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What is the mechanical advantage of a 6-m long ramp that extends from a ground-level sidewalk to a 2-m high porch?
Question Date: 2008-12-30
Answer 1:

You need several constants to answer this one, such as the coefficient of friction and whatnot. If there is no friction, then the force needed to push a weight up a ramp is equal to the weight of the object times the sine of the angle the ramp makes with horizontal. Sine is a trig function, is usually abbreviated Sin, and is calculated as the opposite side from the angle in question on a right triangle divided by the hypotenuse. The opposite side, the height of the porch, is 2 m. If you are lifting the weight straight up, then the sine of 90 degrees (i.e. vertical) is 1, so you have to exceed the weight of the object. You unfortunately haven't said whether the 6 m of the ramp is the distance from the point on the ground where the ramp begins to the point on the porch (the hypotenuse), or the distance from the point on the ground to the base of the porch (the adjacent). If it's from ground to porch, then 2 m / 6 m = 1/3, so you will need force exceeding only 1/3 of the object's weight. However, if it's from ground to base of porch, you need to calculate the hypotenuse using the Pythagorean Theorem (a2 + b2 = c2) before using it to divide the height of the porch.

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