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. 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?
O |p1x|=|p2x|
O |v1x|=|v2x|
O m1=m2
O none of the above

Answer 1

When the Center of Mass velocity is 0, the momentum of the first block will be equal in magnitude to the momentum of the second block. Hence, |p1x| = |p2x|.

Step-by-step explanation:

In a system where the Center of Mass velocity (vcm) is 0, the conservation of momentum principle dictates that the momentum of the first block (p1x) must be equal in magnitude to the momentum of the second block (p2x). Hence, the correct option is |p1x| = |p2x|.

Answer 2

None of the options listed are true for the equation, vcm = 0. Option D

In this system with vcm =0, Let's analyze each option, we have that;

|p1x|=|p2x|: This statement relates the magnitudes of the individual momenta (px) of the blocks.

However, knowing the center of mass velocity being zero doesn't guarantee equal magnitudes for individual momenta.

|v1x|=|v2x|: This statement relates the magnitudes of the individual velocities (vx) of the blocks. Similarly to momenta, knowing the center of mass velocity being zero doesn't guarantee equal magnitudes for individual velocities.

m1=m2: This statement relates the masses of the blocks. Knowing the center of mass velocity being zero doesn't imply anything about the individual masses. The center of mass can be at any point on the x-axis regardless of the mass ratio.

Therefore, none of the options are true for vcm = 0