If the torque required to loosen a nut that

is holding a flat tire in place on a car has a
magnitude of 31 N · m, what minimum force
must be exerted by the mechanic at the end
of a 24 cm-long wrench to loosen the nut?
Answer in units of N

F * 0.24m = 31Nm

so
F = 31 Nm/0.24m

Ah, the age-old question of nuts and wrenches. It seems you want to know the minimum force required to loosen a nut. Well, let me calculate that for you.

Now, torque is calculated as the product of force and the lever arm (distance from the pivot point). In this case, the torque is already given as 31 N · m. The lever arm is provided as 24 cm.

To find the minimum force, we'll use the equation: torque = force × lever arm.

31 N · m = force × 24 cm.

But, being a bot, I prefer working with SI units, so let's convert that 24 cm to meters. It's equal to 0.24 m.

31 N · m = force × 0.24 m.

Now, solving for force, we get:

force = 31 N · m / 0.24 m.

Calculating that gives us the answer:

force ≈ 129.17 N.

So, the minimum force the mechanic needs to exert at the end of the wrench to loosen the nut is approximately 129.17 Newtons. Just make sure they don't accidentally launch the nut into orbit in the process!

To find the minimum force required to loosen the nut, we can use the formula for torque:

Torque = Force * Distance

Given:
Torque = 31 N · m
Wrench length = 24 cm = 0.24 m

We can rearrange the formula to solve for force:

Force = Torque / Distance

Plugging in the values:

Force = 31 N · m / 0.24 m

Calculating the force:

Force = 129.17 N

Therefore, the minimum force required to loosen the nut is approximately 129.17 N.

To find the minimum force required to loosen the nut, we can use the formula for torque:

Torque = Force x Distance

Given:
Torque = 31 N · m
Distance = 24 cm = 0.24 m

Rearranging the formula, we have:

Force = Torque / Distance

Substituting the given values:

Force = 31 N · m / 0.24 m

Now, let's calculate the minimum force:

Force = 129.17 N

Therefore, the minimum force that must be exerted by the mechanic at the end of the 24 cm-long wrench to loosen the nut is approximately 129.17 N.

1.33 N