Question

Two objects of mass m move in opposite directions toward each other. The green object moves at velocity , and the blue object moves at velocity 2. Which diagram correctly shows the direction and velocity for each of the objects after an elastic collision?

(A) A diagram of two blocks. The block on the left is labeled m with a velocity vector to the left, labeled . The block on the right is labeled m with a velocity vector to the left, labeled 2.

(B) A diagram of two blocks. The block on the left is labeled m with a velocity vector to the right, labeled 2. The block on the right is labeled m with a velocity vector to the right, labeled 2.

(C) A diagram of two blocks. The block on the left is labeled m with a velocity vector to the left, labeled 2. The block on the right is labeled m with a velocity vector to the right, labeled .

Answer 1

An elastic collision between two objects of equal mass results in the conservation of both momentum and kinetic energy. By applying these conservation laws, the velocities of the objects after the collision can be predicted. The momentum and kinetic energy before the collision equal the momentum and kinetic energy after the collision, respectively.

Step-by-step explanation:

When two objects of equal mass collide elastically, both the principle of conservation of momentum and conservation of kinetic energy apply. In an elastic collision, total momentum and total kinetic energy before and after the collision are conserved.

For example, if two cars of equal mass collide elastically and one car is initially moving faster than the other, after the collision, they will exchange velocities. The car that was moving faster will now move at the initial velocity of the slower one, and vice versa.

Using Conservation of Momentum

Momentum is the product of mass and velocity. Before the collision, the total momentum is the sum of the momentums of both objects. After an elastic collision, that total momentum must be the same. So, if mass A is now moving in the opposite direction with a new velocity, we can calculate the new velocity of mass B by setting the initial total momentum equal to the final total momentum.

Using Conservation of Kinetic Energy

Similarly, kinetic energy is ½ mass times the velocity squared. By setting the initial kinetic energy equal to the final kinetic energy, we can solve for the unknown velocity of one of the masses after the collision, given that the collision is elastic.