Question

Consider a system of two blocks that have masses m1 and m2 . Assume that the blocks are point-like particles and are located along the x axis at the coordinates x1 and x2 as shown (Figure 1) . In this problem, the blocks can only move along the x axis.

Part G
Suppose that v⃗cm=0 . Which of the following must be true?
a. |p1x|=|p2x|
b. |v1x|=|v2x|
c. m1=m2
d. none of the above

Answer 1

If the center of mass velocity is 0, the momenta of the two blocks along the x-axis must be equal, but the velocities and masses of the blocks may still be different.

Step-by-step explanation:

In this problem, we have two blocks with masses m1 and m2 located along the x-axis at coordinates x1 and x2. If the center of mass velocity, vcm, is equal to 0, it means the blocks are not moving in any direction. Based on this information, we can conclude that:

a. |p1x| = |p2x|: This statement is true because if the blocks are not moving, their momenta along the x-axis should be equal.

b. |v1x| = |v2x|: This statement is not necessarily true. Although the blocks may not be moving, their individual velocities may be different.

c. m1 = m2: This statement is not necessarily true. The masses of the blocks can be different even if they are not moving.

d. None of the above: This statement is not true since statement a is correct.

Answer 2

For the system's center of mass to have zero velocity, each block must have momentum of equal magnitude but opposite direction, confirming that |p1x| = |p2x| is true.

Step-by-step explanation:

Given that the velocity of the center of mass v⟳cm is zero, we must consider the concept of momentum to answer the question. The momentum along the x-axis for a system is given by p = m × v, where p is momentum, m is mass, and v is velocity. Since the center of mass is not moving, the total momentum of the system is zero, implying the momentum of each block must be equal in magnitude but opposite in direction. Therefore, it leads us to conclude that the correct statement must be a. |p1x| = |p2x|, indicating the magnitudes of their momenta are equal.