Momentum and Energy
What is an inclined plane?
A ramp is an example of an inclined plane. Instead of lifting an object to the height at the end of the ramp, you move it a much longer distance on the surface of the ramp, but it requires much less force. So, the ramp has a larger output force than an input force; it has a mechanical advantage greater than one. That is, MA = Foutput / Finput = (length of ramp) / (height of ramp).
According to the Americans with Disabilities Act a wheelchair ramp should have a maximum increase in height of 1’ for every 12” length of the ramp. The Act says that the maximum rise should be 2-1/2’, so the ramp must be 30’ long. The input work is Finput x L, where L is the length of the ramp. The output work is Foutput x d, where d is the rise and Foutput is the weight of the person plus wheelchair. If there is no sliding or rolling friction, then Finput X L = Foutput X d. The mechanical advantage is L/d. So Finput = Foutput/MA and the force needed to push a wheelchair up the ramp is given by Finput = Foutput / (L/d). If the weight of the person plus the wheelchair is 200 lbs., then the force needed to push the person up the ramp is Finput = 200lbs / (30’/2.5’) = 17 lbs.
Look at the cutting edge of a scissors. It’s an inclined plane where the input is the force and motion of the closing blades and the output is the outward movement of the paper after it is cut.