Please help. A person with mass 60kg is sitting on a Ferris wheel at a distance of 10m from the center. If the person experiences a constant force of 600N on them as they go around, what is the period of the motion?
To find the period of the motion, we need to use the formula for the centripetal force acting on an object moving in a circle.
The formula for centripetal force is Fc = (m * v^2) / r, where Fc is the centripetal force, m is the mass of the object, v is the velocity, and r is the radius of the circle.
In this case, we are given the force (600N), the mass of the person (60kg), and the radius (10m). We can rearrange the formula to solve for the velocity.
Fc = (m * v^2) / r
v^2 = (Fc * r) / m
v = √((Fc * r) / m)
Substituting the given values, we get:
v = √((600N * 10m) / 60kg)
v = √(100m^2/s^2)
v = 10m/s
Now, we can find the period using the formula for the period of an object moving in a circle.
The formula for the period is T = (2π * r) / v, where T is the period, r is the radius, and v is the velocity.
Substituting the given values, we get:
T = (2π * 10m) / 10m/s
T = 2πs
Therefore, the period of the motion is 2π seconds.