32 Work Energy

8/2/2019 32 Work Energy

1/28

2142211 Dynamics, NAV 1

Chapter 3

Kinetics of Particles


2/28


3-2 Work and

Energy


3/28


1. Work and Kinetic Energy Definition of Work Calculation of WorkWork of Linear SpringWork and Curvilinear Motion

Principle of Work and Kinetic Energy Advantage of Work-Energy Method Power Examples

2. Potential EnergyGravitational PE Elastic PE Examples

Examples

3-2. Work and Energy


4/28


1. Introduction


Recall Newtons second law and notice that this is aninstantaneous relationship.

When we want to see changes in velocity or position dueto motion, we have to integrate Newtons second law by

using appropriate kinematic equations. However, we may integrate Newtons 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 systemsconfigurations.

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


5/28


2. Definition of Work



6/28


3. Calculation of Work



7/28



Notes:



8/28



Example 1: Collar and Guide


Find the work done by the 8 N force on thecollar when itmoves from point A to point B.


9/28



Example 2: Collar and Guide


Find the work done by the forceF on thecollar when itmoves from point A to any point.


10/28



Example 2: continued



11/28


4. Work of Linear Spring


Linear spring F= kx

where Fis the forceacting on the spring tocompress/extend

Work done on the spring by thebody use F

Work done on the body by thespring use P =-F

Thus work done on the bodyby the springis


12/28


5. Work and Curvilinear Motion



13/28


6. Work and Kinetic Energy



14/28





15/28



Example 3: Collar and Guide again



16/28


7. Power



17/28


8. Potential Energy


Gravitational PE

Elastic PE

8.1 Gravitational PE (Vg)

Reference


18/28


3-2. Work and Energy8.1 Gravitational PE (Vg)

Start low finish high = go up

Vg = +

Start high finish low = go down

Vg = -


19/28


3-2. Work and Energy8.2 Elastic PE (Ve)

xis how much the spring iscompressed or extended fromits relaxed (original length)


20/28


3-2. Work and Energy9. Alternate form of Work-KE equation


21/28




22/28




23/28



Special Case (when there is no work from the external forceother than mg and spring)Law of Conservation of Mechanical Energy


24/28


Example 4: Slider

Ans: 4.48 m/s



25/28


Example 5: Swinging Ball


Ans: 3.59 m/s


26/28


Example 6: Spring and Slider


Ans: 1.16 m/s


27/28


Example 7: Spring and Slider


Ans: 3.59 m/s


28/28


Example 8: Slider


The spring of stiffness kis compressed and released, sendingthe particle of mass msliding along the track. Determine theminimum spring compression for which the particle will notlose contact with the track. The sliding surface is smooth

except shown.

Documents

32 Work Energy