Question

Problem 1 The force arm of a lever is 8 m long and the length of the load arm is 2 m. Calculate the force F needed to lift a 500 N load and find out the mechanical advantage of the lever.

Answer 1

Answer:

The force needed to lift a 500 newton-load is 125 newtons.

The mechanical advantage of the lever is 4.

Explanation:

Needed force is equal to the weight of the load. The Law of Lever, which is a particular case of the definition of Torque, states that force is inversely proportional to distance from fulcrum, that is:

$F_{F} \cdot r_{F} = F_{L}\cdot r_{L}$ (1)

Where:

$F_{F}$ - Needed force, in newtons.

$r_{F}$ - Force arm, in meters.

$F_{L}$ - Load force, in newtons.

$r_{L}$ - Load arm. in meters.

The mechanical advantage of the lever ($n$), no unit, is determined by following formula:

$n = \frac{F_{F}}{F_{L}}$ (2)

If we know that $F_{F} = 500\,N$, $r_{F} = 2\,m$ and $r_{L} = 8\,m$, then the load force needed to lift is:

$F_{L} = F_{F} \cdot \left(\frac{r_{F}}{r_{L}} \right)$

$F_{L} = 125\,N$

The force needed to lift a 500 newton-load is 125 newtons.

And the mechanical advantage of the lever is:

$n = 4$

The mechanical advantage of the lever is 4.