these are six cases for velocity vs time for objects moving along a straight, ho

Question

these are six cases for velocity vs time for objects moving along a straight, horizontal and frictionless path. a single external force acts on each object, the masses of each object are given next to the respective graph of motion. for the 4 second intervals shown, rank the work done on the objects by the external force from greatest positive to the greatest negative for cases A-F.

B +2 m/s mp 4 kg A +2 m/s mc 4 kg 0. s 4s -2 m/s 2 m/s 2 m/s D +2 m/s E +2 m/s E +2 m's F +2 m/s 4 s 2s 4s -2 m's -2 m/s -2m/s

Explanation / Answer

As the slope of all the curves are constants for all times

So, the acceleration for all the curves are constants (may be different for each curve)

So, work done by the force = change in Kinetic energy

For curve A:

change in KE = 0.5*m*(2^2 - (-2)^2) = 0

for curve B:

change in KE = 0.5*m*(1^2 - 2^2) = -0.5*m*3 = -1.5*m

For cuve C:

change in KE = 0.5*m*(1^2 - (-2)^2) = -1.5*m

For curve D:

change in KE = 0.5*m*((-2)^2 - 2^2) = 0

for curve E:

change in KE = 0.5*m*(2^2 - 1^2) = 1.5*m

For F:

= 0.5*m*(2^2-1^2) = 1.5*m

So, (E = F ) > (D = A) > (B = C)

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