A billiard ball strikes and rebounds from the cushion of a pool table perpendicularly. The mass of the ball is 0.38 kg. The ball approaches the cushion with a velocity of +2.10 m/s and rebounds with a velocity of -2.00 m/s. The ball remains in contact with the cushion for a time of 3.10 × 10-3 s. What is the average net force (magnitude and direction) exerted on the ball by the cushion?
F•Δt=Δp=p2-p1=mv2-mv1=m(v2-v1),
F=m(v2-v1)/Δt =
=0.38[2.1-(-2)]/3.1•10⁻³=502.58 N.
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To find the average net force exerted on the ball by the cushion, we can use Newton's second law, which states that force equals mass multiplied by acceleration. In this case, since the direction of the force changes, we need to consider the change in momentum.
The initial momentum of the ball is given by:
p1 = m * v1 = 0.38 kg * 2.10 m/s = 0.798 kg*m/s
The final momentum of the ball is given by:
p2 = m * v2 = 0.38 kg * (-2.00 m/s) = -0.76 kg*m/s
The change in momentum is:
Δp = p2 - p1 = (-0.76 kg*m/s) - (0.798 kg*m/s) = -1.558 kg*m/s
Since the time of contact is given, we can find the average force using the formula:
F = Δp / Δt
Plugging in the values:
F = -1.558 kg*m/s / (3.10 × 10^-3 s) = -502.58 N
The magnitude of the average net force exerted on the ball by the cushion is approximately 502.58 N, and the direction is opposite to the initial velocity of the ball. So, the average net force is -502.58 N, indicating that it acts in the opposite direction to the ball's initial motion. Keep practicing your rebound skills, you never know when you might become a professional billiard player!
To find the average net force exerted on the ball by the cushion, we can use Newton's second law of motion, which states that force is equal to the change in momentum divided by the change in time.
First, we need to calculate the initial momentum of the ball before the collision with the cushion. Momentum is calculated as the product of mass and velocity, so the initial momentum (p1) is given by:
p1 = mass × velocity
= 0.38 kg × +2.10 m/s (since velocity is positive)
= 0.798 kg·m/s
Next, we calculate the final momentum of the ball after the collision with the cushion. The final velocity is in the opposite direction, so it's negative. The final momentum (p2) is given by:
p2 = mass × velocity
= 0.38 kg × (-2.00 m/s)
= -0.76 kg·m/s
The change in momentum (Δp) is given by the difference between the final and initial momenta:
Δp = p2 - p1
= -0.76 kg·m/s - 0.798 kg·m/s
= -1.558 kg·m/s
The change in time (Δt) is given as 3.10 × 10^(-3) s.
Finally, we can calculate the average net force (F) exerted on the ball using Newton's second law:
F = Δp / Δt
= (-1.558 kg·m/s) / (3.10 × 10^(-3) s)
To find the magnitude and direction of the net force, we need to determine the sign of the force. Since the velocity changes direction (from positive to negative), we know that the net force acts in the direction opposite to the initial velocity.
Now, let's calculate the average net force:
F = (-1.558 kg·m/s) / (3.10 × 10^(-3) s)
= -502.58 N
The negative sign indicates that the average net force exerted on the ball by the cushion is in the opposite direction of the initial velocity. Therefore, the magnitude of the average net force is 502.58 N, and it acts in the opposite direction of the initial velocity.
So, the answer is that the average net force exerted on the ball by the cushion is 502.58 N in the opposite direction of the initial velocity.
A billiard ball strikes and rebounds from the cushion of a pool table perpendicularly. The mass of the ball
is 0.38 kg. The ball approaches the cushion with a velocity of +2.1 m/s and rebounds with a velocity of -
2.0 m/s. The ball remains in contact with the cushion for a time of 3.3 x 10-3
s. What is the average net
force (magnitude and direction) exerted on the ball by the cushion?