Dynamics- Why do objects move as they do? What

makes an object at rest, begin to move? What makes a

body accelerate or decelerate? What makes an object

move in a circle?

Force• A Force is simply a push or a pull.

• A Force gives energy to an object.

• What can that energy do? CHANGE the motion of an object.

• What do we call a CHANGE in the motion (speed or direction) of an object? ACCELERATION

• Forces are vectors with magnitude and direction.

• Not all objects will move when forces are applied to them. (push a wall!)

Measuring force

One way to measure small forces is by

use of a spring scale. As a push or pull

is applied to the spring scale attached to

a block (Or your fruit in the

supermarket), the scale reads the

measure of the force applied by

stretching a spring calibrated in

increments of force (Newtons or Dynes).

Newton’s First Law of Motion• Isaac Newton (1642-1727) built off the ideas

of Aristotle and Galileo regarding the

relationship between force and motion.

• Aristotle claimed a moving object would

come to rest if left alone.

• Galileo idealized the world to say if friction

were removed, all moving objects would

maintain their motion (speed and direction)

and moving objects slow down only when a

force is exerted on them.

Newton’s First Law Newton’s First Law of Motion is very close to

Galileo’s conclusions:

Every body continues in its state of rest or

uniform speed in a straight line unless acted on

by a nonzero net force.

The tendency of a body to maintain its state

(rest or motion uniformly) is called inertia.

Newton’s First Law is often called the Law of

Inertia.

Frames of Reference Newton’s first law does not hold for all frames of

reference.

If you are fixed in a moving car and an object is

resting on the dashboard, it may move toward you

if the car accelerates though neither you nor

anything else touched the cup to make it do that.

Inertial Reference frames are those frames where

Newton’s first law DOES hold true. Most frames

fixed on Earth are inertial.

Reference frames where this law DOES NOT hold

true are called noninertial reference frames.

Mass

Newton used mass as synonym for “quantity

of matter”.

Quantity of matter is difficult to define.

More precisely we say mass is the measure

of inertia of an object.

More mass = more inertia = more difficult to

change motion. (Converse is true also)

Weight is NOT mass

Though the mass of an object is a

relatively fixed quantity, gravity is always

present…

The force of gravity acting on a mass

gives the object “weight” which has a

magnitude and direction.

Weight is a force. Mass responding to

the force of gravity.

Your mass on the moon vs your weight?

Newton’s Second Law

Newton’s first law describes an object when

NO NET force acts on it. What happens

when there IS a NET FORCE?

A net force may increase or decrease the

speed of an object OR change its direction of

motion.

A net force gives rise to ACCELERATION.

Greater the net force, greater the

acceleration.

aF

What about mass?

The greater the mass of an object, the LESS

the acceleration for the same net force.

Mass and acceleration are inversely related.

ma

1

Newton’s Second Law summed

up “The acceleration of an object is directly

proportional to the net force acting on it and

inversely proportional to its mass. The

direction of the acceleration is in the direction

of the net force acting on the object.”

ΣF is the vector sum of all forces acting on

the body which we call the Net Force.

m

Fa maF

Components and units of Forces

• Since a force is an action capable of

accelerating an object, we need to look at each

component of any given force separately.

• In SI units, with mass in Kilograms, the unit of

force is the Newton (N) where 1N = 1kg*m/s/s

• IN the cgs system, with mass in grams, the unit

of force is the dyne where

1 dyne = 1g*cm/s/s

xx maF yy maFzz maF

Ex1: Force to accelerate a fast car

Estimate the net force needed to accelerate

a 1000-kg car at ½ g.

Solution: The car’s acceleration is a = ½ g =

½(9.80m/s2 ) ≈5.0m/s/s. We use Newton’s

second law to get the net force needed to

achieve this acceleration.

NsmkgmaF 5000)/5)(1000( 2

Ex2: Force to stop a car

What net force is required to bring a 1500-kg

car to rest from a speed of 100km/h within a

distance of 55 m?

Solution: We use Newton’s second law,

ΣF=ma, but first we must determine the

acceleration, a, which we assume is

constant. We assume the motion is along

the +x axis. We are given the initial velocity

v0 = 100 km/h = 28 m/s, the final velocity v =

0, and the distance traveled x-x0 = 55 m.

Carry it out…

From equation 2-10c, we have

So we can rearrange and solve for a we get:

The net Force required is then

Force is exerted in the opposite direction of

velocity which is what the negative sign tells.

)(2 0

2

0

2 xxavv

22

0

2

0

2

/1.7)55(2

)/28(0

)(2sm

m

sm

xx

vva

NxsmkgmaF 42 101.1)/1.7)(1500(

Newton’s Third Law of Motion

In any interaction between objects, a force is

exerted on an object by another object.

Forces come in pairs.

Newton’s Third law of motion states “whenever

one object exerts a force on a second object, the

second exerts an equal and opposite force on the

first.” Consider a hammer and a nail: The hammer

exerts a force on the nail and at the same time the

nail exerts an equal and opposite force on the

hammer.

Newton’s Third Law

Sometimes this law is paraphrased as “to

every action there is an equal and opposite

reaction.”

It is important to realize the “action” force

and “reaction” force are acting on different

objects.

Which force is which?

Consider an ice skater. Since there is very little

friction between the skates and the ice, she will

move freely if a force is exerted on her. If she

pushes on the railing, she moves backwards.

Does her push on the railing cause this? Or is it

the reaction force that causes her acceleration?

Remember, an object accelerates in the

direction of the net force acting on it…

Your turn to Practice