Efficiency and Law of conservation for a skateboarder in a skate park

[pageb]

I have to design a track for a skate boarder that is 50% efficient (friction must be present) from the start of the skater's drop-in, to his furthest point along the track.
My skater's mass will be 75kg
efficiency=energy output/energy input x100%
I am not really sure where to go next and how to get what my height of the track should be, and if the shape of the track will be a 'U' or a 'W'
Any comments help at this point!
Thank You all

 

[sophiecentaur]

Hi and welcome.
This is a hard question to answer satisfactorily.
Your definition of efficiency is fine and you are right that there is always friction. But I am not sure how you can design the efficiency to be a particular value by just changing the dimensions in this case because you cannot know the friction coefficients (friction may be the only cause of wasted energy here). You could, I suppose, build in some sort of partial 'stop', in the form of a hard angle of direction change but even that would be difficult to get right without knowing the characteristic of the wheels and suspension and the way your knees could absorb some of your Kinetic Energy as you go over the angle,

There are systems where the maximum efficiency (ignoring friction) can be calculated or designed. Such systems involve levers with mass or pulley blocks where raising a load will involve extra work input to lift parts of the mechanism (so called dead weight). I don't think the board represents dead weight in your case because it acquires its own Kinetic Energy due to its own Gravitational Potential Energy.

 

[pageb]

Thank you for the reply!

The whole project was based on this skate board ramp stimulation https://phet.colorado.edu/en/simulation/energy-skate-park
and asked questions about the potential energy and kinetic energy at different heights on the ramp in the stimulation without friction. In the last section of the project it asks you to add friction to the same stimulation, and there is a graph provided in the link that shows the thermal energy, kinetic energy and potential energy amounts which was all very straight forward.. but then the very last question was to sketch my own track with an efficiency of exactly 50%. As you said without any other information it is very hard come up with values... and this being a physics 11 question I don't feel it is supposed to be this challenging. I'm stumped though! haha

 

[sophiecentaur]

If the graph contains thermal energy then that represents lost energy and you can. presumably, change variables to make that 50%. It could be just that simple.

 

[pageb]

oh okay, so in that case...
efficiency= output/input x 100%
and then do 0.5=output/input .. and solve for height variables? is that where your leaning towards maybe? if so any suggestions on what the input and output is... my thought was input= Ep_i + Ek_i (at the top of the ramp.. Eki will be 0... no movement yet)
and then output is where I get stumped... maybe Ek_f - thermal (friction is negative)...
then solve for height?
graph values of ramp with friction if this helps:
When Skater is stopped due to friction in the middle of the parabola (halfpipe)
Thermal: 3767.38J
KE: 0.00 J
PE: 1104.91J
Total: 4872.29
Skater at top of ramp:
PE: 4872.29 J
Thermal: 0 J
KE: 0 J

I may be just a confusing mess at this point ... if so don't mind me :P Thank you for letting me pick your brain though!

 

[sophiecentaur]

I haven't seen the graph (problem downloading and running that applet) but I can suggest it may be easiest to take an iterative approach. Start with a fixed drop section and a fixed rising section (half as high) and vary the horizontal bottom section until the thermal energy at the end of the run is half the initial PE. A couple of guesses will give a rough idea of a suitable length (straddling the 50% value) and then you can choose a mid point between starting values to take you nearer. If you are familiar with linear interpolation, you should be able to home in on the right answer with very few steps.