Chapter 3 Kinetics of Particles

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Chapter 3

Kinetics of Particles

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3-2 Work and

Energy

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

1. Work and Kinetic Energy

 Definition of Work

 Calculation of Work

 Work of Linear Spring

 Work and Curvilinear Motion

 Principle of Work and Kinetic Energy

 Advantage of Work-Energy Method

 Power

 Examples



2. Potential Energy

 Gravitational PE

 Elastic PE

 Examples



Examples

3-2. Work and Energy

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1. Introduction

 Recall Newton’s second law and notice that this is an instantaneous relationship.

 When we want to see changes in velocity or position due to motion, we have to integrate Newton’s second law by using appropriate kinematic equations.

 However, we may integrate Newton’s second law directly and avoid solving for acceleration first.

 In general, there is two classes of problems

 Integration with respect to displacement → Work-Energy equation → velocity between two positions of a particle or system’s

configurations.

 Integration with respect to time → Impulse-Momentum equation → changes in velocity between two points in time.

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2. Definition of Work

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3. Calculation of Work

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3. Calculation of Work Notes:

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3. Calculation of Work

Example 1: Collar and Guide

Find the work done by the 8 N force on the collar when it moves from point A to point B.

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3. Calculation of Work

Example 2: Collar and Guide

Find the work done by the force F on the collar when it moves from point A to any point.

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3. Calculation of Work Example 2: continued

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5. Work and Curvilinear Motion

3-2. Work and Energy

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Example 3: Collar and Guide again

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7. Power

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Example 4: Slider

Ans: 4.48 m/s

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Example 5: Swinging Ball

Ans: 3.59 m/s

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8. Potential Energy

 Gravitational PE

 Elastic PE

8.1 Gravitational PE (V

_g

)

Reference

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3-2. Work and Energy

8.1 Gravitational PE (V

_g

)

 Start low finish high = go up ΔV_g = +

 Start high finish low = go down ΔV_g = -

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8.2 Elastic PE (V

_e

)

x is how much the spring is

compressed or extended from its relaxed (original length)

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9. Alternate form of Work-KE equation

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3-2. Work and Energy

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Special Case (when there is no work from the external force other than mg and spring)

Law of Conservation of Mechanical Energy

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Example 6: Spring and Slider

Ans: 1.16 m/s

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Example 7: Spring and Slider

Ans: 3.59 m/s

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Example 8: Slider

The spring of stiffness k is compressed and released, sending the particle of mass m sliding along the track. Determine the minimum spring compression for which the particle will not lose contact with the track. The sliding surface is smooth except shown.