Learning Goal: 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 Fuet acting on the bicycle as it crosses the finish line?

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter7: Rotational Motion And Gravitation
Section: Chapter Questions
Problem 66AP: The pilot of an airplane executes a constant-speed loop-the-loop maneuver in a vertical circle as in...
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Learning Goal:
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?
PROBLEM-SOLVING STRATEGY 8.1 Circular-motion problems
MODEL: Model the object as a particle and make other simplifying assumptions.
VISUALIZE: Draw a pictorial representation. Use rtz-coordinates.
▪ Establish a coordinate system with the r axis pointing toward the center of the circle.
Show important points in the motion on a sketch. Define symbols, and identify what the problem is trying to find.
Identify the forces, and show them on a free-body diagram.
SOLVE: Newton's second law is
■
(Fnet )r = Σ F, = mar
(Fnet)t = Σ Ft = mat
(Fnet ) z = Σ F₂ = 0
mv² = mw²r
p
▪ Determine the force components from the free-body diagram. Be careful with signs.
= 0.
▪ The tangential acceleration for uniform circular motion is at =
■
Solve for the acceleration, and then use kinematics to find velocities and positions.
REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question.
Model
The cyclist moves in a circle at an increasing speed. This means that the cyclist has both centripetal and tangential acceleration. Moreover, the rate at which the cyclist's speed is increasing is constant.
Thus, to simplify the problem, you can model the bicycle + rider as a particle in nonuniform circular motion and use constant-acceleration kinematics to work out your solution.
Transcribed Image Text:Learning Goal: 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? PROBLEM-SOLVING STRATEGY 8.1 Circular-motion problems MODEL: Model the object as a particle and make other simplifying assumptions. VISUALIZE: Draw a pictorial representation. Use rtz-coordinates. ▪ Establish a coordinate system with the r axis pointing toward the center of the circle. Show important points in the motion on a sketch. Define symbols, and identify what the problem is trying to find. Identify the forces, and show them on a free-body diagram. SOLVE: Newton's second law is ■ (Fnet )r = Σ F, = mar (Fnet)t = Σ Ft = mat (Fnet ) z = Σ F₂ = 0 mv² = mw²r p ▪ Determine the force components from the free-body diagram. Be careful with signs. = 0. ▪ The tangential acceleration for uniform circular motion is at = ■ Solve for the acceleration, and then use kinematics to find velocities and positions. REVIEW: Check that your result has the correct units and significant figures, is reasonable, and answers the question. Model The cyclist moves in a circle at an increasing speed. This means that the cyclist has both centripetal and tangential acceleration. Moreover, the rate at which the cyclist's speed is increasing is constant. Thus, to simplify the problem, you can model the bicycle + rider as a particle in nonuniform circular motion and use constant-acceleration kinematics to work out your solution.
Identify which of the following forces act on the bicycle + rider system, and sort them accordingly.
Drag the appropriate items to their respective bins.
normal force gravity air resistance static friction
Acts on particle
Submit
Request Answer
rolling friction
Reset Help
kinetic friction
Does not act on particle
Transcribed Image Text:Identify which of the following forces act on the bicycle + rider system, and sort them accordingly. Drag the appropriate items to their respective bins. normal force gravity air resistance static friction Acts on particle Submit Request Answer rolling friction Reset Help kinetic friction Does not act on particle
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