Question

Given 2 concentric wheels; what weight will an applied force FA of 40.0N down and tangent to the 18.0 cm radius wheel will balance an unknown weight tangent and down on the 10.0 cm radius wheel? Draw the situation

Answer 1

The given problem can be exemplified using the following diagram:

We will determine the magnitude of the force "F" that will balance the concentric wheels.

To do that we will add the torques produced by the forces. If the torque is counterclockwise we will set it a positive and if it is clockwise it will be negative.

`T_(40)-T_F=0`

Where:

`\begin{gathered} T_(40)=\text{ torque produced by the 40 N force} \\ T_F=\text{ torque produced by the unknown force. } \end{gathered}`

The sum of toques adds up to zero because we want to determine the force "F" when the system is in equilibrium.

Now, we substitute the formula for the torques:

`F_(40)r_(18)-Fr_(10)=0`

Where:

`\begin{gathered} r_(18)=\text{ 18 cm radius} \\ r_(10)=\text{ 10 cm radius} \end{gathered}`

Now, we solve for the force "F":

First, we will add "Fr10" to both sides:

`F_(40)r_(18)=Fr_(10)`

Now, we divide both sides by r10:

`(F_(40)r_(18))/(r_(10))=F`

Now, we plug in the values:

Solving the operations:

`72N=F`

Therefore, the required force is 72N.