Two ice skaters stand at rest in the center of an ice rink. When they push off against one another the 61-kg skater acquires a speed of 0.63 m/s.
If the speed of the other skater is 0.86 m/s, what is this skater's mass?
conserve momentum:
.86m = .63*61
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the skaters push off against each other is equal to the total momentum after they push off.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Before the skaters push off, they are at rest, so their initial momentum is zero. After the push, the 61-kg skater acquires a speed of 0.63 m/s, and the other skater has a speed of 0.86 m/s.
Let's assume the mass of the other skater is m kg. Now we can set up the equation:
(61 kg × 0) + (m kg × 0) = (61 kg × 0.63 m/s) + (m kg × 0.86 m/s)
Simplifying the equation:
0 = 38.43 kg·m/s + 0.86 m/s × m kg
0 = 38.43 kg·m/s + 0.86 m·kg/s × m
Now we can solve this quadratic equation to determine the mass of the other skater.