During a contest, competitors have to drag a log for 15 m across a horizontal fl

Question

During a contest, competitors have to drag a log for 15 m across a horizontal floor by pulling horizontally with an attached rope. Under the same conditions (mass and coefficient of friction), competitor A moves the log at 3.6 km/h, competitor B at 10.8 km/h, and competitor C at a speed increasing at a constant acceleration from 10.8 km/h to 14.4 km/h. Rank the net work done on the log Wnet in each case(choose one)

Wnet,C>Wnet,A>Wnet,B

Wnet,B>Wnet,A>Wnet,C

Wnet,B>Wnet,C>Wnet,A

Wnet,A=Wnet,B<Wnet,C

Wnet,A>Wnet,B>Wnet,C

Wnet,A=Wnet,B=Wnet,C=0

Wnet,C>Wnet,B>Wnet,A

Wnet,A=Wnet,B=Wnet,C0

Explanation / Answer

Given

three competitors pulling the same long about 15 m under same conditions

let the competitor A pulling the log from rest with 3.6 km/h = 3.6*5/18 = 1 m/s  

competitor B pulling the log from 1m/s to 3.6 km/h = 10.8*5/18 = 3 m/s and

competitor C pulling the log from 3 m/s to 14.4 km/h = 14.4*5/18 = 4 m/s  

now the work done = change in kinetic energy

W_A = 0.5*m*(v2^2-v1^2) = 0.5*m*(1-0) = 0.5*m

W_B = 0.5*m*(v2^2-v1^2) = 0.5*m*(3^2-1^2) = 4 *m

W_C = 0.5*m*(v2^2-v1^2) = 0.5*m*(4^2-3^2) = 3.5*m

so the work done raking by the competitors is  

W_B > W_C > W_A

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