To balance this lever the torques on each side of the fulcrum must be equal. Torque is weight x distance from the fulcrum so the equation for equilibrium is:

R_ad_a = R_bd_b

Solving for d_a, our missing value, and plugging in our variables yields:

d_a = \( \frac{R_bd_b}{R_a} \) = \( \frac{45 lbs. \times 7 ft.}{40 lbs.} \) = \( \frac{315 ft⋅lb}{40 lbs.} \) = 7.88 ft.

Collinear forces act along the same line of action, concurrent forces pass through a common point and coplanar forces act in a common plane.

If you apply the resistance to the axle and the effort to the wheel, the wheel and axle will multiply force and if you apply the resistance to the wheel and the effort to the axle, it will multiply speed.

The efficiency of a machine describes how much of the power put into the machine is turned into movement or force. A 100% efficient machine would turn all of the input power into output movement or force. However, no machine is 100% efficient due to friction, heat, wear and other imperfections that consume input power without delivering any output.

An inclined plane is a simple machine that reduces the force needed to raise an object to a certain height. Work equals force x distance and, by increasing the distance that the object travels, an inclined plane reduces the force necessary to raise it to a particular height. In this case, the mechanical advantage is to make the task easier. An example of an inclined plane is a ramp.