Momentum and EnergyEnergy |
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 = F_{output} / F_{input} = (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 F_{input} x L, where L is the length of the ramp. The output work is F_{output} x d, where d is the rise and F_{output} is the weight of the person plus wheelchair. If there is no sliding or rolling friction, then F_{input} X L = F_{output} X d. The mechanical advantage is L/d. So F_{input} = F_{output}/MA and the force needed to push a wheelchair up the ramp is given by F_{input} = F_{output} / (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 F_{input} = 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.