Conservation of Momentum Problem

[jli10]

Homework Statement

A ball of mass m_1 travels along the x-axis in the positive direction with an initial speed of v_0. It collides with a ball of mass m_2 that is originally at rest. After the collision, the ball of mass m_1 has velocity {v_1}_{x}{\hat{x}}+{v_1}_{y}{\hat{y}} and the ball of mass m_2 has velocity {v_2}_{x}{\hat{x}}+{v_2}_{y}{\hat{y}}. Consider the following five statements:

I) 0=m_1{v_1}_x+m_1{v_2}_x
II) m_1v_0=m_1{v_1}_y+m_2{v_2}_y
III)0=m_1{v_1}_y+m_2{v_2}_y
IV) m_1v_0=m_1{v_1}_x+m_1{v_1}_y
V) m_1v_0=m_1{v_1}_x+m_2{v_2}_x

Of these statements, the system must satisfy
a) I and II
b) III and V
c) II and V
d) III and IV
e) I and III

Homework Equations

(mv)_i=(mv)_f

The Attempt at a Solution

I've never learned how to incorporate conservation of momentum into a 3-d plane...

 

[PeterO]

Homework Statement

A ball of mass m_1 travels along the x-axis in the positive direction with an initial speed of v_0. It collides with a ball of mass m_2 that is originally at rest. After the collision, the ball of mass m_1 has velocity {v_1}_{x}{\hat{x}}+{v_1}_{y}{\hat{y}} and the ball of mass m_2 has velocity {v_2}_{x}{\hat{x}}+{v_2}_{y}{\hat{y}}. Consider the following five statements:

I) 0=m_1{v_1}_x+m_1{v_2}_x
II) m_1v_0=m_1{v_1}_y+m_2{v_2}_y
III)0=m_1{v_1}_y+m_2{v_2}_y
IV) m_1v_0=m_1{v_1}_x+m_1{v_1}_y
V) m_1v_0=m_1{v_1}_x+m_2{v_2}_x

Of these statements, the system must satisfy
a) I and II
b) III and V
c) II and V
d) III and IV
e) I and III

Homework Equations

(mv)_i=(mv)_f

The Attempt at a Solution

I've never learned how to incorporate conservation of momentum into a 3-d plane...

This looks like only 2-D to me?

 

[jedishrfu]

write down the initial total momentum

then write down the final total momentum

then group the X components into one eqn and the Y components in another and see whether you can answer the question.

show your work and we can help

 

[jli10]

Whoops, sorry, I meant 2-d.
But I think I understand now... You just have to do conservation of momentum for each axis, right? Since the initial momentum is all in the x-direction, the final momentum for the y-components must sum to 0, which is shown in equation III. The initial x-momentum is given by m_1v_0, so the sum of components for the final x-momentum should be exactly that, given by equation V. Final answer (B).

 

[PeterO]

Whoops, sorry, I meant 2-d.
But I think I understand now... You just have to do conservation of momentum for each axis, right? Since the initial momentum is all in the x-direction, the final momentum for the y-components must sum to 0, which is shown in equation III. The initial x-momentum is given by m_1v_0, so the sum of components for the final x-momentum should be exactly that, given by equation V. Final answer (B).

That is correct.