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Motion, in physics, changes with the time of the position or orientation of a body. Motion along a line or a curve is called translation.

1.
Physics 111: Mechanics

Lecture 4

Dale Gary

NJIT Physics Department

Lecture 4

Dale Gary

NJIT Physics Department

2.
The Laws of Motion

Newton’s first law

Force

Mass

Newton’s second law

Newton’s third law

Examples

Isaac Newton’s work represents

one of the greatest

contributions to science ever

made by an individual.

Feb. 11-15, 2013

Newton’s first law

Force

Mass

Newton’s second law

Newton’s third law

Examples

Isaac Newton’s work represents

one of the greatest

contributions to science ever

made by an individual.

Feb. 11-15, 2013

3.
Dynamics

Describes the relationship between the

motion of objects in our everyday world

and the forces acting on them

Language of Dynamics

Force: The measure of interaction between two

objects (pull or push). It is a vector quantity – it has a

magnitude and direction

Mass: The measure of how difficult it is to change

object’s velocity (sluggishness or inertia of the object)

Feb. 11-15, 2013

Describes the relationship between the

motion of objects in our everyday world

and the forces acting on them

Language of Dynamics

Force: The measure of interaction between two

objects (pull or push). It is a vector quantity – it has a

magnitude and direction

Mass: The measure of how difficult it is to change

object’s velocity (sluggishness or inertia of the object)

Feb. 11-15, 2013

4.
Forces

The measure of interaction

between two objects (pull or

push)

Vector quantity: has

magnitude and direction

May be a contact force or

a field force

Contact forces result from

physical contact between two

objects

Field forces act between

disconnected objects

Also called “action at a

distance”

Feb. 11-15, 2013

The measure of interaction

between two objects (pull or

push)

Vector quantity: has

magnitude and direction

May be a contact force or

a field force

Contact forces result from

physical contact between two

objects

Field forces act between

disconnected objects

Also called “action at a

distance”

Feb. 11-15, 2013

5.
Forces

Gravitational Force

Archimedes Force

Friction Force

Tension Force

Spring Force

Normal Force

Feb. 11-15, 2013

Gravitational Force

Archimedes Force

Friction Force

Tension Force

Spring Force

Normal Force

Feb. 11-15, 2013

6.
Vector Nature of Force

Vector force: has magnitude and direction

Net Force: a resultant force acting on

object Fnet F F1 F2 F3 ......

You must use the rules of vector addition to

obtain the net force on an object

| F | F12 F22 2.24 N

F1

tan 1 ( ) 26.6

F2

Feb. 11-15, 2013

Vector force: has magnitude and direction

Net Force: a resultant force acting on

object Fnet F F1 F2 F3 ......

You must use the rules of vector addition to

obtain the net force on an object

| F | F12 F22 2.24 N

F1

tan 1 ( ) 26.6

F2

Feb. 11-15, 2013

7.
Newton’s First Law

An object at rest tends to stay at rest and an

object in motion tends to stay in motion with

the same speed and in the same direction

unless acted upon by an unbalanced force

An object at rest remains at rest as long as no net force acts on it

An object moving with constant velocity continues to move with

the same speed and in the same direction (the same velocity) as

long as no net force acts on it

“Keep on doing what it is doing”

Feb. 11-15, 2013

An object at rest tends to stay at rest and an

object in motion tends to stay in motion with

the same speed and in the same direction

unless acted upon by an unbalanced force

An object at rest remains at rest as long as no net force acts on it

An object moving with constant velocity continues to move with

the same speed and in the same direction (the same velocity) as

long as no net force acts on it

“Keep on doing what it is doing”

Feb. 11-15, 2013

8.
Newton’s First Law

An object at rest tends to stay at rest and an

object in motion tends to stay in motion with

the same speed and in the same direction

unless acted upon by an unbalanced force

When forces are balanced, the acceleration of the object is

zero

Object at rest: v = 0 and a = 0

Object in motion: v 0 and a = 0

The net force is defined as the vector sum of all the

external forces exerted on the object. If the net force is

zero, forces are balanced. When forces are balances, the

object can be stationary, or move with constant velocity.

Feb. 11-15, 2013

An object at rest tends to stay at rest and an

object in motion tends to stay in motion with

the same speed and in the same direction

unless acted upon by an unbalanced force

When forces are balanced, the acceleration of the object is

zero

Object at rest: v = 0 and a = 0

Object in motion: v 0 and a = 0

The net force is defined as the vector sum of all the

external forces exerted on the object. If the net force is

zero, forces are balanced. When forces are balances, the

object can be stationary, or move with constant velocity.

Feb. 11-15, 2013

9.
Mass and Inertia

Every object continues in its state of rest, or uniform

motion in a straight line, unless it is compelled to change

that state by unbalanced forces impressed upon it

Inertia is a property of objects

to resist changes is motion!

Mass is a measure of the

amount of inertia.

Mass is a measure of the resistance of an object

to changes in its velocity

Mass is an inherent property of an object

Scalar quantity and SI unit: kg

Feb. 11-15, 2013

Every object continues in its state of rest, or uniform

motion in a straight line, unless it is compelled to change

that state by unbalanced forces impressed upon it

Inertia is a property of objects

to resist changes is motion!

Mass is a measure of the

amount of inertia.

Mass is a measure of the resistance of an object

to changes in its velocity

Mass is an inherent property of an object

Scalar quantity and SI unit: kg

Feb. 11-15, 2013

10.
Newton’s Second

Law

The acceleration of an object is directly

proportional to the net force acting on

it and inversely proportional to its mass

a

F

Fnet

m m

Fnet F ma

Feb. 11-15, 2013

Law

The acceleration of an object is directly

proportional to the net force acting on

it and inversely proportional to its mass

a

F

Fnet

m m

Fnet F ma

Feb. 11-15, 2013

11.
Units of Force

Newton’s second law:

Fnet F ma

SI unit of force is a Newton (N)

kg m

1 N 1

s2

US Customary unit of force is a pound (lb)

1 N = 0.225 lb

Weight, also measured in lbs. is a force (mass

x acceleration). What is the acceleration in

that case?

Feb. 11-15, 2013

Newton’s second law:

Fnet F ma

SI unit of force is a Newton (N)

kg m

1 N 1

s2

US Customary unit of force is a pound (lb)

1 N = 0.225 lb

Weight, also measured in lbs. is a force (mass

x acceleration). What is the acceleration in

that case?

Feb. 11-15, 2013

12.
More about Newton’s 2nd

Law

You must be certain about which body we are

applying it to

Fnet must be the vector sum of all the forces

that act on that body

Only forces that act on that body are to be

included in the vector sum

Net force component along an

axis gives rise to the acceleration

along that same axis

Fnet , x ma x Fnet , y ma y

Feb. 11-15, 2013

Law

You must be certain about which body we are

applying it to

Fnet must be the vector sum of all the forces

that act on that body

Only forces that act on that body are to be

included in the vector sum

Net force component along an

axis gives rise to the acceleration

along that same axis

Fnet , x ma x Fnet , y ma y

Feb. 11-15, 2013

13.
Sample Problem

One or two forces act on a puck that moves over frictionless

ice along an x axis, in one-dimensional motion. The puck's

mass is m = 0.20 kg. Forces F1 and F2 and are directed

along the x axis and have magnitudes F1 = 4.0 N and F2 = 2.0

N. Force F3 is directed at angle = 30° and has magnitude F3

= 1.0 N. In each situation, what is the acceleration

a) F1 ma xof the

puck? a 1

F 4.0 N

20 m/s 2

x

m 0.2 kg

b) F1 F2 ma x

F1 F2 4.0 N 2.0 N

ax 10 m/s 2

m 0.2 kg

c) F3, x F2 max F3, x F3 cos

Fnet , x ma x F3 cos F2 1.0 N cos 30 2.0 N

ax 5.7 m/s 2

m 0.2 kg

Feb. 11-15, 2013

One or two forces act on a puck that moves over frictionless

ice along an x axis, in one-dimensional motion. The puck's

mass is m = 0.20 kg. Forces F1 and F2 and are directed

along the x axis and have magnitudes F1 = 4.0 N and F2 = 2.0

N. Force F3 is directed at angle = 30° and has magnitude F3

= 1.0 N. In each situation, what is the acceleration

a) F1 ma xof the

puck? a 1

F 4.0 N

20 m/s 2

x

m 0.2 kg

b) F1 F2 ma x

F1 F2 4.0 N 2.0 N

ax 10 m/s 2

m 0.2 kg

c) F3, x F2 max F3, x F3 cos

Fnet , x ma x F3 cos F2 1.0 N cos 30 2.0 N

ax 5.7 m/s 2

m 0.2 kg

Feb. 11-15, 2013

14.
Gravitational Force

Gravitational force is a vector

Expressed by Newton’s Law of Universal

Gravitation: mM

Fg G

R2

G – gravitational constant

M – mass of the Earth

m – mass of an object

R – radius of the Earth

Direction: pointing downward

Feb. 11-15, 2013

Gravitational force is a vector

Expressed by Newton’s Law of Universal

Gravitation: mM

Fg G

R2

G – gravitational constant

M – mass of the Earth

m – mass of an object

R – radius of the Earth

Direction: pointing downward

Feb. 11-15, 2013

15.
Weight

The magnitude of the gravitational force acting on

an object of mass m near the Earth’s surface is

called the weight w of the object: w = mg

g can also be found from the Law of Universal

Gravitation

Weight has a unit of N

mM

Fg G 2 w Fg mg

R

M

g G 2 9.8 m/s 2

R

Weight depends upon location R = 6,400 km

Feb. 11-15, 2013

The magnitude of the gravitational force acting on

an object of mass m near the Earth’s surface is

called the weight w of the object: w = mg

g can also be found from the Law of Universal

Gravitation

Weight has a unit of N

mM

Fg G 2 w Fg mg

R

M

g G 2 9.8 m/s 2

R

Weight depends upon location R = 6,400 km

Feb. 11-15, 2013

16.
Normal Force

Force from a solid

surface which

keeps object from w Fg mg

falling through

Direction: always

perpendicular to

the surface N Fg ma y

Magnitude:

N mg ma y

depends on

situation N mg

Feb. 11-15, 2013

Force from a solid

surface which

keeps object from w Fg mg

falling through

Direction: always

perpendicular to

the surface N Fg ma y

Magnitude:

N mg ma y

depends on

situation N mg

Feb. 11-15, 2013

17.
Tension Force: T

A taut rope exerts

forces on whatever

holds its ends

Direction: always

along the cord (rope,

cable, string ……) T1

and away from the T1 = T = T2

object T2

Magnitude: depend

on situation

Feb. 11-15, 2013

A taut rope exerts

forces on whatever

holds its ends

Direction: always

along the cord (rope,

cable, string ……) T1

and away from the T1 = T = T2

object T2

Magnitude: depend

on situation

Feb. 11-15, 2013

18.
Newton’s Third Law

If object 1 and object 2 interact, the force

exerted by object 1 on object 2 is equal

in magnitude but opposite in direction to

the force exerted by object 2 on object 1

Fon A Fon B

Equivalent to saying a single isolated force

cannot exist Feb. 11-15, 2013

If object 1 and object 2 interact, the force

exerted by object 1 on object 2 is equal

in magnitude but opposite in direction to

the force exerted by object 2 on object 1

Fon A Fon B

Equivalent to saying a single isolated force

cannot exist Feb. 11-15, 2013

19.
Newton’s Third Law cont.

F12 may be called the

action force and F21

the reaction force

Actually, either force

can be the action or

the reaction force

The action and

reaction forces act

on different objects

Feb. 11-15, 2013

F12 may be called the

action force and F21

the reaction force

Actually, either force

can be the action or

the reaction force

The action and

reaction forces act

on different objects

Feb. 11-15, 2013

20.
Some Action-Reaction Pairs

mM

Fg G

R2

GM

Fg mg m 2

mM R

Fg G 2 Gm

R Fg Ma M 2

R

Feb. 11-15, 2013

mM

Fg G

R2

GM

Fg mg m 2

mM R

Fg G 2 Gm

R Fg Ma M 2

R

Feb. 11-15, 2013

21.
Free Body Diagram

The most important step in

solving problems involving F hand on book

Newton’s Laws is to draw

the free body diagram

Be sure to include only the

forces acting on the object

of interest

Include any field forces F Earth on book

acting on the object

Do not assume the normal

force equals the weight

Feb. 11-15, 2013

The most important step in

solving problems involving F hand on book

Newton’s Laws is to draw

the free body diagram

Be sure to include only the

forces acting on the object

of interest

Include any field forces F Earth on book

acting on the object

Do not assume the normal

force equals the weight

Feb. 11-15, 2013

22.
Hints for Problem-Solving

Read the problem carefully at least once

Draw a picture of the system, identify the object of primary

interest, and indicate forces with arrows

Label each force in the picture in a way that will bring to mind

what physical quantity the label stands for (e.g., T for tension)

Draw a free-body diagram of the object of interest, based on

the labeled picture. If additional objects are involved, draw

separate free-body diagram for them

Choose a convenient coordinate system for each object

Apply Newton’s second law. The x- and y-components of

Newton second law should be taken from the vector equation

and written individually. This often results in two equations

and two unknowns

Solve for the desired unknown quantity, and substitute the

numbers F ma F ma

net , x x net , y y

Feb. 11-15, 2013

Read the problem carefully at least once

Draw a picture of the system, identify the object of primary

interest, and indicate forces with arrows

Label each force in the picture in a way that will bring to mind

what physical quantity the label stands for (e.g., T for tension)

Draw a free-body diagram of the object of interest, based on

the labeled picture. If additional objects are involved, draw

separate free-body diagram for them

Choose a convenient coordinate system for each object

Apply Newton’s second law. The x- and y-components of

Newton second law should be taken from the vector equation

and written individually. This often results in two equations

and two unknowns

Solve for the desired unknown quantity, and substitute the

numbers F ma F ma

net , x x net , y y

Feb. 11-15, 2013

23.
Objects in Equilibrium

Objects that are either at rest or moving

with constant velocity are said to be in

equilibrium

a 0 of an object can be modeled

Acceleration

as zero:

Mathematically, the

F net

0 force acting on

the object is zero

Equivalent to the set of component

Fx by

equations given 0 Fy 0

Feb. 11-15, 2013

Objects that are either at rest or moving

with constant velocity are said to be in

equilibrium

a 0 of an object can be modeled

Acceleration

as zero:

Mathematically, the

F net

0 force acting on

the object is zero

Equivalent to the set of component

Fx by

equations given 0 Fy 0

Feb. 11-15, 2013

24.
Equilibrium, Example 1

A lamp is suspended from

a chain of negligible mass

The forces acting on the

lamp are

the downward force of

gravity

the upward tension in the

chain

Applying equilibrium gives

Fy 0 T Fg 0 T Fg

Feb. 11-15, 2013

A lamp is suspended from

a chain of negligible mass

The forces acting on the

lamp are

the downward force of

gravity

the upward tension in the

chain

Applying equilibrium gives

Fy 0 T Fg 0 T Fg

Feb. 11-15, 2013

25.
Equilibrium, Example 2

A traffic light weighing 100 N hangs from a vertical cable

tied to two other cables that are fastened to a support.

The upper cables make angles of 37° and 53° with the

horizontal. Find the tension in each of the three cables.

Conceptualize the traffic light

Assume cables don’t break

Nothing is moving

Categorize as an equilibrium

problem

No movement, so acceleration is

zero

F 0 Fy 0

Model xas an object in equilibrium

Feb. 11-15, 2013

A traffic light weighing 100 N hangs from a vertical cable

tied to two other cables that are fastened to a support.

The upper cables make angles of 37° and 53° with the

horizontal. Find the tension in each of the three cables.

Conceptualize the traffic light

Assume cables don’t break

Nothing is moving

Categorize as an equilibrium

problem

No movement, so acceleration is

zero

F 0 Fy 0

Model xas an object in equilibrium

Feb. 11-15, 2013

26.
Equilibrium, Example 2

Need 2 free-body diagrams

Apply equilibrium equation to

light Fy 0 T3 Fg 0 F y 0 T3 Fg 0

T3 Fg 100 N

T3 Fg 100 N

Apply equilibrium equations to

F

knot

x T1x T2x T1 cos 37

T2 cos 53 0

F y T1 y T2 y T3 y

T1 sin 37 T2 sin 53 100 N 0

cos 37

T2 T1 1.33T1

cos 53

T1 60 N T2 1.33T1 80 N

Feb. 11-15, 2013

Need 2 free-body diagrams

Apply equilibrium equation to

light Fy 0 T3 Fg 0 F y 0 T3 Fg 0

T3 Fg 100 N

T3 Fg 100 N

Apply equilibrium equations to

F

knot

x T1x T2x T1 cos 37

T2 cos 53 0

F y T1 y T2 y T3 y

T1 sin 37 T2 sin 53 100 N 0

cos 37

T2 T1 1.33T1

cos 53

T1 60 N T2 1.33T1 80 N

Feb. 11-15, 2013

27.
Accelerating Objects

If an object that can be modeled as a

particle experiences an acceleration, there

must be a nonzero net force acting on it

Draw a free-body diagram

Apply Newton’s Second Law in component

form

F ma

F x ma x F y ma y

Feb. 11-15, 2013

If an object that can be modeled as a

particle experiences an acceleration, there

must be a nonzero net force acting on it

Draw a free-body diagram

Apply Newton’s Second Law in component

form

F ma

F x ma x F y ma y

Feb. 11-15, 2013

28.
Accelerating Objects,

Example 1

A man weighs himself with a scale in an elevator.

While the elevator is at rest, he measures a

weight of 800 N.

What weight does the scale read if the elevator

accelerates upward at 2.0 m/s2? a = 2.0 m/s2

What weight does the scale read if the elevator

accelerates

Upward: Fy downward at 2.0 m/s2? a = - 2.0 m/s2

N mg ma N

N mg ma m( g a ) N 80(2.0 9.8) 624 N

N

w 800 N

m

g 9.8 m/s 2

80 N N mg

Downward: N 80( 2.0 9.8) 624 N

N mg mg mg

Feb. 11-15, 2013

Example 1

A man weighs himself with a scale in an elevator.

While the elevator is at rest, he measures a

weight of 800 N.

What weight does the scale read if the elevator

accelerates upward at 2.0 m/s2? a = 2.0 m/s2

What weight does the scale read if the elevator

accelerates

Upward: Fy downward at 2.0 m/s2? a = - 2.0 m/s2

N mg ma N

N mg ma m( g a ) N 80(2.0 9.8) 624 N

N

w 800 N

m

g 9.8 m/s 2

80 N N mg

Downward: N 80( 2.0 9.8) 624 N

N mg mg mg

Feb. 11-15, 2013