How Does Efficiency Impact Velocity Ratio in a Third Class Lever?

[junkie_ball]

Homework Statement

Calculate the velocity ratio of the system.

Third Class Lever

Efficiency = 65%
Mechanical Advantage = 1/6
Work Put In 3000J

(I know if the system was theoretically 100% efficient the velocity ratio is 1/6 or 0.167)

Homework Equations

Velocity Ratio = Mechanical Advantage / Efficiency

The Attempt at a Solution

VR = MA / E

VR = 0.167 / 0.65

VR = 0.257

This to me is a confusing answer as of the system was 100% efficient the ratio is only 0.167 and calculating it on 65% I'm getting a larger velocity ratio this can not be correct can it? Could someone please point me in the right direction?

 

[haruspex]

i'm getting a larger velocity ratio

You are thinking about it backwards. A higher velocity ratio means you are having to move faster on the driving side.

 

[Merlin3189]

VR is the constant: it is MA which is reduced by friction/inefficiency.
You can't calculate the VR from the inefficient MA , other than by correcting for efficiency.

So you calculated the VR as 1/4 ie. the output moves 4x faster than input
which gives an ideal MA (at 100% efficiency) of 1/4 ie. the output force is 1/4 the input force
Friction (inefficiency) reduces that to 1/6 because friction provides a force opposing the movement, but the VR will still be the same.

If friction were great enough, MA could be reduced to 0 and the output would not move! Then the VR is sort of imaginary! But if you can oil it a bit, as soon as it moves, it does so 4x faster and further than the input, so the VR=1/4 as it always must be.

Whatever you do the MA (of this machine) can never get to be more than 1/4 nor less than 0.