# An object with a mass of 4 kg is hanging from an axle with a radius of 5 m. If the wheel attached to the axle has a radius of 15 m, how much force must be applied to the wheel to keep the object from falling?

Jan 15, 2016

Assuming that the force is applied tangentially to the circumference of the wheel.

13.3N
gravitational acceleration is taken to be 10${\text{m/s}}^{2}$

#### Explanation:

The wheel is subject to 3 force acting on it. The force by the 4kg mass, the applied counter force, and the force exerted by the support at the center of the wheel. The force exerted by the support is to prevent translational motion of the wheel. It is calculatable but not required in this question.

Now we must find the conditions to prevent rotational motion of the wheel. From Newton's second law, the wheel must experience no net torque everywhere for it to not rotate.

Consider the net torque at the center of the wheel. The force of the support does not contribute to the net torque as there is no distance. (Torque = Force x Distance). The torque by the 4kg mass is

(4"kg")(10"m/s"^2)(5"m")=200"Nm"

The torque of the applied force should also give 200Nm but in the opposite direction.

$F \left(15 m\right) = 200 N m$

$F = 13.3 N$