The first two I understand, but I am stuck on the last question. An automobile o

Question

The first two I understand, but I am stuck on the last question.

An automobile of mass m = 103 kg is being towed by a truck whose driver observes that the tension in the rope is T = 3400 N while the rig (truck plus car) is uniformly accelerating such that its velocity increases from vi = 4 m/s to vf = 1.7*vi over the time interval t = 4 s. The wheels turn without slipping on the road and there is some friction within the car.

1) How far does the car travel in this time interval?

d =

2) What is the work done on the car by the rope?

Wrope =

3) What is the work done to overcome friction in the car?

Wfriction =

Explanation / Answer

Firstly, the acceleration is a = (1.7-1)Vi/t = 0.7*4/4 = 0.7 m/s^2

Tension in the rope is 3400 N

Tension in rope - Friction of car = Mcar x Acar

3400 - Friction of car = 1000 x 0.7 =700 N

Friction of car = 3400 - 700 = 2700 N (which is constant)

Distance travelled by car = ut + 0.5*a.t^2 = 4*4 + 0.5*0.7*4^2 = 16(1 + 0.35) = 1.35 *16 = 21.6 m

So, work done to overcome friction = 21.6 * 2700 = 58.32 KJ

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