Two ice skaters stand at rest in the center of an ice rink. When they push off against one another the 45 kg skater acquires a speed of 0.71 m/s. If the speed of the other skater is 0.84 m/s, what is this skater's mass?
Momentum is converved. The momentum initial is zero, the momentum after if
skatermass*.84+45*(-.71)=0
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the interaction is equal to the total momentum after the interaction.
The momentum of an object is given by the product of its mass and velocity. Therefore, we can write the equation as:
(Mass1 * Velocity1) + (Mass2 * Velocity2) = (Mass1 * Final Velocity1) + (Mass2 * Final Velocity2)
In this case, the initial velocities are zero because both skaters are at rest. The final velocities are given as 0.71 m/s and 0.84 m/s for the skaters, respectively. The mass of the first skater is 45 kg. We need to find the mass of the second skater.
Plugging in the given values into the equation, we have:
(45 kg * 0) + (Mass2 * 0) = (45 kg * 0.71 m/s) + (Mass2 * 0.84 m/s)
Simplifying the equation, we get:
0 = 31.95 kgm/s + (Mass2 * 0.84 m/s)
Subtracting 31.95 kgm/s from both sides of the equation, we have:
-31.95 kgm/s = Mass2 * 0.84 m/s
Dividing both sides of the equation by 0.84 m/s to solve for Mass2, we get:
Mass2 = -31.95 kgm/s / 0.84 m/s
Calculating this, we find:
Mass2 ≈ 38 kg
Therefore, the mass of the second skater is approximately 38 kg.