Torque & Equilibrium Video Lessons

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# Problem: A wrench 40 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction (0, 4, -3) at the end of the wrench. Find the magnitude of the force needed to supply 90 N-m of torque to the bolt.In order to find |F|, we will have to find the angle between F and r. We can use the equationUsing the equation above, we see that the angle is as follows. (Round your answer to one decimal place.)

###### FREE Expert Solution

Torque formula is:

$\overline{){\mathbf{\tau }}{\mathbf{=}}{\mathbf{r}}{\mathbf{F}}{\mathbf{s}}{\mathbf{i}}{\mathbf{n}}{\mathbf{\theta }}}$

In this problem, we'll compute the angle between r and F from the equation:

$\overline{){\mathbf{\theta }}{\mathbf{=}}{\mathbf{c}}{\mathbf{o}}{{\mathbf{s}}}^{\mathbf{-}\mathbf{1}}{\mathbf{\left(}}\frac{\mathbf{r}\mathbf{.}\mathbf{F}}{\mathbf{|}\mathbf{r}\mathbf{|}\mathbf{|}\mathbf{F}\mathbf{|}}{\mathbf{\right)}}}$

We'll also use vector magnitude:

$\overline{){\mathbf{|}}{\mathbf{r}}{\mathbf{|}}{\mathbf{=}}\sqrt{{\mathbf{x}}^{\mathbf{2}}\mathbf{+}{\mathbf{y}}^{\mathbf{2}}\mathbf{+}{\mathbf{z}}^{\mathbf{2}}}}$

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###### Problem Details

A wrench 40 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction (0, 4, -3) at the end of the wrench. Find the magnitude of the force needed to supply 90 N-m of torque to the bolt.

In order to find |F|, we will have to find the angle between F and r. We can use the equation

Using the equation above, we see that the angle is as follows. (Round your answer to one decimal place.)

What scientific concept do you need to know in order to solve this problem?

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