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?
if the ice skate was skating with the snowball initially, then
initial momentum=final momentum
68*2.55+.16*2.55=68*vf+.16*27.5
solve for vf.
b.initial monetum=final momentum
60.50*0+.16*27.5=(60.50+.16)Vf
solve for vf
Thanks!
I am having trouble rearranging the formula. Could you please try to explain it to me?
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as there are no external forces acting on the system.
(a) To find the velocity of the ice skater after throwing the snowball, we need to consider the initial momentum and final momentum of the system. The initial momentum is given by the formula:
Initial Momentum = Mass × Initial Velocity
For the ice skater, the initial momentum is:
Initial Momentum (ice skater) = Mass (ice skater) × Initial Velocity (ice skater)
= 68.0 kg × 2.55 m/s
The snowball has a mass of 0.16 kg, and its initial velocity relative to the ground is 27.5 m/s. So, the initial momentum of the snowball is:
Initial Momentum (snowball) = Mass (snowball) × Initial Velocity (snowball)
= 0.16 kg × 27.5 m/s
Now, to find the final momentum of the system, we need to add the initial momenta of the ice skater and the snowball since they move in the same direction. Thus,
Final Momentum (system) = Initial Momentum (ice skater) + Initial Momentum (snowball)
The final momentum of the system is simply the mass of the ice skater (68.0 kg) multiplied by the final velocity of the ice skater (let's call it V):
Final Momentum (system) = Mass (ice skater) × Final Velocity (ice skater)
Now, using the conservation of momentum principle, we have:
Initial Momentum (ice skater) + Initial Momentum (snowball) = Final Momentum (system)
68.0 kg × 2.55 m/s + 0.16 kg × 27.5 m/s = 68.0 kg × V
Simplifying and solving for V:
V = (68.0 kg × 2.55 m/s + 0.16 kg × 27.5 m/s) / 68.0 kg
Now, calculate the value for V to find the velocity of the ice skater after throwing the snowball.
(b) Now, let's consider the second skater who catches the snowball. Since this is a perfectly inelastic collision, the two skaters stick together after the collision. Therefore, their final velocity is the same.
Using the principle of conservation of momentum, we can set up the equation:
Initial Momentum (snowball) + Initial Momentum (second skater) = Final Momentum (system)
The initial momentum of the second skater is given by:
Initial Momentum (second skater) = Mass (second skater) × Initial Velocity (second skater)
Since the second skater is initially at rest, the initial velocity is 0 m/s. So,
Initial Momentum (second skater) = 60.50 kg × 0 m/s = 0 kg·m/s
After the collision, the second skater and the snowball move at the same final velocity. So, the final momentum of the system is:
Final Momentum (system) = (Mass (snowball) + Mass (second skater)) × Final Velocity (final system)
Using the conservation of momentum principle:
Initial Momentum (snowball) + Initial Momentum (second skater) = Final Momentum (system)
0.16 kg × 27.5 m/s + 60.50 kg × 0 m/s = (0.16 kg + 60.50 kg) × Final Velocity (final system)
Simplifying and solving for Final Velocity (final system), we can find the velocity of the second skater after catching the snowball in a perfectly inelastic collision.
Please perform the calculations to find the answers for parts (a) and (b).