Answer :
To determine the outcome of the collision between the bowling ball and the pin, we need to consider the conservation of momentum.
The momentum of an object is given by the product of its mass and velocity. The initial momentum of the bowling ball can be calculated as:
Initial momentum of the bowling ball = mass of the bowling ball × initial velocity of the bowling ball
= 5.0 kg × 6.0 m/s
= 30 kg·m/s
The momentum of the pin before the collision is negligible compared to the momentum of the bowling ball.
During the collision, momentum is conserved. Therefore, the total momentum after the collision will be equal to the initial momentum of the bowling ball.
Let's assume the final velocity of the bowling ball and the pin together is v. The momentum after the collision can be calculated as:
Momentum after the collision = (mass of the bowling ball + mass of the pin) × final velocity
Since the mass of the pin is given in grams, we need to convert it to kilograms:
mass of the pin = 1.64 g = 1.64 × 10^(-3) kg
Now, we can equate the initial momentum and the momentum after the collision:
30 kg·m/s = (5.0 kg + 1.64 × 10^(-3) kg) × v
Simplifying the equation:
30 kg·m/s = (5.0 kg) × v + (1.64 × 10^(-3) kg) × v
Now we can solve for the final velocity (v):
v = 30 kg·m/s / (5.0 kg + 1.64 × 10^(-3) kg)
Calculating the final velocity:
v ≈ 5.996 m/s
Therefore, the final velocity of the bowling ball and the pin together after the collision is approximately 5.996 m/s.
The momentum of an object is given by the product of its mass and velocity. The initial momentum of the bowling ball can be calculated as:
Initial momentum of the bowling ball = mass of the bowling ball × initial velocity of the bowling ball
= 5.0 kg × 6.0 m/s
= 30 kg·m/s
The momentum of the pin before the collision is negligible compared to the momentum of the bowling ball.
During the collision, momentum is conserved. Therefore, the total momentum after the collision will be equal to the initial momentum of the bowling ball.
Let's assume the final velocity of the bowling ball and the pin together is v. The momentum after the collision can be calculated as:
Momentum after the collision = (mass of the bowling ball + mass of the pin) × final velocity
Since the mass of the pin is given in grams, we need to convert it to kilograms:
mass of the pin = 1.64 g = 1.64 × 10^(-3) kg
Now, we can equate the initial momentum and the momentum after the collision:
30 kg·m/s = (5.0 kg + 1.64 × 10^(-3) kg) × v
Simplifying the equation:
30 kg·m/s = (5.0 kg) × v + (1.64 × 10^(-3) kg) × v
Now we can solve for the final velocity (v):
v = 30 kg·m/s / (5.0 kg + 1.64 × 10^(-3) kg)
Calculating the final velocity:
v ≈ 5.996 m/s
Therefore, the final velocity of the bowling ball and the pin together after the collision is approximately 5.996 m/s.
