Two ice skaters of equal mass grab hands and spin in a circle once every four seconds. their arms are 0.76 m and they each have mass of 55.0 kg. how hard are they pulling on one another?
To find out the force with which the ice skaters are pulling on each other, we can use the concept of centripetal force.
The centripetal force (F) is given by the equation:
F = (m * v²) / r
Where:
m = mass of the ice skaters (since they have equal mass, we can use either value)
v = velocity of the ice skaters, which can be calculated by dividing the circumference of their circular path by the time taken to complete one revolution
r = radius of the circular path, which is equal to the length of their arms
Let's calculate step-by-step:
1. Calculate the velocity (v):
The circumference of the circular path is equal to the length of the circular path they travel in one revolution. It can be calculated using the formula:
Circumference = 2 * π * r
Given that the radius is equal to the length of their arms (0.76 m), we can substitute this value into the equation:
Circumference = 2 * π * 0.76
2. Calculate the time taken per revolution (T):
Given that they complete one revolution every 4 seconds, the time taken to complete one revolution is:
T = 4 seconds
3. Calculate the velocity (v):
The velocity of the ice skaters can be calculated by dividing the circumference by the time taken:
v = Circumference / T
4. Calculate the centripetal force (F):
Now we can substitute the given mass (55.0 kg), the calculated velocity (v), and the radius (0.76 m) into the equation for centripetal force:
F = (m * v²) / r
Substitute the values and calculate F.
By following these steps, you can determine the force with which the ice skaters are pulling on each other.
To determine how hard the ice skaters are pulling on one another, we need to calculate the centripetal force acting on them. Centripetal force is the force that keeps an object moving in a circular path.
To calculate the centripetal force, we need to use the following formula:
F = m * (v^2 / r)
Where:
F is the centripetal force
m is the mass of one of the ice skaters
v is the linear velocity of the skaters
r is the radius of the circular path
First, let's calculate the linear velocity of the skaters. Since they are completing one full rotation every four seconds, we can determine their angular velocity using the formula:
ω = 2π / T
Where:
ω is the angular velocity
T is the time for one revolution (4 seconds in this case)
Plugging in the values:
ω = 2π / 4
ω ≈ 1.57 rad/s
Now, to convert the angular velocity to linear velocity, we can use the formula:
v = r * ω
Given that their arms have a length of 0.76 m, the radius (r) is half of that:
r = 0.76 / 2
r = 0.38 m
Plugging in the values:
v = 0.38 * 1.57
v ≈ 0.5966 m/s
Now that we have the linear velocity, we can calculate the centripetal force:
F = 55.0 * (0.5966^2 / 0.38)
F ≈ 86.05 N
Therefore, the ice skaters are pulling on each other with a force of approximately 86.05 Newtons.