A cable that can withstand 2,25 pounds is used to pull cargo up an inclined ramp.  If the inclination of the ramp is 21.5 degrees, what is the heaviest piece of cargo that can be pulled up the ramp, ignoring friction?

Expert Answers

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You need to notice that you need to decompose the weight into two components, one along x axis, that is parallel to the inclined surface of the plane and one along y axis, that is perpendicular to the inclined surface.

You need to use the component that is parallel to x axis, hence, you need to set up the following equation, using the information provided by the problem, that the cable withstands 2,25 pounds, such that:

`W*sin theta = 2,25 => W = (2,25)/(sin theta) `

Since the problem provides the angle `theta = 21.5^o` , yields:

`W = (2,25)/(sin 21.5^o) => W = (2,25)/(0.366) => W = 6,147` pounds

Hence, evaluating the weight of the heaviest piece that can be pulled up the ramp, without friction yields `W = 6,147` pounds.

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