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
Find the x coordinate x cm of the center of mass of the system.
Part B
If m 2≫ m 1, then the center of mass is located:
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to the left of m 1 at a distance much greater than x 2− x 1 |
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to the left of m 1 at a distance much less than x 2− x 1 |
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to the right of m 1 at a distance much less than x 2− x 1 |
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to the right of m 2 at a distance much greater than x 2− x 1 |
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to the right of m 2 at a distance much less than x 2− x 1 |
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to the left of m 2 at a distance much less than x 2− x 1 |
Part C
If m 2= m 1, then the center of mass is located:
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at m 1 |
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at m 2 |
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half-way between m 1 and m 2 |
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the answer depends on x 1 and x 2 |
Part D
Recall that the blocks can only move along the x axis. The x components of their velocities at a certain moment are v 1x and v 2x. Find the x component of the velocity of the center of mass ( v cm) x at that moment. Keep in mind that, in general: vx = dx / dt .
Part E
Suppose that v 1x and v 2x have equal magnitudes. Also, v 1→ is directed to the right and v 2→ is directed to the left. The velocity of the center of mass is then:
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directed to the left |
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directed to the right |
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zero |
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the answer depends on the ratio m 1 m 2 |
Part F
Assume that the x components of the blocks’ momenta at a certain moment are p 1x and p 2x. Find the x component of the velocity of the center of mass ( v cm) x at that moment.
Express your answer in terms of m 1, m 2, p 1x, and p 2x.
Part G
Suppose that v ⃗ cm=0. Which of the following must be true?
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| p 1 x |=| p 2 x | |
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| v 1 x |=| v 2 x | |
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m 1= m 2 |
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none of the above |
Part H
Assume that the blocks are accelerating, and the x components of their accelerations at a certain moment are a 1xand a 2x. Find the x component of the acceleration of the center of mass ( a cm) x at that moment. Keep in mind that, in general, ax = dvx / dt .
Part I
Consider the same system of two blocks. An external force F ⃗ is now acting on block m 1. No forces are applied to block m 2 as shown (Figure 2) . Find the x component of the acceleration of the center of mass ( a cm) x of the system.
Part J
Consider the same system of two blocks. Now, there are two forces involved. An external force F 1→ is acting on block m 1 and another external force F 2→ is acting on block m 2. (Figure 3) Find the x component of the acceleration of the center of mass ( a cm) x of the system.
Part K
Consider the previous situation. 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.
Consider the previous situation. Under what condition would the acceleration of the center of mass be zero? Keep in mind that and represent the components , of the corresponding forces.
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F 1 x =− F 2 x |
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F 1 x = F 2 x |
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m 1= m 2 |
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m 1≪ m 2 |
Part L
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.
