A 2.76 kg cart rolls down a track while subjected to a variable force opposing i

Question

A 2.76 kg cart rolls down a track while subjected to a variable force opposing its forward motion that decreases linearly with distance along the entire length of the 16.3 cm track. The force starts with a value of 22 N opposing the direction of motion of a cart moving along it and reduces to zero at the end of the track.

(a) How much work is done by the force while the cart is on the track?


(b) If the cart was originally moving at a speed 1.62 m/s, then what is its final speed after it moves off the track?

Explanation / Answer

a] Work done = area under F-s curve = -0.5*22*0.163 = -1.793 J

b] Final KE = 0.5*2.76*1.62^2 -1.793 = 1.8286 J

speed = sqrt(2KE/m) = sqrt(2*1.8286/2.76) = 1.151 m/s

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