A 67.0 kg ice skater moving to the right with a velocity of 2.02 m/s throws a 0.12 kg snowball to the right with a velocity of 21.5 m/s relative to the ground.
(a) What is the velocity of the ice skater after throwing the snowball? Disregard the friction between the skates and the ice.
m/s to the right
(b) A second skater initially at rest with a mass of 61.50 kg catches the snowball. What is the velocity of the second skater after catching the snowball in a perfectly inelastic collision?
m/s to the right
To solve this problem, we can apply the principle of conservation of momentum. The total momentum before the snowball is thrown is equal to the total momentum after it is caught.
(a) The initial momentum of the system is given by the equation:
Initial momentum = (mass of the ice skater) × (velocity of the ice skater)
Plugging in the given values, we have:
Initial momentum = (67.0 kg) × (2.02 m/s) = 135.34 kg·m/s to the right
The momentum of the snowball is given by the equation:
Momentum of snowball = (mass of snowball) × (velocity of snowball)
Plugging in the given values, we have:
Momentum of snowball = (0.12 kg) × (21.5 m/s) = 2.58 kg·m/s to the right
Since the ice skater throws the snowball to the right, the direction of both the skater and the snowball is the same.
Therefore, the momentum after the snowball is thrown is:
Final momentum = Initial momentum + Momentum of snowball
Final momentum = 135.34 kg·m/s + 2.58 kg·m/s = 137.92 kg·m/s to the right
The final velocity of the ice skater after throwing the snowball is equal to the final momentum divided by the mass of the ice skater:
Final velocity = Final momentum / (mass of the ice skater)
Plugging in the values, we have:
Final velocity = 137.92 kg·m/s / 67.0 kg ≈ 2.06 m/s to the right
(b) In a perfectly inelastic collision, the snowball and the second skater stick together and move as one entity after the collision. Thus, the final velocity of the second skater will be the same as the ice skater's final velocity, which is 2.06 m/s to the right.
To solve this problem, we can apply the law of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event.
(a) The initial momentum of the ice skater is given by the product of their mass and velocity:
Initial momentum = (mass of ice skater) x (velocity of ice skater)
Initial momentum = (67.0 kg) x (2.02 m/s)
The momentum of the snowball can be calculated using the same formula:
Momentum of snowball = (mass of snowball) x (velocity of snowball)
Momentum of snowball = (0.12 kg) x (21.5 m/s)
Since the snowball is thrown in the same direction as the skater's initial motion, the final momentum of the ice skater will be the sum of the initial momentum of the ice skater and the momentum of the snowball:
Final momentum of ice skater = Initial momentum of ice skater + Momentum of snowball
Calculate the final momentum of the ice skater:
Final momentum of ice skater = (67.0 kg x 2.02 m/s) + (0.12 kg x 21.5 m/s)
(b) In a perfectly inelastic collision, the two skaters will stick together after the collision. Therefore, their final velocity will depend on the conservation of momentum.
The initial momentum of the second skater at rest is zero since initial velocity is zero. The final momentum of the combined system will be the sum of the initial momentum of the second skater and the momentum of the snowball.
Final momentum of the combined system = Initial momentum of the second skater + Momentum of snowball
To find the final velocity of the second skater, divide the final momentum of the combined system by the mass of the second skater:
Final velocity of the second skater = Final momentum / (mass of the second skater)
Calculate the final velocity of the second skater using:
Final velocity of the second skater = (initial momentum of second skater + momentum of snowball) / (mass of second skater)
Remember that momentum is a vector quantity, so the final velocity will have the same direction as the snowball.