A 73.5 kg ice skater moving to the right with a velocity of 2.97 m/s throws a 0.21 kg snowball to the right with a velocity of 29.3 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
initial mass = 73.5 + .21
initial momentum = (73.5 + .21)(2.97)
final momentum is the same
= .21 (29.3) + 73.5 v
solve for v
solve the second part the same way
initial momentum = .21*29.3
= (.21+61.5)v
To solve these problems, we can apply the principle of conservation of momentum. The total momentum before the event (throwing the snowball) should equal the total momentum after the event.
(a) To find the velocity of the ice skater after throwing the snowball, we can calculate the initial momentum and final momentum separately and equate them.
First, let's calculate the initial momentum of the system (ice skater + snowball) before throwing the snowball. We can use the equation: momentum (p) = mass (m) x velocity (v).
Initial momentum of the ice skater = mass of the ice skater x velocity of the ice skater
= 73.5 kg x 2.97 m/s
= 218.7955 kg·m/s (rounded to 4 decimal places)
The snowball was thrown to the right, so its momentum in this direction will be positive. Hence, the initial momentum of the snowball is:
Initial momentum of the snowball = mass of the snowball x velocity of the snowball
= 0.21 kg x 29.3 m/s
= 6.153 kg·m/s (rounded to 3 decimal places)
The total initial momentum of the system (ice skater + snowball) will be the sum of the ice skater's and the snowball's momenta:
Total initial momentum = Initial momentum of the ice skater + Initial momentum of the snowball
= 218.7955 kg·m/s + 6.153 kg·m/s
= 224.9485 kg·m/s (rounded to 4 decimal places)
Now, let's consider the final momentum of the system (ice skater after throwing the snowball).
After throwing the snowball, the ice skater will have a new velocity. Let's call it "V" m/s. The momentum of the ice skater after throwing the snowball will be:
Final momentum of the ice skater = mass of the ice skater x velocity of the ice skater (after throwing the snowball)
= 73.5 kg x V m/s
= 73.5V kg·m/s
As stated earlier, the total momentum of the system should be conserved, so the total final momentum of the system should be equal to the total initial momentum:
Total final momentum = Total initial momentum
73.5V kg·m/s = 224.9485 kg·m/s
Now we can solve for V by dividing both sides of the equation by 73.5 kg:
V = 224.9485 kg·m/s / 73.5 kg
V ≈ 3.058 m/s
So, the velocity of the ice skater after throwing the snowball is approximately 3.058 m/s to the right.
(b) In a perfectly inelastic collision, the two skaters will stick together after the catch. To find the velocity of the second skater after catching the snowball, we can again apply the principle of conservation of momentum.
Using the same approach as before, let's calculate the initial and final momenta:
Initial momentum of the snowball = 0.21 kg x 29.3 m/s = 6.153 kg·m/s (same as before)
Initial momentum of the second skater = 61.50 kg x 0 m/s (since the second skater is initially at rest)
= 0 kg·m/s
The total initial momentum of the system (snowball + second skater) will be the sum of the snowball's and the second skater's momenta:
Total initial momentum = Initial momentum of the snowball + Initial momentum of the second skater
= 6.153 kg·m/s + 0 kg·m/s
= 6.153 kg·m/s
After the catch, the snowball and the second skater will move together as one entity. Let's call their combined mass "M" kg. The final momentum of the system (snowball + second skater) will be:
Final momentum of the system = Mass of the system (M) x Velocity of the system
The final momentum is 0 since the system is now at rest after the catch:
Final momentum of the system = 0 kg·m/s
According to the conservation of momentum principle, the total final momentum of the system should be equal to the total initial momentum:
Total final momentum = Total initial momentum
0 kg·m/s = 6.153 kg·m/s
The mass of the system (M) can be found by dividing both sides of the equation by the velocity of the system:
M = 6.153 kg·m/s / 0 kg·m/s
As the denominator is zero, it means that the velocity of the second skater after catching the snowball is undefined.
Therefore, the velocity of the second skater after catching the snowball in a perfectly inelastic collision cannot be determined due to the division by zero error.