Question

An inelastic collision occurs in one dimension, in which a 10 kg block traveling at 5 m/s collides with a 5 kg block traveling at 3 m/s in the same direction, and they stick together. What are the velocities of the blocks immediately after the collision?

Answer 1

The velocity of the blocks immediately after an inelastic collision, where a 10 kg block traveling at 5 m/s collides with a 5 kg block traveling at 3 m/s in the same direction, is 4.33 m/s in the same direction.

Step-by-step explanation:

To determine the velocity of the blocks immediately after an inelastic collision, we use the principle of conservation of momentum. Since the blocks stick together, their combined mass after the collision will be the sum of their individual masses, which is 10 kg + 5 kg = 15 kg. According to the conservation of momentum, the total momentum before the collision must equal the total momentum after the collision. The formula to calculate the final velocity (v') after the inelastic collision is:

m1×v1 + m2×v2 = (m1+m2)×v'

Substituting the values:

10 kg × 5 m/s + 5 kg × 3 m/s = (10 kg + 5 kg) × v'

50 kg·m/s + 15 kg·m/s = 15 kg × v'

65 kg·m/s = 15 kg × v'

v' = 65 kg·m/s / 15 kg

v' = 4.33 m/s

Therefore, the velocity of the blocks immediately after the collision is 4.33 m/s in the same direction they were initially moving.