Question

a force is applied to a see - saw as shown. which one of the following statements regarding the resulting torque and rotation is true? tap to select or deselect an answer. the torque will cause a counter - clockwise rotation; its sign would be positive. the torque will cause a clockwise rotation; its sign would be positive. the torque will cause a counter - clockwise rotation; its sign would be negative. the torque will cause a clockwise rotation; its sign would be negative. because of the direction of this force, there is no torque and no rotation. check answer

Explanation:

To determine torque, we use the formula \(\tau = r \times F = rF\sin\theta\), where \(\theta\) is the angle between the position vector \(r\) (from the pivot to the force application point) and the force vector \(F\). In the see - saw diagram, the force is applied vertically downward on the right - hand side of the pivot. The position vector \(r\) is horizontal (from the pivot to the point of force application) and the force vector \(F\) is vertical. So, \(\theta = 90^{\circ}\) and \(\sin\theta=1\). Torque causes rotation: a clockwise torque (when the force tends to rotate the object clockwise) is often assigned a negative sign, and a counter - clockwise torque is assigned a positive sign. When a downward force is applied on the right of the pivot, it will tend to rotate the see - saw in the clockwise direction. By the sign convention (where clockwise torques are negative), the torque will cause a clockwise rotation and have a negative sign. The option saying there is no torque is wrong because \(\sin\theta = 1\) (not \(0\)), so torque is non - zero. The options with counter - clockwise rotation are wrong as the force on the right - hand side with a downward force causes clockwise rotation. The option with positive sign for clockwise rotation is wrong due to the sign convention.

Answer:

The torque will cause a clockwise rotation; it's sign would be negative.