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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

3-2. Work and Energy

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

3-2. Work and Energy

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3. Calculation of Work

3-2. Work and Energy

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3. Calculation of Work

Notes:

3-2. Work and Energy

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3. Calculation of Work

Example 1: Collar and Guide

3-2. Work and Energy

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

3-2. Work and Energy

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

3-2. Work and Energy

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5. Work and Curvilinear Motion

3-2. Work and Energy

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6. Work and Kinetic Energy

3-2. Work and Energy

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6. Work and Kinetic Energy

3-2. Work and Energy

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6. Work and Kinetic Energy

Example 3: Collar and Guide again

3-2. Work and Energy

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7. Power

3-2. Work and Energy

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Example 4: Slider

Ans: 4.48 m/s

3-2. Work and Energy

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Example 5: Swinging Ball

3-2. Work and Energy

Ans: 3.59 m/s

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8. Potential Energy

3-2. Work and Energy

Gravitational PE

Elastic PE

8.1 Gravitational PE (Vg)

Reference

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3-2. Work and Energy 8.1 Gravitational PE (Vg)

Start low finish high = go up

ΔVg = +

Start high finish low = go down

ΔVg = -

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3-2. Work and Energy 8.2 Elastic PE (Ve)

x is how much the spring is

compressed or extended from

its relaxed (original length)

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3-2. Work and Energy 9. Alternate form of Work-KE equation

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3-2. Work and Energy 9. Alternate form of Work-KE equation

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3-2. Work and Energy 9. Alternate form of Work-KE equation

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

3-2. Work and Energy

Ans: 1.16 m/s

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Example 7: Spring and Slider

3-2. Work and Energy

Ans: 3.59 m/s

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Example 8: Slider

3-2. Work and Energy

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.