Mechanical Efficiency of a Ramp

[iRamie]

Homework Statement

We have to find the efficiency of a ramp for a lab. We are given an inclined plane, a wooden block and a few masses. We are also given a Newton spring scale.

Homework Equations

efficiency = (Eout/Ein)*100%
Eg = mgh
Work = FD

The Attempt at a Solution

Is the efficiency equal to Eg/Work?
Because the only work i am putting in is me pushing the wooden block up the ramp. That will be the Ein. The Eout will be the gravitational potential energy of the object?


How would i calculate the efficiency of the ramp?

 

[Nahyo]

Substitute the Eg value for the Eout value and substitute the work value into the Ein value. Perform the calculation.

 

[late347]

The ramp is what is called a non-isolated mechanical system.

According to my own high school physics textbook
$W_{intake}= pushing work$ (I'm thinking that this is probably correct, but you have laboratory so why not test it out?)
$W_{benefit}= E_{pot.~at ~highpoint}$ (probably true as well...)
$W_{wasted} = W_{friction}$ (definitely true)

W_intake=W_benefit+W_wasted

W_intake-W_wasted= W_benefit
ramp efficiency η = $\frac { W_{benefit}}{W_{intake}}$Initially static friction will be overcome by the pushing action, and afterwards sliding friction will cause work. Or in other words, friction requires more force in order to be overcome by the ramp-user who pushes the box.
You would have less work required, if the ramp were frictionless. But of course in real-life ramp you most likely have some friction, so therefore more work is required to push the box along the ramp.

Overall, you were on the correct track to solving the problem. The practical problem for you is to simply figure out how you can find out the correct values for W_intake, W_benefit and W_wasted by using measurement and calculation in the lab.

This is my understanding of the situation and anybody more experrienced is welcome to criticize.

η= $\frac {W_{benefit}}{W_{input}}$

 

[ehild]

Measure both the height and the length of the ramp (from the front side of the block to the top. Move the block along the ramp slowly, with constant speed so as the spring scale shows a constant force. Read that force: it is F. The work done is W_intake=FD where D is the length of the ram. You know W_benefit= mgh, so you can calculate the efficiency
$\eta =\frac {W_{benefit}}{W_{input}}$.

 

[late347]

Measure both the height and the length of the ramp (from the front side of the block to the top. Move the block along the ramp slowly, with constant speed so as the spring scale shows a constant force. Read that force: it is F. The work done is W_intake=FD where D is the length of the ram. You know W_benefit= mgh, so you can calculate the efficiency
$\eta =\frac {W_{benefit}}{W_{input}}$.

how should you measure the force in practical terms with Newton-scale (spring scale)?

Especially if you are in the lab alone, and you do all work with only your own two hands?

If the pulling force has different direction in the vector compared to the actual angle in which the distance is traveled that could be problematic.

Therefore the pulling should occur at same angle as the ramp itself.

Its probably easier to use the scale with pulling.

If you pull at some constant speed, then I reckon the force reading should stay at a stable value prety much?

 

[ehild]

how should you measure the force in practical terms with Newton-scale (spring scale)?

Especially if you are in the lab alone, and you do all work with only your own two hands?

If the pulling force has different direction in the vector compared to the actual angle in which the distance is traveled that could be problematic.

Therefore the pulling should occur at same angle as the ramp itself.

Its probably easier to use the scale with pulling.

If you pull at some constant speed, then I reckon the force reading should stay at a stable value prety much?

Yes, you attach the block to the spring scale and pull the scale parallel with the ramp, so as the block moves with constant speed. Usually such a ramp is on a lab table and fixed to it, so you need only one hand, like in the picture