Set Rolling

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A cart is set rolling across a level table?

A cart is set rolling across a level table, at the same speed on every trial. If it runs into a patch of sand, the cart exerts on the sand an average horizontal force of 6 N and travels a distance of 6 cm through the sand as it comes to a stop. If instead the cart runs into a patch of gravel on which the cart exerts an average horizontal force of 9 N, how far into the gravel will the cart roll before stopping?

use the relationship

vf^2=v0^2+2ad

vf=final velocity, in all cases this is 0
v0=initial velocity, and is the same in all cases

a is acceleration, and it 1.5 times greater with the gravel than the sand; you know this since the same mass cart experiences a force 1.5 times greater (9N vs. 6N) in gravel compared to sand

d=distance traveled

since we know vf is zero, we can write

d=v0^2/(-2a) where a is negative since it is slowing down

since v0 is the same for all cases, the only varying parameter is acceleration; if the acceleration increases by a factor of 1.5, the distance traveled must decrease by a factor of 1.5, so the distance traveled in gravel is 6m/1.5 = 4 cm

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