Question

Determine the velocity of the m₂ block just after the collision. (Use a positive sign if the motion is to the right, negative if it is to the left.)

a) Positive velocity
b) Negative velocity
c) Zero velocity
d) Cannot be determined

Answer 1

The velocity of block m2 after an elastic collision with another block of equal mass can be predicted using the conservation of momentum and kinetic energy. For equal masses, the velocities are essentially exchanged, provided it is an elastic collision. By applying these principles, the final velocity of the second block can be determined.

Step-by-step explanation:

The velocity of block m2 after the collision can be determined using the principles of conservation of momentum and, in the case of an elastic collision, the conservation of kinetic energy. When two objects of equal mass collide elastically and one object's velocity after the collision is known, the velocity of the other object can be predicted. To solve this, we set up the equation based on momentum conservation: mAvA + mBvB = mAv'A + mBv'B, where v represents the initial velocities and v' represents the final velocities. For equal masses and given the initial and final velocity of one object, we can plug these values into the equation to find the final velocity of the second object.

As an example, if mass A is initially moving at 4.0 m/s in the +x-direction and after the collision is moving at 8.0 m/s in the -x-direction, and mass B is initially moving at 8.0 m/s in the -x-direction, we can use the conservation of momentum to solve for the final velocity of mass B. Since the masses are equal and the collision is elastic, we know that the velocities will be exchanged due to the conservation of kinetic energy as well. Therefore, mass B will have a final velocity of 4.0 m/s in the +x-direction after the collision.

Answer 2

The velocity of mass B after the collision is negative velocity (Option B).

Step-by-step explanation:

The velocity of mass B after the collision can be determined using the principle of conservation of momentum. In an elastic collision, both momentum and kinetic energy are conserved.

The initial momentum of mass A is given by mA * vAi, where mA is the mass of mass A and vAi is its initial velocity. The initial momentum of mass B is given by mB * vBi, where mB is the mass of mass B and vBi is its initial velocity.

Since the collision is elastic, the final momentum of mass A is mA * vAf and the final momentum of mass B is mB * vBf. Using the principle of conservation of momentum, we can set the initial momentum equal to the final momentum:

mA * vAi + mB * vBi = mA * vAf + mB * vBf

Substituting the given values, mA = mB, vAi = 4.0 m/s, vAf = 8.0 m/s, and solving for vBf, we find that mass B will have a velocity of -4.0 m/s after the collision.

Therefore, the correct answer is b) Negative velocity.