# Simple machine efficiency

## Homework Statement

question: An effort of 3 kN is required to move a mass of 2000 kg in a certain simple machine. If the mass is raised 1.5 meters while the effort moves 12 meters, find the efficiency?

2. equations used in solution:

work input = effort x distance moved by effort
efficiency = work output / work input
3kN = 3000 Newtons

## The Attempt at a Solution

my solution:

efficiency = work output / work input

mass = 2000 kg =19613.3 Newtons x 1.5 meters /

3000 Newtons x 12 meters

effort = 29419.95 Nm / 353039.4 Nm

= 0.817

Now, is it possible to have such a low efficiency in a machine? What simple machine would this be?

## The Attempt at a Solution

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Hootenanny
Staff Emeritus
Gold Member
efficiency = work output / work input

mass = 2000 kg =19613.3 Newtons x 1.5 meters /

3000 Newtons x 12 meters

effort = 29419.95 Nm / 353039.4 Nm

= 0.817
Your solution is correct, although you seemed to have used a nonstandard value for the acceleration due to gravity.
Now, is it possible to have such a low efficiency in a machine? What simple machine would this be?
Why do you think that this efficiency is low? What is the maximum theoretically possible efficiency?

Which nonstandard value did I use?

Why do you think that this efficiency is low? What is the maximum theoretically possible efficiency? The maximum theoretically possible efficiency would be 100%.

I think the efficiency is low because we have a number of .817.The efficiency of any machine depends upon the amount of friction and air resistance present. A frictionless machine would have an efficiency of 100%. Here we have .817 for efficiency, so we must have a lot friction or air resistance.

Hootenanny
Staff Emeritus
Gold Member
Which nonstandard value did I use?
You used g = 9.80665, which is indeed the standard acceleration due to gravity; however, g is more commonly approximated to 9.81 since the actual value of g varies greatly depending on location. It is not a serious problem though.
The maximum theoretically possible efficiency would be 100%.
I think the efficiency is low because we have a number of .817
Note here, that 0.817 is not a percentage efficiency.

Ok, the percentage efficiency is 81.7%. How can I find out what kind of simple machine this would be?

Hootenanny
Staff Emeritus