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 0.60 m/s.If the speed of the other skater is 0.90 m/s, what is this skater's mass?
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To solve this problem, we can use the concept of conservation of momentum. According to this principle, the total momentum of a system remains constant if there are no external forces acting on it.
The momentum of an object is calculated by multiplying its mass by its velocity (p = mv). In this case, we have two ice skaters, and the total momentum before they push off against each other is zero since they are both at rest. After they push off, the total momentum should still be zero, but now they have acquired individual velocities.
Let's assume the mass of the second skater (with a velocity of 0.90 m/s) is m. The mass of the first skater is given as 61 kg, and the velocity acquired is 0.60 m/s.
Using the conservation of momentum, we can write the equation:
(61 kg) * (0.60 m/s) + m * (0.90 m/s) = 0
Simplifying the equation:
36.6 kg⋅m/s + 0.9m = 0
Subtracting 0.9m from both sides:
36.6 kg⋅m/s = -0.9m
Dividing both sides by -0.9:
m = -(36.6 kg⋅m/s) / (0.9 m/s)
Calculating this:
m ≈ -40.7 kg
Since mass cannot be negative, we discard this negative value. Hence, the mass of the second skater is approximately 40.7 kg.