Question

A collision occurs between a 4 g projectile and a 4 kg block, which changes the block's velocity by 7 m/s. Determine the impulse of the collision on the projectile in N s.

Answer 1

The impulse of the collision on the 4 g projectile is -28 N·s. This is calculated using the change in momentum of the block (4 kg with a velocity change of 7 m/s), and by Newton's third law, this impulse is equal and opposite for the projectile.

Step-by-step explanation:

To determine the impulse of the collision on the projectile, we must first understand that impulse is equal to the change in momentum of an object. The momentum change of the block is given by the mass of the block multiplied by the change in velocity (Δv), which we know is 7 m/s. The formula for impulse (ℒ) is ℒ = m × Δv, where m is mass and Δv is the change in velocity.

First, we calculate the change in momentum for the block:

• Mass of the block (m) = 4 kg
• Change in velocity (Δv) = 7 m/s
• Change in momentum for the block (Δp_block) = m × Δv = 4 kg × 7 m/s = 28 kg·m/s

According to Newton's third law, the impulse exerted on the block is equal and opposite to the impulse exerted on the projectile. Hence, the impulse on the projectile is -28 kg·m/s (negative indicating opposite direction).

After converting the projectile mass to kilogram to match units (0.004 kg), the impulse on the projectile is:

• ℒ = -28 N·s