Forces and

Newton’s Laws of Motion

Chapter 4

All objects naturally tend to continue moving in the same direction at the same speed.

All objects resist changing their velocity. (velocity is speed and direction)

Resistance to changing velocity is inertia.

The amount of inertia is the mass.

Mass is measured in kilograms (kg).

Inertia

Forces

External forces can change an object's velocity.

Total external force is called net force .

Net force determines how quickly and in what direction the velocity changes.

When net force is zero, the velocity remains unchanged. If the object is moving, it keeps moving in a straight line.

F

F

F

Newton's first law

When net force , the velocity stays the same. (same speed and same direction)

0F

The reverse is also true.

When the velocity stays the same, the net force .0F

Newton's first law is also called the law of inertia because an object's inertia keeps it moving in the same direction at the same speed if the net force is zero.

An inertial reference frame is a coordinate system in which Newton’s law of inertia is valid.

Inertial frames have a constant velocity.

All accelerating reference frames are non-inertial because Newton’s law of inertia is not valid in accelerated coordinate systems.

Non-inertial frame: A car when speeding up, slowing down, or turning a corner.

Inertial reference frame

Individual Forces Net Force

10 N4 N

The net force is the vector sum of all external forces acting on a single object.

F

The SI unit of force is the newton (N).

1 2 3F F F F

Net force F

6 NF

Individual Forces Net Force

Net force F

1 2F F F

3 N1F

4 N

2F

3 N1F

4 N

2F

F

5 N37

F

Newton's second law

FAn object's acceleration vector is equal to the

net force acting on the object divided by the object's mass.

mF

a

Acceleration direction is same direction as net force .F

xx maF

yy maFF ma

orNewton's second law

Use x and y components when you need more than + and - to specify directions.

2 2

m kg mN = kg

s s

mF a

SI unit of force

mF

a

newton N is the SI unit for force

Force diagram (also known as free-body diagram)

275 395 560 110F N N N N

Net force is in the +x direction.F

mass 1850 kg

ALWAYS draw a force diagram with a force vector for each individual, external force acting on a single object.

2

+110 N m0.059

1850 kg s

Fa

m

The “+” sign indicates the +x direction.

Example: What is the car's acceleration?

Net force is +110 N and car's mass is 1850 kg

Newton's third law

Two objects always exert equal and opposite forces on each other.

Forces always occur in pairs.

Each object experiences the force equally, but the forces are in opposite directions.

Example: You are pushing down on the chair with some force and the chair is pushing on you with the same amount of force but in the opposite direction (up).

Astronaut pushes with 36 N on a spacecraft. What are their accelerations?

Example

11,000 kg 92 kg

The two objects exert 36 N of force on each other.

2

36 N0.0033

11,000 kgspacecraftspacecraft

F m

m s

a

2

36 N0.39

92 kgastronautastronaut

F m

m s

a

Find the tension in the trailer drawbar and the force D that propels the truck forward.

Ignore the forces of friction and air resistance.

NF

gF

NF

gF

Unbalanced horizontal forcesUnbalanced horizontal force

Equal and opposite forceson different objects

Example

There are two general types of forces in nature,fundamental and non-fundamental.

Fundamental

gravity electromagnetismweak nuclearstrong nuclear

Forces

Non-fundamental

pushpullsupport friction tension...

211

26.673 10

N mG

kg

Universal law of gravity

Every two objects in the universe attract each other with the gravity force.

221

r

mmGF magnitude

Equal attracting forces in exactly opposite directions.

centerline

universal gravity constant

(Newton's 3rd law: equal and opposite forces on two objects)

gF mg

Weight is the gravity force on an object

2 29.8 9.8EM N m

g Gr kg s

2 2E E

g

E E

M m MF G m G mg

R R

where

Example: a 5 kg mass "weighs" 49 N

5 9.8 49g

NF mg kg N

kg

gF

gF

Contact forces

Normal means perpendicular so the support force is often called the normal force.

NF

f

Support

Perpendicular to the contact surfaces

Friction

Tangent to the contact surfaces

Sliding friction (kinetic)

Non-sliding (static)

kf

sf

0

11 N 15 N 0

26 N

N hand g

N

N

F ma

F F F F

F F

F

0

11 N 15 N 0

4 N

N rope g

N

N

F ma

F F F F

F F

F

15 N

15 N

15 N block

Examples: Forces on the block

Apparent weight is the reading of the scale.It is equal to the support force the scale exerts on the person and the person exerts on the scale.

Apparent weight

( )N by scale gF ma F F forces on

the person

Friction force direction opposes the impending relative motion between two objects.

Static friction

Static friction magnitude is just enough to prevent motion.

MAX0 static static s Nf f F 10 sstatic friction coefficient

Static means the two surfaces are not sliding across each another.

Kinetic friction opposes sliding motion

Nkk Ff 0 1k kinetic friction coefficient

Kinetic friction

Friction forces do not depend on contact area.Friction depends on contact force FN .

force diagram

0.05k

k N kf F

2

180 90 90 180

40

40 0 40 9.8

0 392 392 392 0.05 19.6

40 19.6 0.49 32.65

g N k

g N k

x x k N k

y g N N

N N k

x x

F ma F F f

ma F F f

F kg a f F

NF kg F F kg F

kg

N F F N f N N

mkg a N a x m

s

Kinetic friction force causes the sled to slow down.

Example: Find sliding distance

0°a

get the directions

analyze the x and y components

Tension force

Flexible things like rope, string, cables exert tension forces.

Force direction is always tangent to the rope, etc.

Tension force has the same magnitude at each end.

Pulleys change the direction of a tension force, but not the magnitude of the force.

Newton's third law tells us that the rope exerts the same amount of force on the man as the man exerts on the rope.

To simplify things, physics ropes and cables are usually massless and pulleys are usually frictionless. The rope has no weight that needs to be considered.

Tension force

force of the rope on the block

force of the man on the rope

gF

NF

tensionF

man

tensionF

gF

0xF

0yF0F

or

Equilibrium

Equilibrium mean balanced.

For equilibrium the forces are balanced and the net force .

Velocity magnitude & direction stay the same.

0F

Select an object to analyze.

Draw a force diagram showing only the forces acting on the object, but not forces that the object exerts on other things.

Choose a set of x and y axes.

Set up balanced force equationsThe sum of the x force components add up to zero.The sum of the y force components add up to zero.

Solve for any unknown quantities.

Equilibrium Reasoning Strategy

2.2 kg

tensionF

22.2 9.8 21.56g

mF mg kg N

s

Example

find F

Object is the pulley, but first find the tension in the rope

First, select the block as the object.If the block stays at rest, then the forces acting on it are balanced. Therefore, the tension and gravity forces are balanced. ( Second law: )0F

1 2 0

180 21.56 35 21.56 35 0

F F T T

F F N N

0

0

18021.56 N

If the pulley stays at rest, then the forces on the pulley are balanced. (Second law: )0F

Second, select the pulley as the object

180 21.56 35 21.56 35 0

35.32

F F N N

F N

Fx=F cos θ Fy=F sin θ

-F 0

17.66 N 12.37 N

17.66 N -12.37 N

0 0

180F 21.56 35N

21.56 35N 0F

100

10

90

1 2100 10 3150 90 0F T T N

Engine weighs 3150 N

Example

The End