Quote:
Originally Posted by 19bonestock88
In theory yes, but in practice, no.
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In theory no, unless you hold constant velocity up and down the hill (i.e. acceleration = 0)
and assume no increase in rolling resistance due to the trailer, which wouldn't be accurate. Even with the added mass of the trailer, the extra help you get from gravity is not enough to overcome the additional work required to move it in the first place. If you draw the FBD and do some algebra--
M = mass of car
m = mass of trailer
T = angle of hill (assuming same angle up and down)
d = distance of hill, and assuming d
uphill = d
downhill
F
D = aerodynamic drag force, assumed same for both
F
R,car < F
R,car+trailer = force of rolling resistance
You end up with the following work required for each situation to go up and down a hill of distance d at inclination T:
W
car = 2d(2Ma + 2F
D + 2F
R,car)
W
car+trailer = 2d(2Ma + 2ma +2F
D + 2F
R,car+trailer)
The gravitational force does indeed cancel out, but it cancels out in both situations and you still have the force required to move the trailer around, whether uphill or downhill, which doesn't cancel. So, even if a = 0 it requires more work to get the car and trailer up
and down the hill than the car alone, and thus more fuel.