Question

003 10.0 points if the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 47 n·m, what minimum force must be exerted by the mechanic at the end of a 20 cm - long wrench to loosen the nut? answer in units of n.

Explanation:

Step1: Recall Torque Formula

Torque ($\tau$) is given by $\tau = rF\sin\theta$. For minimum force, $\sin\theta = 1$ (when $\theta = 90^\circ$), so $\tau = rF$.

Step2: Convert Units

Convert wrench length $r$ from cm to m: $20\ \text{cm} = 0.2\ \text{m}$.

Step3: Solve for Force

Rearrange formula: $F = \frac{\tau}{r}$. Substitute $\tau = 47\ \text{N·m}$, $r = 0.2\ \text{m}$: $F = \frac{47}{0.2} = 235\ \text{N}$.

Answer:

235