**Part A**

Suppose v_{cm} = 0, it implies that the pomentum, p = mv_{cm} = 0.

m_{1}v_{1} = m_{2}v_{2} = 0

m_{1}v_{1} = - m_{2}v_{2}

Consider a system of two blocks that have masses *m*1 and *m*2 . Assume that the blocks are point-like particles and are located along the *x* axis at the coordinates *x*1 and *x*2 as shown (Figure 1) . In this problem, the blocks can only move along the *x* axis.

Part A

Suppose that *v*⃗cm=0 . Which of the following must be true?

A) |*p*1*x*|=|*p*2*x*|

B) |*v*1*x*|=|*v*2*x*|

C) *m*1=*m*2

D) none of the above

Part B

(*a*cm)*x* = *F*1x+*F*2x*m*1+*m*2

Under what condition would the acceleration of the center of mass be zero? Keep in mind that *F*1x and *F*2x represent *the components*, of the corresponding forces.

A)*F*1*x*=−*F*2*x*

B) *F*1*x*=*F*2*x*

C) *m*1=*m*2

D) *m*1≪*m*2

Part C

Consider the same system of two blocks. Now, there are two *internal* forces involved. An *internal* force *F*⃗12 is applied to block *m*1 by block *m*2 and another *internal* force *F*⃗21 is applied to block *m*2 by block *m*1 (Figure 4) . Find the *x* component of the acceleration of the center of mass (*a*cm)*x* of the system.

Express your answer in terms of the *x* components *F*12x and *F*21x of the forces, *m*1 and *m*2 .

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Intro to Center of Mass concept. You can view video lessons to learn Intro to Center of Mass. Or if you need more Intro to Center of Mass practice, you can also practice Intro to Center of Mass practice problems.