Question

A wrench 30cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction <0, 3, -4> at the end of the wrench. Find the magnitude of the force needed to supply 100 N m of torque to the bolt.

Answer 1

@dumbsearch2

Answer 2

Hello! Have you made any progress working this out on your own, @raffle_snaffle ?

The formula for torque is \(\vec\tau=\vec r\times\vec F\)

\(\vec r\) is the radius from the pivot. Your radius is \(30\ [cm]\), and in the positive \(y\) direction.

Now, \(\left|\left|\vec F\right|\right|=100\ [N]\). Note that they give you the direction separately. You'll want to turn it into a unit vector!

To turn a vector into a unit vector, do this!
\(\overrightarrow{a_u}=\dfrac{\vec a}{\left|\left|\vec a\right|\right|}\), where \(\left|\left|\vec a\right|\right|=\sqrt{a_x^2+a_y^2+a_z^2}\), like Pythagorean Theorem.

Notice that \(\vec F= \left|\left|\vec F\right|\right|\ \ \ \overrightarrow{F_u}\).

There you have it! If you're unfamiliar with the cross product, there are many sites that explain it!

If you have problems or this is not a proper way to solve the problem for you class, let me know! We can work on getting it proper together.