To practice problem-solving strategy 8.1 for circular-motion problems. a cyclist competes in a one-lap race around a flat, circular course of radius 140 m . starting from rest and speeding up at a constant rate throughout the race, the cyclist covers the entire course in 60 s . the mass of the bicycle (including the rider) is 76 kg . what is the magnitude of the net force fnet acting on the bicycle as it crosses the finish line?

Explanation:

distance travelled

s = 2πR

= 2 X 3.14 X 140

= 880 m

final velocity = v

initial velocity = u

distance travelled = s

time = 60 s

s = ut + 1/2 at²

880 = .5 x a x 60²

a = .244 m/s²

final velocity v = at

= .244 x 60

= 14.66

centripetal acceleration at final moment

v² /R

14.66 X 14.66 / 140

= 1.53 m/s⁻²

1.53 m/s²

this is centripetal acceleration which acts towards the centre.

tangential acceleration calculated a _t = .244

redial acceleration ( centripetal ) = 1.53

Resultant acceleration

R²= 1.53² + .244 ²

R = 1.55 m/s²

total force = 1.55 x 76

= 118 N  

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle