Question

A fly of mass 2.00 g is sunning itself on a phonograph turntable at a location that is 4.00 cm from the center. When the turntable is turned on and rotates at 45.0 rev/min, calculate the centripetal force needed to keep the fly from slipping

Answer 1

The centripetal force needed to keep the fly from slipping is 8.013 N.

Step-by-step explanation:

To calculate the centripetal force needed to keep the fly from slipping, we can use the formula:

Fc = m * r * ω^2

Where Fc is the centripetal force, m is the mass of the fly, r is the distance from the center, and ω is the angular velocity. First, we need to convert the mass of the fly from grams to kilograms, which is 0.002 kg. The distance from the center is 0.04 m. The angular velocity (ω) can be calculated by first converting the rotational speed from rev/min to rad/s. 1 rev/min is equivalent to 2π rad/s, so the angular velocity is (45.0 rev/min) * (2π rad/1 min) = 282.743 rad/s. Now we can substitute these values into the formula: Fc = (0.002 kg) * (0.04 m) * (282.743 rad/s)^2 = 8.013 N. Therefore, the centripetal force needed to keep the fly from slipping is 8.013 N.