A loaded truck (truck 1) has a maximum engine power P and is able to attain a ma

Question

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 same before and after the cable is connected, and, C) That the power that each truck's engine can generate is independent of the truck's speed.

Find vmax, the maximum speed of the two trucks when they are connected, assuming both engines are running at maximum power.

Express the maximum speed in terms of v.

Explanation / Answer

The resistance force acting on the to trucks separately are

FR1 = P/v, FR2 =2P/1.5v

The total resistace force

FR =FR1+FR2 = 7P/3v

The total poer PT of the two trucks are

PT =P1+P2 = 3P

The maxium velocity attained by the trucks that experience an resistive force of FR is

vmax = PT/FR = 3P(3v/7P) = 9v/7

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