To practice Problem-Solving Strategy 8.1 for circular-motion problems. A cyclist

Question

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 F_net acting on the bicycle as it crosses the finish line? Identify which of the following forces act on the bicycle + rider system, and sort them accordingly.

Explanation / Answer

(a)

Fnet = sqrt (net tangential force^2 + net radial force^2)

Tangential acceleration of the cyclist:
2r = (1/2)(a1)t²
2(140 m) = (1/2)( a1)(60 s)²
a1 = 0.489 m/s² ----------(1)

The radial acceleration is given by: a2 = v²/r ------------(2)

The tangential speed is given by:
v² = 2(a1)(2r)
v² = 4(a1)(r)
substituting v in (2)
a2 = 4(a1)(r) / r
a2 = 4(a1)

Tangential and radial accelerations are perpendicular to each other. The net acceleration is given by:
anet = sqrt[(a1)² + (a2)²]
a = sqrt[(a1)² + {4(a1)}²]
a = (a1) sqrt[1 + 16²]
a = (0.489 m/s²) sqrt[1 + 16²]
a = 6.16 m/s²

Hence, the net force on the cyclist.
F = ma
F = (76 kg)(6.16 m/s²)
F = 468 N

(b)

Acts on a particle

air resistance, rolling friction, gravity, normal forces, static friction

Does not acts on a particle:

kinectic friction

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