To balance this lever the torques at the green box and the blue arrow 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_b, our missing value, and plugging in our variables yields:

d_b = \( \frac{R_ad_a}{R_b} \) = \( \frac{70 lbs. \times 1 ft.}{75 lbs.} \) = \( \frac{70 ft⋅lb}{75 lbs.} \) = 0.93 ft.

Power is the rate at which work is done, P = w/t, or work per unit time. The watt (W) is the unit for power and is equal to 1 joule (or newton-meter) per second. Horsepower (hp) is another familiar unit of power used primarily for rating internal combustion engines. 1 hp equals 746 watts.

W_in = W_out
F_effort x d_effort = F_resistance x d_resistance

In this problem, the effort work is 200 ft⋅lb and the resistance force is 50 lbs. and we need to calculate the resistance distance:

W_in = F_resistance x d_resistance
200 ft⋅lb = 50 lbs. x d_resistance
d_resistance = \( \frac{200ft⋅lb}{50 lbs.} \) = 4 ft.

The mechanical advantage of a wheel and axle is the input radius divided by the output radius:

MA = \( \frac{r_i}{r_o} \)

In this case, the input radius (where the effort force is being applied) is 8 and the output radius (where the resistance is being applied) is 3 for a mechanical advantage of \( \frac{8}{3} \) = 2.67

MA = \( \frac{load}{effort} \) so effort = \( \frac{load}{MA} \) = \( \frac{90 lbs.}{2.67} \) = 33.71 lbs.

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.