conservation of kinetic energy}}} \right) \hfill \\ \end{gathered} \right.$ where $$\large u_1, \; u_2$$ are the speed after collision, and $$\large v$$ is the speed of the sphere $$\large A$$ before collision. Please solve that system for $$\large u_1, \; u_2$$

Find more explanations on OpenStudy