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 +2.30 m/s and rebounds with a velocity of -1.90 m/s. The ball remains in contact with the cushion for a time of 3.00 × 10-3 s. What is the average net force (magnitude and direction) exerted on the ball by the cushion?

Well, it seems like the cushion decided to be a bit of a "rebound relationship" for the billiard ball. Let's see if we can calculate the average net force involved.

To calculate the average net force exerted on the ball by the cushion, we can use Newton's second law, which states that the force equals the change in momentum divided by the time interval.

The change in momentum of the ball can be calculated by subtracting its initial momentum from its final momentum. The initial momentum is the product of the mass and velocity of the ball (0.38 kg × 2.30 m/s), and the final momentum is the product of the mass and velocity after rebounding (-1.90 m/s).

The change in momentum is calculated as: Δp = (0.38 kg × -1.90 m/s) - (0.38 kg × 2.30 m/s).

Now, we divide the change in momentum by the time interval of 3.00 × 10-3 s to get the average net force: F = Δp / Δt.

However, before we proceed with the calculations, it's important to note that we need to take the negative sign into account for the final force because we're considering it as the direction of the cushion.

So, after plugging in the numbers and doing the math, the average net force exerted on the ball by the cushion is approximately -222.42 N.

In simpler terms, the cushion pushed back on the ball with an average force of approximately 222.42 Newtons in the opposite direction during the contact.

Remember, this is just a calculation using the given information. In reality, the actual force might vary depending on various factors like the elasticity of the ball and the cushion.

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 the net force acting on an object is equal to the rate of change of its momentum.

1. Calculate the momentum of the ball before and after the collision:
Momentum before collision = mass × velocity = 0.38 kg × 2.30 m/s = 0.874 kg·m/s (in the positive direction)
Momentum after collision = mass × velocity = 0.38 kg × (-1.90 m/s) = -0.722 kg·m/s (in the negative direction)

2. Calculate the change in momentum:
Change in momentum = Momentum after collision - Momentum before collision
= -0.722 kg·m/s - 0.874 kg·m/s
= -1.596 kg·m/s

3. Use the equation for average net force:
Average net force = Change in momentum / Time
= -1.596 kg·m/s / (3.00 × 10-3 s)
= -532 N (Note: negative sign indicates the force is in the opposite direction of the initial velocity)

Therefore, the average net force exerted on the ball by the cushion is 532 N in the direction opposite to the initial velocity.

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 the net force acting on an object is equal to the product of its mass and acceleration.

First, let's find the change in velocity of the ball during the collision with the cushion. The initial velocity of the ball is +2.30 m/s, and the final velocity after rebounding is -1.90 m/s. The change in velocity can be found by subtracting the initial velocity from the final velocity:

Change in velocity = Final velocity - Initial velocity
= (-1.90 m/s) - (+2.30 m/s)
= -4.20 m/s

Next, we can calculate the acceleration of the ball using the equation:

Acceleration = Change in velocity / Time
= (-4.20 m/s) / (3.00 × 10^-3 s)
= -1400 m/s²

Since the velocity of the ball changes in the opposite direction (+ to -), the acceleration has a negative sign.

Now, we can find the average net force using Newton's second law:

Net force = Mass × Acceleration
= 0.38 kg × (-1400 m/s²)
= -532 N

The magnitude of the average net force exerted on the ball by the cushion is 532 N, and the direction is opposite to the motion of the ball.

F=ma=mΔv/Δt=m[v₂-v₁]/Δt=

=0.38•[-1.9-2.3]/3•10⁻³ = - 532 N
( direction: from the wall)