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dynamic lectrure course #3, Lecture notes of Mechanical Engineering

Prince Sattam bin Abdulaziz University (PSAU)Mechanical Engineering

Kinetics of Particles: Energy and Momentum Methods

Typology: Lecture notes

2018/2019

Uploaded on 05/09/2019

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VECTOR MECHANICS FOR ENGINEERS:

DYNAMICS

Tenth

Edition

Ferdinand P. Beer

E. Russell Johnston, Jr.

Phillip J. Cornwell

Lecture Notes:

Brian P. Self

California Polytechnic State University

CHAPTER

13

Kinetics of Particles:

Energy and Momentum

Methods

Discover Lecture notes of Mechanical Engineering Prince Sattam bin Abdulaziz University (PSAU)

Partial preview of the text

Download dynamic lectrure course #3 and more Lecture notes Mechanical Engineering in PDF only on Docsity!

VECTOR MECHANICS FOR ENGINEERS:

DYNAMICS

Tenth

Edition

Ferdinand P. Beer

E. Russell Johnston, Jr.

Phillip J. Cornwell

Lecture Notes:

Brian P. Self

California Polytechnic State University

CHAPTER

Kinetics of Particles:

Energy and Momentum

Methods

Vector Mechanics for Engineers: Dynamics

Introduction

13 - 4

Previously, problems dealing with the motion of

particles were solved through the fundamental

equation of motion,

The current chapter introduces two additional

methods of analysis.

 F  ma.



Method of work and energy : directly relates force,

mass, velocity and displacement.

Method of impulse and momentum : directly

relates force, mass, velocity, and time.

Vector Mechanics for Engineers: Dynamics

Introduction

2 - 5

Forces and

Accelerations

Velocities and

Displacements

Velocities and

Time

Approaches to Kinetics Problems

Newton’s Second

Law (last chapter)

Work-Energy

Impulse-

Momentum

1 1 2 2

T  U  T

 G

F  ma





 2

1

1 2

t

mv  F dt  mv





 

Vector Mechanics for Engineers: Dynamics

Work of a Force

13 - 7

Work of a force during a finite displacement,

 

  

 

 



2

1

2

1

2

1

2

1

cos

1 2

A

x y z

s

t

s

A

F dx F dy F dz

F ds F ds

U F d r



Work is represented by the area under the

curve of F

t

plotted against s.

F

t

is the force in the direction of the

displacement ds

Vector Mechanics for Engineers: Dynamics

Work of a Force

13 - 8

What is the work of a constant force in

rectilinear motion?

 

1 2

U F cos  x



 

1 2

U F sin  x



1 2

U F x



1 2

U 0



a)

b)

c)

d)

Vector Mechanics for Engineers: Dynamics

Work of a Force

13 - 10

Magnitude of the force exerted by a spring is

proportional to deflection,

springconstant  N/morlb/in.



k

F kx

Work of the force exerted by spring ,

2

1

2

1

2

1

1 2

2

1

U kxdx kx kx

dU Fdx kx dx

x

  

Work of the force exerted by spring is positive

when x

2

< x

1

, i.e., when the spring is returning to

its undeformed position.

Work of the force exerted by the spring is equal to

negative of area under curve of F plotted against

x ,

U   F  F   x

 1 2

2

1

1 2

Vector Mechanics for Engineers: Dynamics

Work of a Force

13 - 11

As the block moves from A

0

to A

1

, is

the work positive or negative?

Positive Negative

As the block moves from A

2

to A

o

, is

the work positive or negative?

Positive Negative

Displacement is

in the opposite

direction of the

force

Vector Mechanics for Engineers: Dynamics

2 - 13

Does the normal force do work as the

block slides from B to A?

YES NO

Does the weight do work as

the block slides from B to A?

YES NO

Positive or

Negative work?

Vector Mechanics for Engineers: Dynamics

Work of a Force

13 - 14

Forces which do not do work (ds = 0 or cos :

Weight of a body when its center of gravity

moves horizontally.

Reaction at a roller moving along its track, and

Reaction at frictionless surface when body

in contact moves along surface,

Reaction at frictionless pin supporting rotating body,

Vector Mechanics for Engineers: Dynamics

Applications of the Principle of Work and Energy

13 - 16

The bob is released

from rest at position A

1

.

Determine the velocity

of the pendulum bob at

A

2

using work & kinetic

energy.

Force acts normal to path and does no

work.

P



v gl

v

g

W

Wl

T U T

2

1

0

2

1 1 2 2



 



Velocity is found without determining

expression for acceleration and integrating.

All quantities are scalars and can be added

directly.

Forces which do no work are eliminated

from the problem.

Vector Mechanics for Engineers: Dynamics

Applications of the Principle of Work and Energy

13 - 17

Principle of work and energy cannot be

applied to directly determine the acceleration

of the pendulum bob.

Calculating the tension in the cord requires

supplementing the method of work and

energy with an application of Newton’s

second law.

As the bob passes through A

2

,

W

l

gl

g

W

P W

l

v

g

W

P W

F m a

n n

3

2

  

 



v 2 gl

2



If you designed the rope to hold twice the weight of the bob, what would happen?

Vector Mechanics for Engineers: Dynamics

Sample Problem 13.

13 - 19

An automobile weighing 4000 lb is

driven down a 5

o

incline at a speed of

60 mi/h when the brakes are applied

causing a constant total breaking force

of 1500 lb.

Determine the distance traveled by the

automobile as it comes to a stop.

SOLUTION:

Evaluate the change in kinetic energy.
Determine the distance required for the

work to equal the kinetic energy

change.

Vector Mechanics for Engineers: Dynamics

Sample Problem 13.

13 - 20

SOLUTION:

Evaluate the change in kinetic energy.

 4000 32. 2  88  481000 ft lb

88 ft s

3600 s

h

mi

5280 ft

h

mi

60

2

1

2

1

2

1

   









































T mv

v

481000 ft lb  1151 lb 0

1 1 2 2

  

 



x

T U T

x  418 ft

Determine the distance required for the work

to equal the kinetic energy change.

    

  x

U x x

1151 lb

1500 lb 4000 lb sin 5

1 2

 

   



0 0

2 2

v  T 

dynamic lectrure course #3, Lecture notes of Mechanical Engineering

Related documents

Partial preview of the text

Download dynamic lectrure course #3 and more Lecture notes Mechanical Engineering in PDF only on Docsity!

VECTOR MECHANICS FOR ENGINEERS:

DYNAMICS

DYNAMICS

Contents

Introduction

Previously, problems dealing with the motion of

particles were solved through the fundamental

equation of motion,

The current chapter introduces two additional

methods of analysis.

Method of work and energy : directly relates force,

mass, velocity and displacement.

Method of impulse and momentum : directly

relates force, mass, velocity, and time.

Introduction

Approaches to Kinetics Problems

Work of a Force

Work of a Force

What is the work of a constant force in

rectilinear motion?

U F x

U 0

Work of a Force

Work of a Force

As the block moves from A

to A

, is

the work positive or negative?

Positive Negative

As the block moves from A

to A

, is

the work positive or negative?

Positive Negative

Does the normal force do work as the

block slides from B to A?

YES NO

Does the weight do work as

the block slides from B to A?

YES NO

Positive or

Negative work?

Work of a Force

Weight of a body when its center of gravity

moves horizontally.

Reaction at a roller moving along its track, and

Reaction at frictionless surface when body

in contact moves along surface,

Reaction at frictionless pin supporting rotating body,

Applications of the Principle of Work and Energy

Applications of the Principle of Work and Energy

Sample Problem 13.

Sample Problem 13.