M1 qu

A cyclist and her bicycle have a combined mass of 78kg. While riding on level ground and using her greatest driving force, she is able to accelerate uniformly from rest to 10m/s in 15 seconds against a constant resistive forces that total 60N.

a)Show that her maximum driving force is 112N.

The cyclist begins to ascend a hill, inclined at an angle alpha to the horizontal, riding with her maximum driving force and against the same resistive forces. In this case, she is able to maintain a steady speed.

b)Find the angle alpha, giving your answer to the nearest degree

u = 0, v = 10, t = 15
=> 10 = 0 + 15a
=> a = 10/15 = 2/3 ms^-2

F = ma
=> F_D - 60 = 78(2/3)
=> F_D = 156/3 + 60 = 52 + 60 = 112 N


a = 0

=> F = 0
=> 112 - 60 - mgsin(alpha) = 0
=> 52 - 78(9.81)sin(alpha) = 0
=> sin(alpha) = 52/[78(9.81)]
=> alpha = 4 Deg (Nearest Degree)