To calculate the average force exerted by the ball during the collision, we can use Newton's second law of motion, which states that force (F) is equal to the change in momentum (Δp) divided by the time interval (Δt):
F = Δp / Δt
The momentum (p) of an object is given by the product of its mass (m) and velocity (v):
p = m * v
First, let's calculate the initial momentum (p1) of the ball before the collision:
p1 = m * v1
where m = mass of the ball = 0.5 kg v1 = initial velocity of the ball = 12 m/s
p1 = 0.5 kg * 12 m/s p1 = 6 kg·m/s
Next, let's calculate the final momentum (p2) of the ball after the collision:
p2 = m * v2
where v2 = final velocity of the ball = 8 m/s
p2 = 0.5 kg * 8 m/s p2 = 4 kg·m/s
Now we can find the change in momentum (Δp) during the collision:
Δp = p2 - p1 Δp = 4 kg·m/s - 6 kg·m/s Δp = -2 kg·m/s
The negative sign indicates that the momentum of the ball is in the opposite direction after the collision.
Finally, we can calculate the average force (F) during the collision:
F = Δp / Δt
where Δt = time interval of the collision = 0.10 s
F = (-2 kg·m/s) / (0.10 s) F = -20 N
The negative sign indicates that the force is in the opposite direction of the initial motion. The magnitude of the average force is 20 Newtons.