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how to design an incline plane.  how do I raise a 300 lb barrell three feet with 100...

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user9548519 | eNotes Newbie

Posted May 23, 2013 at 11:35 PM via web

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how to design an incline plane.  how do I raise a 300 lb barrell three feet with 100 lbs of force?

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 25, 2013 at 3:13 AM (Answer #1)

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If you wish to move a 300lb barrell three feet vertically than you know that the vertical component of your incline plane is equal to 3 ft.  Next you need to solve what angle the incline plane must be at in order to reduce the amount of force neecded to lift the barrell from 300 lbs to 100lbs.

The formula for an inclined plane is defined as follows:

`MA=L/h=F_w/F_i=R/E`

L= length of the plane
h= height of the plane = 3 ft
R = weight of the barrell = 300 lb
E = force required to raise the barrell

Therefore:

`L=(Rh)/E=((300)(3))/100=9`

Therefore, the inclined plane must be 9 ft in length.

The angle that it is raised at to be 3 ft high is defined as:

`sintheta=h/L=3/9-gttheta=19.5`

Therefore, a 9ft plank raised at an angle of 19.5 deg will move a 300 lb barrell vertically 3 ft if the force of 100 lbs is applied on the barrell.

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