Questions: Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

Transcript text: Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

Solution

Solution Steps

Step 1: Formula for Torque

The torque (τ) exerted by a force (F) about an axis is given by τ = rFsinθ, where 'r' is the distance from the axis to the point where the force is applied, and 'θ' is the angle between the force vector and the vector pointing from the axis to the application point.

Step 2: Analyzing the scenarios

Since all cylinders are identical and forces have the same magnitude, maximizing torque depends on maximizing 'r' and 'sin θ'. 'r' is maximized when the force is applied at the edge of the cylinder, which is true for all scenarios. 'sin θ' is maximized when θ = 90°, meaning the force is perpendicular to the radius vector.

Step 3: Identifying the maximum torque

Options 'c' and 'e' maximize both 'r' and 'sin θ', as the force is applied tangentially at the edge. Options 'a' and 'e' have θ less than 90°, thus producing a smaller torque. Option 'b' has θ = 0° meaning sin θ is zero. Hence no torque will be generated. Option 'd' has also θ = 0° meaning sin θ is zero. Hence no torque will be generated.

Final Answer:

The forces in 'c' and 'e' exert the biggest torque.

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