A ramp is inclined at 12 degrees to the horizontal. A cart is pulled 8m up the ramp by a force of 120N, at an angle of 10 degrees to the surface of the ramp. Determine the mechanical work done against gravity. Do not use physics formulas to solve this... use calculus and vectors.

The cart is lifted to a height, h:

h = (8 meters)*sin(12

h = (8 meters)*sin(12

^{o}) = 1.66 mThe force in the vertical direction is:

Fy = 120N*sin(22

^{o}) = 44.95NWork = F*d = (44.95)*(1.66) = 74.62 joules

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74.62 J = Mgh

Where M is the cart's mass, g is the acceleration due to gravity, and h is the height the cart is pulled up.

74.62 J= M*(9.8 m/s

^{2})*(1.66 m)4.59 kg = M, the mass of the cart