A 2.50 kg ball strikes a wall with a velocity of 10.0 m/s to the left. The ball bounces off with a velocity of 4.5 m/s to the right. If the ball is in contact with the wall for 0.10 s, what is the constant force exerted on the ball by the wall?
N to the right
To find the constant force exerted on the ball by the wall, we can use Newton's second law of motion, which states that force is equal to the rate of change of momentum.
First, let's calculate the initial momentum of the ball before the collision. The momentum of an object is given by the product of its mass and velocity. So, the initial momentum (p_initial) can be calculated as:
p_initial = mass * velocity
Given:
mass = 2.50 kg
velocity = 10.0 m/s (to the left)
p_initial = 2.50 kg * (-10.0 m/s) (Remember, the velocity is to the left, so we use a negative sign)
Next, let's calculate the final momentum of the ball after the collision. The final momentum (p_final) can be calculated using the same formula as above, but with the final velocity:
Given:
velocity = 4.5 m/s (to the right)
p_final = 2.50 kg * (4.5 m/s)
Now, since the ball bounces off the wall, its velocity changes direction. This means the change in momentum (Δp) is equal to the difference between the initial and final momentum:
Δp = p_final - p_initial
Next, let's calculate the time duration (Δt) for which the ball is in contact with the wall:
Given:
time duration = 0.10 s
Now, we can calculate the force exerted on the ball by the wall using the formula:
force = Δp / Δt
Plugging in the values:
force = (p_final - p_initial) / time duration
force = [(2.50 kg * 4.5 m/s) - (2.50 kg * (-10.0 m/s))] / 0.10 s
Simplifying the equation will give us the answer:
force = (11.25 kg·m/s + 25.0 kg·m/s) / 0.10 s
force = 36.25 kg·m/s / 0.10 s
force = 362.5 N (to the right)
So, the constant force exerted on the ball by the wall is 362.5 N to the right.