Calculating Center of Mass Velocity for Moving Blocks: m1=m2, p1, p2

[ProBasket]

1.)Let us assume that the blocks are in motion, and the x-components of their momenta at a certain moment are $$p_1$$ and $$p_2$$, respectively. (there's a pic attached)

Find the x-component of the velocity of the center of mass at that moment.

Express your answer in terms of $$m_1,m_2,p_1, p_2$$


my answer is $$v_{cm} = \frac{m_1*p_1+m_2*p_2}{m_1+m_2}$$ but it's incorrect and i don't understand why.

i think p stands for point particle.

also, i have one more quick quesiton:

2.)Suppose that $$v_{cm} = 0$$. Therefore, the following must be true
A.) $$p_1 = p_2$$
B.) $$v_1 = v_2$$
c.) m1 = m2
d.) none of the above
for this one, i think that if it's equal to zero, both masses should be equal, is this correct?

 

[StatusX]

As a general rule, the total momentum of a system is the vector sum of the momenta of all the particles. This is equal to M_total v_cm.

In this case, the position of the center of mass is (m_1 x_1 + m_2 x_2) /(m_1 + m_2). So the velocity is it's change in time, which is (m_1 v_1 + m_2 v_2) /(m_1 + m_2) = (p_1 + p_2)/(m_1+m_2).

For the MC question, remember you can pick the velocity of the center of mass to be anything you want by adding some velocity to both masses. So you can always make it 0 with the right choice of this velocity. Based on what I said in the first paragraph, what does this tell you?

 

[thepatientmental]

Your answer for the first part is almost correct. The correct formula for the x-component of the center of mass velocity is v_{cm} = \frac{m_1*p_1+m_2*p_2}{m_1+m_2}. This formula represents the weighted average of the individual velocities of the blocks, where the weights are the masses of the blocks. This means that the velocity of the center of mass will be closer to the velocity of the block with the larger mass.

For the second question, the correct answer is d.) none of the above. The fact that the center of mass velocity is zero does not necessarily mean that the masses are equal. It is possible for the center of mass to have a zero velocity even if the masses are not equal, as long as the individual velocities are balanced in a way that results in a zero net velocity for the center of mass.