A heavy box, full of parts for your pumpkin launcher, arrives at the sidewalk ou

Question

A heavy box, full of parts for your pumpkin launcher, arrives at the sidewalk outside your dorm building. There is a ramp from the sidewalk, having an angle of incline of  = 15 to the horizontal, that leads from the sidewalk to the building lobby. The change in elevation from the bottom to the top of the ramp is 62:1[in]. The box weighs 64:9[lbs] and the dynamic coecient of friction between the box and ramp is 0.41, how much work must you expend, in [J], to push the box up the ramp? If you are applying the force by pushing on the box, and your forearms make an angle of  = 45 to the horizontal, then what force, expressed in units of [lbf ], must you exert in order to keep the box moving at constant speed up the incline? If you weigh 140[lbs], and the static coecient of friction between your shoes and the ramp is 0.88, what is the heaviest box you could possible move up the ramp?

Explanation / Answer

W = change in Potential energy = mgh h = 62.1 in =1.57734 m g = 9.8 m/s^2 m = 64.9 lbs = 29.4381 kg W = 455.05 J F cos 45 = mg sin 15 = 64.9 x 32.174 x sin 15 F = 764.295 lbf

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