Question

A rope attached to a truck pulls a 180−kg motorcycle at 9.0m/s.The rope exerts a 400−N force on the motorcycle at an angle of 15∘ above the horizontal. a. What is the work that the rope does in pulling the motorcycle 300m?b. How will your anwer change if the speed is 12m/s? c. How will your answer change if the truck accelerates?

Answer 1

Answer:

115911.09915 J

Unchanged

Decreased

Explanation:

m = Mass of motorcycle = 180 kg

v = Velocity of motorcycle = 9 m/s

F = Force = 400 N

s = Displacement = 300 m

$\theta$ = Angle above the horizontal = 15°

Work done is given by

$W=Fscos\theta\\\Rightarrow W=400\times 300\times cos15\\\Rightarrow W=115911.09915\ J$

The work done is 115911.09915 J

It can be seen that the force applied is constant so it does not matter if the speed of the motorcycle changes.

Tension on the rope would be

$Fcos\theta-T=ma\\\Rightarrow T=Fcos\theta-ma$

Work done

$W=Ts\\\Rightarrow W=(Fcos\theta-ma)s$

So, the work done would be reduced.