Question

Figure 10-25ais an overhead view of a horizontal bar that can pivot; two horizontal forces act on the bar, but it is stationary. If the angle between the bar and ${\overrightarrow{\mathbf{F}}}_{\mathbf{2}}$is now decreased from ${\mathbf{90}}^{\mathbf{°}}$and the bar is still not to turn, should ${\overrightarrow{\mathbf{F}}}_{\mathbf{2}}$be made larger, made smaller, or left the same?

Short answer

The force ${\mathrm{F}}_2$ will increase.

Step-by-step solution

Step 1: Given information

The diagram showing an overhead view of a horizontal bar

Understanding the concept

The effect of the decrease in angle on torque from the formula can be predicted. Then to keep it constant, find the force acting on it ${\mathbf{F}}_{\mathbf{2}}$

Formulae are as follows:

$$\begin{gathered} \mathrm{\tau }=\mathrm{r}\times \mathrm{F} \\ =\mathrm{rF}\sin \mathrm{\varphi } \end{gathered}$$

Where, r is radius, F is force and $\tau$ is torque.

Determining the change in force F2  to make the bar stationary:

$$\begin{gathered} \mathrm{\tau }=\mathrm{r}\times \mathrm{F} \\ =\mathrm{rF}\sin \mathrm{\varphi } \end{gathered}$$

From the formula for torque, it can be concluded that if the angle is decreased, the corresponding torque will decrease. To keep it constant, so asthebar should not be turned, the force${\mathrm{F}}_2$must be increased.

Therefore, to keep an object non-rotating, the torque acting on it should be constant.