What force must be applied to roll a 120-pound barrel up an inclined plane 9 feet long to a height of 3 feet (disregard friction)?
Using the formula solve the equation.

(L/I=R/E)
L = Length of ramp, measured along the slope.
I = Height of ramp.
R= Weight of object to be raised or lowered.
E = Force required to raise or lower object.

Question

What force must be applied to roll a 120-pound barrel up an inclined plane 9 feet long to a height of 3 feet (disregard friction)?
Using the formula solve the equation.

(L/I=R/E) 
L = Length of ramp, measured along the slope.
I = Height of ramp.
R= Weight of object to be raised or lowered.
E = Force required to raise or lower object.

BlackTom AI · Accepted Answer

Rephrase of the problem: You need to determine the force E required to lift a 120-pound barrel up a ramp that is 9 feet long (slope length L = 9 ft) and raises the barrel to a height of 3 feet (rise I = 3 ft), neglecting friction. The given relation is L/I = R/E, where R is the weight of the object and E is the force applied.
First, solve the equation for E: starting from L/I = R/E, cross-multiply to obtain E = (R * I) / L.
Next, substitute the known values: R = 120 pounds, I (height) = 3 feet, L (ramp length) = 9 feet.
Compute the numerator: R * I = 120 lb * 3 ft = 360 lb·ft.
Divide by L: 360 lb·ft / 9 ft = 40 lb.
Therefore, the required force E to raise the barrel, ignoring friction, is 40 pounds.
Note: If there were alternative options, you would compare each option by checking whether it equals 40 pounds; any value other than 40 of course would not satisfy E = (R * I) / L. This calculation assumes the only work done is to raise the weight along the vertical rise, with no frictional losses present.
In practical terms, the ramp geometry shows that only a portion of the weight must be overcome directly by the applied force, due to the height-to-length ratio (I/L = 3/9 = 1/3), which implies E = R * (I/L) = 120 * (1/3) = 40 pounds. Any deviation from this relation would indicate either a misapplication of the formula or the presence of friction or other forces, which are explicitly disregarded here.

AMT&111 36402 Physics for Aviation

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