Question

A machine has a velocity ratio of 6 and is 80% efficient. What effort would be needed to lift a load of 300N with the aid of the machine?

Answer 1

First, we need to determine the ideal mechanical advantage (IMA) of the machine, which is calculated using the velocity ratio formula:

IMA = output distance ÷ input distance

Since this formula is not given, we can use the definition of velocity ratio:

velocity ratio = output velocity ÷ input velocity

and substitute output distance for output velocity and input distance for input velocity.

velocity ratio = output distance ÷ input distance

6 = output distance ÷ input distance

Therefore, the IMA of the machine is 6.

Next, we can use the efficiency formula:

efficiency = (output work ÷ input work) x 100%

Rearranging the formula:

output work = (efficiency ÷ 100%) x input work

We know that the input work is equal to the work done by the effort, which can be calculated as:

work = force x distance

where force is the effort required to lift the load and distance is the distance the effort moves.

We don't know the distance the effort moves yet, but we can solve for the force using the IMA formula:

IMA = load ÷ effort

6 = 300N ÷ effort

effort = 300N ÷ 6

effort = 50N

Now we can use the work formula to find the distance the effort moves:

work = force x distance

input work = effort x distance

output work = load x distance

Substituting the values we know:

(80% ÷ 100%) x (50N x distance) = 300N x distance

0.8 x 50N x distance = 300N x distance

40N x distance = 300N x distance

Simplifying:

40N = 300N

distance = 7.5m

Therefore, the effort required to lift a load of 300N with the aid of the machine is 50N.