Questions: Calculate the torque (magnitude and direction) about point O due to the force F in each of the situations sketched in the figure below (Figure 1). In each case, the force F and the rod both lie in the plane of the page, the rod has length 6.00 m, and the force has magnitude 7.00 N. Let counterclockwise torques be positive.

Calculate the torque (magnitude and direction) about point O due to the force F in each of the situations sketched in the figure below (Figure 1). In each case, the force F and the rod both lie in the plane of the page, the rod has length 6.00 m, and the force has magnitude 7.00 N. Let counterclockwise torques be positive.

Transcript text: Calculate the torque (magnitude and direction) about point $O$ due to the force $\overrightarrow{\boldsymbol{F}}$ in each of the situations sketched in the figure below (Figure 1). In each case, the force $\vec{F}$ and the rod both lie in the plane of the page, the rod has length 6.00 m, and the force has magnitude 7.00 N. Let counterclockwise torques be positive.

Solution

Solution Steps

Step 1: Identify the given information

The force, _F_, has a magnitude of 7.00 N. The distance from the pivot point _O_ to the point of application of the force is 2.00 m. The angle between the force vector and the lever arm is 60.0°.

Step 2: Calculate the torque

Torque (_τ_) is calculated as the cross product of the position vector (_r_) and the force vector (_F_): _τ_ = _r_ × _F_. The magnitude of the torque is given by _τ_ = _rF_sin(_θ_), where _θ_ is the angle between _r_ and _F_. In this case, _r_ = 2.00 m, _F_ = 7.00 N, and _θ_ = 60.0°. Therefore, the magnitude of the torque is:

_τ_ = (2.00 m)(7.00 N)sin(60.0°) = 14.00 N⋅m * sin(60.0°) ≈ 12.12 N⋅m

Step 3: Determine the direction of the torque

The torque is counterclockwise, which is defined as positive in this problem.