An automobile of mass m = 1100 kg is being towed by a truck whose driver observe

Question

An automobile of mass m = 1100 kg is being towed by a truck whose driver observes that the tension in the rope is T = 3800 N while the rig (truck plus car) is uniformly accelerating such that its velocity increases from vi= 5 m/s to vf= 1.9*vi over the time interval t = 5 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 = ? m  

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

Wrope = ? J  

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

Wfriction = ? J

Explanation / Answer

1) vf = vi + a t

(5 x 1.9) = 5 + 5 a

a = 0.90 m/s^2

vf^2 - vi^2 = 2 a d

(1.9 x 5)^2 - 5^2 = 2(0.90)(d)

d = 36.25 m

(2) W = T.d = 3800 x 36.25

= 137750 J

3) work done by tension + work doneby friction = change in KE

137750 + ( - W) = 1100( (1.9 x 5)^2 - 5^2)/2

W = 101862.5 J

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