Torque and force on a tire iron

The torque you apply to the tire iron is applied to the nut as forces in multiple different places around the circumference of the nut. Because these individual forces are in different directions, the bulk of the forces can cancel out, leaving just a net 10 pounds of force being applied to the nut. The individual torques, on the other hand, are all applied in the same direction (the direction that causes counter-clockwise motion, for instance) and so they just add up. By increasing all the individual forces, the increased forces for each piece cancel out, but the increased torques do not, and so you can have increasing torque without increasing the net weight applied to the car.

To make the analysis easier assume that your wheel is held on with a central nut as shown in the diagram below ie like an old Rolls Royce or an F1 car.

Without the tire iron the car is in equilibrium and so the net force on it is zero

$N_{rm b} + N_{rm f} - mg = 0$

as is the net torque about $A$

$N_{rm b} b = mga = 0$.

Now consider what happens when you apply a force $F$ on your tire iron with the nut firmly in position.

$(N_{rm b} + N_{rm f} - mg - F= 0$

which means that the sum of the normal reactions will increase.
So it the car was being weighed on a weighing machine its weight would appear to have increased.

$N_{rm b} b + Fc = mga = 0$.

Which will mean that $N_{rm b}$ will decrease and $N_{rm a}$ will increase and there is a possibility?? that if you make distance $c$ and/or force $F$ large enough $N_{rm b}$ will become zero and you will lift the back of the car off the ground.

If it is not a central nut then the ideas that I have presented are still the same but the analysis is just a little more complex.

Torque is best defined as the work per unit angle of rotation which can be done by a force acting in a manner which tends to cause a rotation. With a longer lever arm, your applied force moves through a greater distance and can do more work on the nut or bolt for the same amount of rotation.