Combining Truck Power A loaded truck (truck 1) has a maximum engine power P and

Question

Combining Truck Power A loaded truck (truck 1) has a maximum engine power P and is able to attain a maximum speed v. Another truck (truck 2) has a maximum engine power 2P and can attain a maximum speed of 1.5v The two trucks are then connected by a long cable, as shown. (Figure 1) To solve this problem, assume that each truck, when not attached to another truck, has a speed that is limited only by wind resistance. Also assume (not very realistically) A) That the wind resistance is a constant force (a different constant for each truck though). i.e. It is independent of the speed at which the truck is going B) That the wind resistance force on each truck is the Figure 1 v of 1 Truck I Truck 2 i cable)

Explanation / Answer

The force due to drag o both the trucks is:

F1 = P/v ; F2 = 2P/1.5v

the total resistive force due to air is:

F(tot) = F1 + F2 = P/v + 2P/1.5v = 7P/3v

total power of trucks is:

P(tot) = P1 + P2 = P + 2P = 3P

So the maximum velocity, when the trucks are connected is:

v(max) = P(tot)/F(tot)

v(max) = 3P/(7P/3v) = 9/7 v

Hence, v(max) = 9/7 v

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