Question

1. if a torque of 55.0 n·m is required to turn a bolt and the largest force you can exert is 135 n, how long a lever arm must you use to turn the bolt?

Explanation:

Step1: Recall the torque formula

The formula for torque \(\tau\) is \(\tau = rF\sin\theta\). For a lever, the force is applied perpendicular to the lever arm (so \(\sin\theta = 1\)), so the formula simplifies to \(\tau = rF\), where \(r\) is the length of the lever arm (distance from the pivot), and \(F\) is the force applied. We need to solve for \(r\), so rearranging the formula gives \(r=\frac{\tau}{F}\).

Step2: Identify the given values

The torque \(\tau = 55.0\space N\cdot m\) and the force \(F = 135\space N\).

Step3: Substitute the values into the formula

Substitute \(\tau = 55.0\space N\cdot m\) and \(F = 135\space N\) into \(r=\frac{\tau}{F}\):
\[
r=\frac{55.0\space N\cdot m}{135\space N}
\]

Step4: Calculate the result

Performing the division:
\[
r\approx0.407\space m
\]

Answer:

The length of the lever arm must be approximately \(\boldsymbol{0.407\space m}\) (or more precisely, \(\frac{55}{135}=\frac{11}{27}\approx0.407\space m\)).