Simple machines are frequently used for reducing the amount of force that must b

Question

Simple machines are frequently used for reducing the amount of force that must be supplied to perform a task such as lifting a heavy weight. Such machines include the screw, block-and-tackle systems, and levers, but the simplest of the simple machines is the inclined plane. In Figure 6-32, you are raising a heavy box to the height of the truck bed by pushing it up an inclined plane (a ramp). (a) The mechanical advantage MA of the inclined plane is defined as the ratio of the magnitude of the force it would take to lift the block straight up (at constant speed) to the magnitude of the force it would take to push it up the ramp (at constant speed). If the plane is frictionless, show that MA = 1/sin theta = L/H, where H is the height of the truck bed and L is the length of the ramp. (b) Show that the work you do by moving the block into the truck is the same whether you lift it straight up or push it up the frictionless ramp.

Explanation / Answer

from the figure

sintheta = opposite/hypotnes

sintheta = H/L

1/sintheta = L/H

work done by conservative force does not depends on the path taken

so only depends on the initial and final points

w = mgH

while verticlally lifting also we did smae work done w = mgH

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