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?

Question

Physics

Charmer

23 December, 05:13

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?

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Answers (1)

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Mara · Answer 1

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