an 80 kg skater and a 60 kg skater stand in the middle of an ice rink and push each other away. the 60 kg skater moves away at 2 m/s calculate her momentum and the velocity of the other skater
To calculate the momentum of the 60 kg skater, we can use the formula:
Momentum = mass × velocity
For the 60 kg skater:
Momentum = 60 kg × 2 m/s = 120 kg·m/s
Now, to find the velocity of the 80 kg skater, we can use the principle of conservation of momentum. Since there is no external force acting on the skaters, the total momentum before and after the push remains the same.
Total initial momentum = Total final momentum
Initial momentum for both skaters is 0 since they are at rest.
Final momentum = Momentum of 60 kg skater + Momentum of 80 kg skater
0 = 120 kg·m/s + (80 kg × v)
Where v is the velocity of the 80 kg skater.
Now, we can solve for v:
-120 kg·m/s = 80 kg × v
v = -120 kg·m/s ÷ 80 kg
v = -1.5 m/s
The velocity of the 80 kg skater is -1.5 m/s (negative sign indicates that it moves in the opposite direction of the 60 kg skater).
So, the momentum of the 60 kg skater is 120 kg·m/s and the velocity of the 80 kg skater is -1.5 m/s.
To calculate the momentum of the 60 kg skater, we can use the formula:
Momentum = mass × velocity
Given that the skater's mass is 60 kg and her velocity is 2 m/s, we can substitute these values into the formula:
Momentum = 60 kg × 2 m/s
= 120 kg·m/s
Therefore, the momentum of the 60 kg skater is 120 kg·m/s.
To calculate the velocity of the 80 kg skater, we can use the concept of momentum conservation. Since the two skaters are pushing each other away, the total momentum before and after the push should be the same.
Let's assume the initial velocity of the 80 kg skater is v1. The total momentum before the push is the sum of the momentum of the 60 kg skater and the momentum of the 80 kg skater, which can be written as:
Total momentum before = (60 kg × 2 m/s) + (80 kg × v1)
To find the velocity of the 80 kg skater, we can set the total momentum before to the total momentum after the push. Assuming the skaters move in opposite directions, we can write:
Total momentum before = Total momentum after
(60 kg × 2 m/s) + (80 kg × v1) = (60 kg × 2 m/s) + (80 kg × v2)
Since the final velocity of the 60 kg skater is given as 2 m/s, we can substitute this value:
(60 kg × 2 m/s) + (80 kg × v1) = (60 kg × 2 m/s) + (80 kg × (-2 m/s))
Now we can solve for v1, the velocity of the 80 kg skater:
(80 kg × v1) = (80 kg × (-2 m/s))
v1 = -2 m/s
Therefore, the velocity of the 80 kg skater is -2 m/s, indicating that the skater moves in the opposite direction with a speed of 2 m/s.
To calculate the momentum of an object, you multiply its mass by its velocity. Therefore, to find the momentum of the 60 kg skater, we can use the formula:
Momentum = Mass × Velocity
Given that the mass of the 60 kg skater is 60 kg and the velocity is 2 m/s, we can substitute these values into the formula:
Momentum = 60 kg × 2 m/s = 120 kg·m/s
So, the momentum of the 60 kg skater is 120 kg·m/s.
To find the velocity of the 80 kg skater, we can use the principle of conservation of momentum. According to this principle, in the absence of any external forces, the total momentum before and after the interaction remains constant.
Since the 60 kg skater moves away, there will be an equal but opposite change in momentum in order to satisfy the conservation of momentum. Therefore, the momentum of the 80 kg skater will be -120 kg·m/s (negative since it is in the opposite direction).
Now, we can calculate the velocity of the 80 kg skater using the formula:
Momentum = Mass × Velocity
Substituting the mass of the 80 kg skater and the momentum (-120 kg·m/s) into the formula, we have:
-120 kg·m/s = 80 kg × Velocity
Simplifying the equation, we find:
Velocity = -120 kg·m/s ÷ 80 kg = -1.5 m/s
Therefore, the velocity of the 80 kg skater is -1.5 m/s (negative to indicate the opposite direction).