A 68.0 kg ice skater moving to the right with a velocity of 2.55 m/s throws a 0.16 kg snowball to the right with a velocity of 27.5 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.
(b)A second skater initially at rest with a mass of 60.50 kg catches the snowball. What is the velocity of the second skater after catching the snowball in a perfectly inelastic collision?
momentum after momentum before
sum of m after v after = sum of m before v before
.16 (27.5) + (68) v = 68.16 (2.55)
solve for v
second skater:
(60.5+.16) v = .16(27.5)
solve for second skater v
To solve this problem, we can use the law of conservation of momentum. The law states that in the absence of an external force, the total momentum of a system remains constant.
(a) To find the velocity of the ice skater after throwing the snowball, we need to calculate the momentum of the ice skater before and after the event. The formula for momentum is:
Momentum = mass * velocity
The momentum of the ice skater before throwing the snowball is:
Initial momentum of ice skater = mass of ice skater * initial velocity of ice skater
Initial momentum of ice skater = 68.0 kg * 2.55 m/s
Now, let's calculate the momentum of the snowball:
Momentum of snowball = mass of snowball * velocity of snowball
Momentum of snowball = 0.16 kg * 27.5 m/s
According to the law of conservation of momentum, the total momentum before and after the event remains the same. Therefore, the momentum of the ice skater and the snowball before throwing should be equal to the momentum of the ice skater after throwing.
Final momentum of ice skater = Initial momentum of ice skater + Momentum of snowball
Final momentum of ice skater = (68.0 kg * 2.55 m/s) + (0.16 kg * 27.5 m/s)
Now, we can calculate the final velocity of the ice skater by dividing the final momentum by the mass of the ice skater:
Final velocity of ice skater = Final momentum of ice skater / mass of ice skater
(b) To find the velocity of the second skater after catching the snowball in a perfectly inelastic collision, we can use the principle of conservation of momentum again. In an inelastic collision, the two objects stick together after the collision.
The total momentum of the system before the collision is equal to the total momentum after the collision.
Momentum before collision = Momentum after collision
The initial momentum before the collision is:
Initial momentum before collision = (mass of ice skater + mass of snowball) * (initial velocity of ice skater)
The final momentum after the collision is:
Final momentum after collision = (mass of ice skater + mass of snowball + mass of the second skater) * (final velocity of the second skater)
Setting up the equation:
(mass of ice skater + mass of snowball) * (initial velocity of ice skater) = (mass of ice skater + mass of snowball + mass of second skater) * (final velocity of the second skater)
Now, we can solve for the final velocity of the second skater:
Final velocity of the second skater = [(mass of ice skater + mass of snowball) * (initial velocity of ice skater)] / (mass of ice skater + mass of snowball + mass of second skater)
Substituting the given values into the equation will give us the final answer for both parts (a) and (b).