A 66.5 kg ice skater moving to the right with a velocity of 2.80 m/s throws a 0.16 kg snowball to the right with a velocity of 20.4 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 61.00 kg catches the snowball. What is the velocity of the second skater after catching the snowball in a perfectly inelastic collision?
1a Conservation of momentum.
original momentum= final momentum
I assume the ice skater was carrying snow with her.
(66.5+.16)2.80=66.5V+.16*20.4
solve for V.
b. initialmomentum= final moentum
.16*20.4=(61.16V)
solve for V
(a) To solve for the velocity of the ice skater after throwing the snowball, we can use the principle of conservation of momentum. The total momentum before throwing the snowball is equal to the total momentum after throwing the snowball. The equation for momentum is given by:
Total momentum before = Total momentum after
Let's assign variables to the known quantities:
Mass of the ice skater (m1) = 66.5 kg
Initial velocity of the ice skater (v1) = 2.80 m/s
Mass of the snowball (m2) = 0.16 kg
Velocity of the snowball (v2) = 20.4 m/s
Using the principle of conservation of momentum, we can write the equation as:
(m1 * v1) + (m2 * v2) = (m1 * V) + (m2 * V)
Substituting the known values into the equation:
(66.5 kg * 2.80 m/s) + (0.16 kg * 20.4 m/s) = (66.5 kg + 0.16 kg) * V
Simplifying:
185.7 kg*m/s + 3.264 kg*m/s = 66.66 kg * V
Combining the terms on the left side of the equation:
188.964 kg*m/s = 66.66 kg * V
Dividing both sides by 66.66 kg:
V = 188.964 kg*m/s / 66.66 kg
V ≈ 2.835 m/s
Therefore, the velocity of the ice skater after throwing the snowball is approximately 2.835 m/s to the right.
(b) In a perfectly inelastic collision, the two objects stick together and move as one.
To find the velocity of the second skater after catching the snowball, we again use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Let's assume the velocity of the second skater after the collision is V'.
Using the principle of conservation of momentum, we can write the equation as:
(m1 * V) + (m2 * V) = (m1 + m2) * V'
Substituting the known values into the equation:
(66.5 kg * 2.835 m/s) + (0.16 kg * 20.4 m/s) = (66.5 kg + 0.16 kg) * V'
Simplifying:
188.9275 kg*m/s + 3.264 kg*m/s = 66.66 kg * V'
Combining the terms on the left side of the equation:
192.1915 kg*m/s = 66.66 kg * V'
Dividing both sides by 66.66 kg:
V' = 192.1915 kg*m/s / 66.66 kg
V' ≈ 2.884 m/s
Therefore, the velocity of the second skater after catching the snowball in a perfectly inelastic collision is approximately 2.884 m/s to the right.
To solve this problem, we can use the principle of conservation of momentum. In an isolated system, the total momentum before an event is equal to the total momentum after the event.
(a) First, let's find the initial momentum of the ice skater before throwing the snowball and the momentum of the snowball:
Momentum of the ice skater = mass of the ice skater × velocity of the ice skater
= 66.5 kg × 2.80 m/s
= 185.2 kg·m/s
Momentum of the snowball = mass of the snowball × velocity of the snowball relative to the ground
= 0.16 kg × 20.4 m/s
= 3.264 kg·m/s
The total initial momentum of the system is the sum of the initial momentum of the ice skater and the snowball:
Total initial momentum = Momentum of the ice skater + Momentum of the snowball
= 185.2 kg·m/s + 3.264 kg·m/s
= 188.464 kg·m/s
Now, let's find the final momentum of the ice skater after throwing the snowball. Since there is no external force acting on the system, the total momentum after the event should be equal to the total initial momentum:
Total final momentum = Total initial momentum
Given that the snowball is thrown to the right, the final momentum of the snowball is in the positive x-direction. Therefore, the final momentum of the ice skater must be in the negative x-direction to account for the change in momentum.
Total final momentum = Momentum of the ice skater after throwing the snowball + Momentum of the snowball
= (mass of the ice skater × velocity of the ice skater after throwing) + (mass of the snowball × velocity of the snowball)
= (66.5 kg × velocity of the ice skater after throwing) + (0.16 kg × 20.4 m/s)
Setting the total final momentum equal to the total initial momentum, we can solve for the velocity of the ice skater after throwing the snowball:
188.464 kg·m/s = (66.5 kg × velocity of the ice skater after throwing) + (0.16 kg × 20.4 m/s)
Solving for velocity of the ice skater after throwing:
66.5 kg × velocity of the ice skater after throwing = 188.464 kg·m/s - (0.16 kg × 20.4 m/s)
velocity of the ice skater after throwing = (188.464 kg·m/s - (0.16 kg × 20.4 m/s)) / 66.5 kg
Now, let's calculate the value for the velocity of the ice skater after throwing.
b) To find the velocity of the second skater after catching the snowball in a perfectly inelastic collision, we can again use the principle of conservation of momentum.
Initially, the second skater is at rest, so the initial momentum of the second skater and the snowball is zero.
Since the collision is perfectly inelastic, the two skaters will stick together after the collision, and their final velocity will be the same.
Total initial momentum = Total final momentum
Momentum of the snowball = Momentum of the combined system of the two skaters
Momentum of the snowball = mass of the snowball × velocity of the snowball relative to the ground
= 0.16 kg × 20.4 m/s
= 3.264 kg·m/s
Total initial momentum = Momentum of the snowball
= 3.264 kg·m/s
Total final momentum = (mass of the first skater + mass of the second skater) × final velocity of the combined system
Let the final velocity of the combined system be "v".
Total final momentum = (66.5 kg + 61.0 kg) × v
= 127.5 kg × v
Now, we can set the total initial momentum equal to the total final momentum and solve for the final velocity of the combined system:
Total initial momentum = Total final momentum
3.264 kg·m/s = 127.5 kg × v
Solving for the final velocity of the combined system:
v = 3.264 kg·m/s / 127.5 kg
Now, let's calculate the value for the final velocity of the combined system.
Assume total momentum [of thrower + snowball in (a) and catcher plus snowball in (b)] is conserved in both cases.
The phrase "perfectly inelastic" is rather meaningless