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?
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
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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 \( F_{\text{net}} \) 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 \( rz \)-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
\[ (F_{\text{net}})_r = \Sigma F_r = ma_r = \frac{mv^2}{r} = m\omega^2 r \]
\[ (F_{\text{net}})_t = \Sigma F_t = ma_t \]
\[ (F_{\text{net}})_z = \Sigma F_z = 0 \]
- Determine the force components from the free-body diagram. Be careful with signs.
- The tangential acceleration for uniform circular motion is \( a_t = 0 \).
- 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb7f470a0-93f2-43bf-9ed3-2f125d19f075%2F78926c8a-ff8f-4151-8579-52456c0f272a%2Fyv3ezw_processed.png&w=3840&q=75)
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 \( F_{\text{net}} \) 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 \( rz \)-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
\[ (F_{\text{net}})_r = \Sigma F_r = ma_r = \frac{mv^2}{r} = m\omega^2 r \]
\[ (F_{\text{net}})_t = \Sigma F_t = ma_t \]
\[ (F_{\text{net}})_z = \Sigma F_z = 0 \]
- Determine the force components from the free-body diagram. Be careful with signs.
- The tangential acceleration for uniform circular motion is \( a_t = 0 \).
- 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:**Interactive Learning Task: Forces on a Bicycle + Rider System**
**Objective:** Identify which of the following forces act on a bicycle and rider system, and sort them accordingly.
**Instructions:** Drag the appropriate items to their respective bins.
**Forces to Consider:**
- Normal force
- Gravity
- Air resistance
- Static friction
- Kinetic friction
- Rolling friction
**Bins:**
1. **Acts on particle**
2. **Does not act on particle**
**Interface Controls:**
- **Reset**: Clears your selections and starts the task over.
- **Help**: Provides assistance with the task.
- **Submit**: Finalizes your response for evaluation.
- **Request Answer**: Reveals the correct sorting of forces.
This activity helps in understanding the different forces that interact with objects in motion, particularly in the context of cycling dynamics. It encourages students to apply their knowledge of physics concepts like friction, gravity, and air resistance in a practical scenario.
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