Question

Suppose you lived in a pre-industrial society and needed to lift a heavy (20 kg) block a height of 5 m and had two choices for how to accomplish your task: You could use a lever with a short arm of 1 m and a long arm of 10 m. You'd place the block on the end of the short arm and apply force at the very end of the long arm. You could use a ramp with a length of 8 m and place the block on a cart with wheels. Which choice would you make? Be sure to discuss differences between the effort force of the two options in your answer.

Answer 1

Let's break the question into two parts:

1) The force needed in Ramp scenario.
2) The effort force needed in the lever scenario.

1. Ramp Scenario: 
In an incline, the only component of cart's weight(mg) that is in the direction of motion is $mgsin \alpha$. Therefore the effort force in this case must be equal or greater than $mgsin \alpha$.

Now we need to find $\alpha$. $\alpha$ is the angle between the incline of the ramp and the ground. 

Since the height is 5m and the length of the ramp is 8m, $sin \alpha$ would be 5/8 or 0.625. Now that you have $sin \alpha$, mutiple it with mg.

=> m*g*$sin \alpha$  = 20 * 10 * 5 / 8. (Taking g = 10 m/s² for simplicity) = 125N
Therefore, the minimum Effort force you would require in this case is 125N.

2. Lever Scenario:
Just apply "moment action" in this case, which is:
$F_{e} d_{e} = F_{r} d_{r}$

$F_{e}$ = ?

$F_{r}$ = mg = 20 * 10 = 200N
$d_{e}$ = 10m
$d_{r}$ = 1m


Plug-in the values in the above equation:
$F_{e}$ = 200/10= 20N


As 20N << 125N, the best choice is to use lever.