Download Chapter 3 Kinetics of Particles

Chapter 3
Kinetics of Particles
2103-212 Dynamics, NAV, 2012
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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
 Elastic PE
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
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
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
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
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 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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