Looking from above; a small utility car is pulled along a straight section of ra

Question

Looking from above; a small utility car is pulled along a straight section of railroad tracks by a rope. When the rope pulls the car for 15 seconds the car reaches a final speed, after starting from rest, of 11 m/s. Now the situation is modified slightly so that the rope pulls, just as hard, at a 55 degree angle. 1) How will the final speed 15 seconds after starting from rest now compare to the original? Why? (Ignore friction and other effects). 2) Would it be reasonable to ignore the frictional force in the second situation? If yes, why? If no, why not? 3) How do you think the frictional force would compare to the second case if the rope were pulling at a 40o angle? Explain.

Explanation / Answer

1)   Initial acceleration a =   11/15

                                          =   0.733 m/sec2

       Final acceleration =   0.733 * cos55

                                     =    0.42 m/sec2

         =>     Final velocity = 0.42 * 15

                                       = 6.3 m/sec

   Final speed in second case is less than first case because in second case full force is not provided so, acceleration is less than first .

2) No, it would not be reasonable to ignore the frictional force in the second situation . Because rollling friction acts between tyres and ground .

3)   Frictional force in third case of 40 degrees is more than second case . Because in third case Normal Force is more than second one .

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