A physics professor is going ice skating for the first time. She has gotten herself into the middle of an ice rink and cannot figure out how to make the skates work. Every motion she makes simply cause her feet to slip on the ice and leaves her in the same place she started. She decides that she can get off the ice by throwing both her gloves in the opposite direction. Fortunately she has brought massive insulated gloves.
a) Suppose she has mass 65.0 kg and her gloves together have mass 1.40 kg. If she throws the gloves as hard as she can away from her, they leave her hand with a speed 4.60 m/s. Will she move? (Select yes or no)
b) If yes, determine her speed.
c) If the rink is 10.7 m in diameter, and the skater starts in the centre, how long will it take her to reach the edge, assuming there is no friction at all?
Faith/Laa/Jelaa/Lyn/Davil -- please use the same name for your posts.
a) Yes, she will move. According to the principle of conservation of momentum, the total momentum before the gloves are thrown should be equal to the total momentum after they are thrown. Since the gloves are thrown in the opposite direction, the professor will experience a change in momentum that will cause her to move.
b) To determine her speed, we need to use the principle of conservation of momentum. The total initial momentum is zero (since she is at rest), and the total final momentum is given by the product of her mass (65.0 kg) and her final velocity (v). The momentum of the gloves is given by the product of their mass (1.40 kg) and their velocity (4.60 m/s). Since momentum is conserved, we can write:
0 = (65.0 kg) * v + (1.40 kg) * (4.60 m/s)
Solving for v, we have:
(65.0 kg) * v = - (1.40 kg) * (4.60 m/s)
v = - (1.40 kg) * (4.60 m/s) / (65.0 kg)
v ≈ -0.10 m/s
Therefore, her speed will be approximately -0.10 m/s (negative sign indicates movement in the opposite direction of the thrown gloves).
c) The time it takes for her to reach the edge can be determined using the equation for displacement:
s = v * t
where s is the displacement (10.7 m in this case), v is the speed (-0.10 m/s), and t is the time. Rearranging the equation to solve for time, we have:
t = s / v
Substituting the values, we get:
t = (10.7 m) / (-0.10 m/s)
t ≈ -107 s
Since time cannot be negative, this means that the professor will never reach the edge of the rink if there is no friction at all.
a) Yes, she will move. This is due to the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant if no external forces act on it. In this case, the system consists of the professor and her gloves.
Initially, before throwing the gloves, the professor and the gloves have a total momentum of zero since they are both stationary. When she throws her gloves with a speed of 4.60 m/s, the gloves acquire a positive momentum in one direction, and according to the conservation of momentum, the professor must acquire an equal but opposite momentum in order to keep the total momentum of the system at zero.
b) To determine the professor's speed, we can use the principle of conservation of momentum. The total momentum before throwing the gloves is zero, and since the gloves have a positive momentum, the professor must acquire the same magnitude of momentum in the opposite direction.
The momentum of an object is given by the product of its mass and velocity. We know the mass of the professor is 65.0 kg, and the combined mass of the gloves is 1.40 kg. The velocity of the gloves is 4.60 m/s, and since the professor will move in the opposite direction, her velocity will be negative.
Using the equation for the conservation of momentum:
0 = (65.0 kg)(-v) + (1.40 kg)(4.60 m/s)
Solving for v, we get:
v = (1.40 kg)(4.60 m/s) / 65.0 kg
c) To calculate the time it takes for the professor to reach the edge of the rink, we need to know her speed and the distance she needs to cover.
Since we have determined the professor's speed in part b, we can now use it to calculate the time it takes for her to reach the edge. The distance from the center to the edge of the rink is the radius, which is half the diameter. So, the distance is 10.7 m / 2 = 5.35 m.
We can use the equation for speed:
Speed = Distance / Time
Rearranging the equation, we get:
Time = Distance / Speed
Substituting the values into the equation, we have:
Time = 5.35 m / |v|
Since we obtained a negative velocity in part b, we need to take the absolute value to get the magnitude for the calculation.
After substituting the values, you can calculate the time it takes for the professor to reach the edge of the rink.