Question

Two blocks on a horizontal frictionless track head toward each other as shown. One block has twice the mass and half the velocity of the other. What is the ratio of the kinetic energy of the lighter block to the kinetic energy of the heavier block?

1) 1:2
2) 1:4
3) 2:1
4) 4:1

Answer 1

The kinetic energy of the lighter block is four times that of the heavier block, making the ratio of their kinetic energies 4:1.

Step-by-step explanation:

The question is asking to compare the kinetic energies of two blocks on a frictionless track that have different masses and velocities. The kinetic energy (KE) can be calculated using the formula KE = 1/2 m v2, where m is the mass and v is the velocity of the object.

If one block has twice the mass (m) and half the velocity (v/2) of the other, we can compare their kinetic energies. For the heavier block, its kinetic energy is KE2 = 1/2 (2m) (v/2)2 = 1/2 mv2/2 = 1/4 mv2. For the lighter block with mass m and velocity v, the kinetic energy is KE1 = 1/2 m v2.

Therefore, the ratio of the kinetic energy of the lighter block to that of the heavier block is KE1 / KE2 = (1/2 m v2) / (1/4 mv2) = 4/1. Hence, the kinetic energy ratio is 4:1.