Download Work Energy

Chapter 3
Kinetics of Particles
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3-2 Work and
Energy
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3-2. Work and Energy

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
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3-2. Work and Energy
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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3-2. Work and Energy
2. Definition of Work
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3-2. Work and Energy
3. Calculation of Work
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3-2. Work and Energy
3. Calculation of Work
Notes:
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3-2. Work and Energy
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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3-2. Work and Energy
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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3-2. Work and Energy
3. Calculation of Work
Example 2: continued
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3-2. Work and Energy
4. Work of Linear Spring




Linear spring F = kx
where F is the force
acting on the spring to
compress/extend
Work done on the spring by the
body → use F
Work done on the body by the
spring → use P = -F
Thus work done on the body
by the spring is → → → →
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3-2. Work and Energy
5. Work and Curvilinear Motion
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3-2. Work and Energy
6. Work and Kinetic Energy
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3-2. Work and Energy
6. Work and Kinetic Energy
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3-2. Work and Energy
6. Work and Kinetic Energy
Example 3: Collar and Guide again
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3-2. Work and Energy
7. Power
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3-2. Work and Energy
8. Potential 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
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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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3-2. Work and Energy
Example 4: Slider
Ans: 4.48 m/s
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3-2. Work and Energy
Example 5: Swinging Ball
Ans: 3.59 m/s
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3-2. Work and Energy
Example 6: Spring and Slider
Ans: 1.16 m/s
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3-2. Work and Energy
Example 7: Spring and Slider
Ans: 3.59 m/s
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3-2. Work and Energy
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.
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