Two skaters, one with mass 68 kg and the other with mass 47 kg, stand on an ice rink holding a pole of length 8.8 m and negligible mass. Starting from the ends of the pole, the skaters pull themselves along the pole until they meet. How far does the 47 kg skater move?
I thought this was just a center of mass question, but the answer I get is apparently wrong.
like 9 or somethin
To find how far the 47 kg skater moves, we can consider the conservation of momentum. Initially, the skaters and the pole together have zero momentum because they are at rest. When they start pulling themselves along the pole, they exert forces on each other. Due to the action-reaction pairs (Newton's third law), the total momentum of the system remains constant.
Let's denote the distance moved by the 47 kg skater as x. The distance moved by the 68 kg skater can be calculated as (8.8 - x) since the total distance is 8.8 meters.
According to the conservation of momentum, the initial momentum is equal to the final momentum. Initially, the skaters are at rest, so the initial momentum is zero. In the final state, when they meet, they will have a common velocity.
Now let's write the equation for the conservation of momentum:
(Initial momentum) = (Final momentum)
Since the initial momentum is zero, we only need to consider the final momentum:
0 = mass1 * velocity1 + mass2 * velocity2
Since they meet at a common velocity, we can represent the mass1 * velocity1 and mass2 * velocity2 as the common velocity (v):
0 = (68 kg * x) + (47 kg * (8.8 - x))
Now we can solve this equation to find the value of x, which represents the distance moved by the 47 kg skater.
0 = 68x + 47(8.8 - x)
0 = 68x + 411.6 - 47x
0 = 21x + 411.6
21x = -411.6
x ≈ -19.6
The negative value for x is not physically meaningful in this context, so we discard it. Therefore, the distance moved by the 47 kg skater is approximately 8.8 meters - x.
Let's calculate it:
Distance moved by the 47 kg skater = 8.8 m - x
Distance moved by the 47 kg skater = 8.8 m - (-19.6 m)
Distance moved by the 47 kg skater ≈ 28.4 m
Therefore, the 47 kg skater moves approximately 28.4 meters.