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5.1.3 Dynamics

You should be able to:

(a) demonstrate an understanding that mass is the propertyof a body which resists change in motion.(b) define and use the equation density = mass/volume.(c) recall and use the equation F = ma, in situations wheremass is constant, appreciating that force and accelerationare always in the same direction.(d) define the newton.(e) describe and use the concept of weight as the effect ofa gravitational field on a mass.

(f) recall and use the relationship weight = massxgravitational field strength.(g) describe qualitatively the motion of bodies falling in auniform gravitational field with fluid

resistance.

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How is Mass different from Weight?

Mass Weight

The mass of an object refers tothe amount of matter that iscontained by the object.

Mass is related to "how much

stuffis there.

The mass of an object(measured in kg) will be the sameno matter where in the universe

that object is located.

The weight of an object is theforce of gravity acting upon thatobject.

Weight is related to the pull of

the Earth (or any other planet).

Weight changes according tothe gravitational field

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Mass and Inertia

Newtons First Law of Motion states that

"An object at rest tends to stay at rest and an object inmotion tends to stay in the same state of motion unless

acted upon by an unbalanced force.

" Objects "tend to keep on doing what they're doing."

This tendency to resist changes in their state of motion isdescribed as inertia.

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Newton and Galileo

The dominant thought prior to Newton's day was that it

was the natural tendency of objects to come to a restposition; a force was necessary to keep an objectmoving.

Galileo, before Newton, developed the concept of

inertia. Galileo reasoned that moving objects eventuallystop because of a force called friction.

Homework activity:Research how Galileo developed the concept of inertia.(Use keywords Galileo, inertia and friction in a websearch.)

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Imagine a place in the cosmosfar from all

gravitational and frictional influences.Suppose that an astronaut in that place throws arock. The rock will:

a) gradually stop.b) continue in motion in the same direction at

constant speed.

According to Newton'sfirst law, the rock willcontinue in motion inthe same direction at

constant speed.

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A 0.5 kg object is moving horizontally with a speed

of 4 m/s. How much net force is required to keepthe object moving at this speed and in thisdirection?

Answer: 0 NAn object in motion will maintain its state ofmotion. The presence of an unbalanced forcechanges the velocity of the object.

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Mac and Tosh are arguing in the cafeteria.

Mac says that if he flings his jelly with a greater

speed it will have a greater inertia.Tosh argues that inertia does not depend uponspeed, but rather upon mass.

Who do you agree with ? Explain why.

Tosh is correct.Inertia is that quantity which depends solely upon

mass. The more mass, the more inertia.Momentum is another quantity in Physics whichdepends on both mass and speed. Momentum will bestudied later.

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Supposing you were in space in a weightlessenvironment, would it require a force to set anobject in motion?

Yes!Even in space objects have mass; and if they

have mass, they have inertia.That is, an object in space resists changes in

its state of motion. A force must be applied toset a stationary object in motion.Newton's laws rule - everywhere!

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Mr. Simpson spends mostSunday afternoons atrest on the sofa,watching football games

and consuming largequantities of food andbeer.

What effect (if any) doesthis practice have uponhis inertia? Explain.

Mr. Simpson's inertia will increase!Mr. Simpson will increase his mass if he makes a habit

of this; and if his mass increases, then his inertia

increases.

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Ben Tooclose is being chased through the woods bya huge moose which he was attempting to

photograph. The enormous mass of the bull mooseis extremely intimidating. Yet, if Ben makes azigzag pattern through the woods, he will be ableto use the large mass of the moose to his own

advantage. Explain this in terms of inertia andNewton's first law of motion.

The large mass of the bull moose means that the bull moosehas a large inertia. Thus, Ben can more easily change his ownstate of motion (make quick changes in direction) while themoose has extreme difficulty changing its state of motion.Physics for better living!

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Two bricks are resting on edge of the lab table. ShirleySheshort stands on her toes and spots the two bricks. Sheacquires an intense desire to know which of the two bricks

are most massive. Since Shirley is vertically challenged, sheis unable to reach high enough and lift the bricks; she canhowever reach high enough to give the bricks a push. Discusshow the process of pushing the bricks will allow Shirley todetermine which of the two bricks is most massive. What

difference will Shirley observe and how can this observationlead to the necessary conclusion?

The bricks, like any object, possess inertia. That is, the bricks

will resist changes in their state of motion. If Shirley gives thema push, then the bricks will offer resistance to this push. The onewith the most mass will be the one with the most inertia; this willbe the brick which offers the most resistance. This very methodof detecting the mass of an object can be used on Earth as well

as in locations where gravitational forces are negligible for bricks.

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Density, Mass and Volume

If each ball has the samemass, which box wouldweigh more? Why?

The box that has more balls has more mass.This property of matter is called density.

Density= Mass

VolumeDensity is the amount of matter held in a unit of volume.It is usually measured in kg/m3 or g/cm3.

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Simple questionsWhat is the density ?

1. Mass = 79.4 grams Volume=29.8 cm3.2. Mass= 25.4 grams Volume=29.8 cm3.

What are thematerials ?

Material 1

Density = m/v = 79.4/29.8 =

2.66g/cm^3 (Aluminium)

Material 2

Density = m/v = 25.4/29.8 = 0.85g/cm^3 (oak wood)

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Newtons Second Law

Imagine pushing a shopping trolley.Is a full trolley harder to push thanan empty one ?Would doubling the mass of the trolleymake twice as hard to push ?

If you pushed it twice as hard would

it go faster ?Would it go twice as fast ?Is the speed proportional to theforce applied ?

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An object of mass, m, is pushed with a constant force, F,so that its velocity increases from an initial value, u,

to a final value, v, in time, t.

Change in momentum ForceTime

mv - mu F

t m(v - u ) F

tNow acceleration, a = (v- u)

t F m a

F = k m a ( k is a constant)

Make sure you use the right units: Force in N, Mass in kg, Acceleration in m/s2.

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A 70 kg athlete accelerates to hermaximum speed of 9.5 m/s in a time

of 2.5 s.What is the average force sheapplies to the track?

Work out the acceleration first:v = u + at9.5 = 0 + (a x 2.5)

a = 9.5 2.5= 3.8 m/s2

Now Use F = maF = 70 x 3.8

= 266 N

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A locomotive of mass 100tonnes is hauling a train ofwagons of mass 1200 tonnes

with a pulling force of 180 kN.What is the acceleration ofthe train?

First of all do the conversions:mass of the locomotive = 100 x 1000 = 100 000 kgmass of the train = 1200 x 1000 = 1 200 000 kgpulling force = 180 000 N

Now find the total mass of the train:Mass = mass of locomotive + mass of wagonsmass = 100 000 kg + 1 200 000 kg = 1 300 000 kgNow use F = ma180 000 N = 1 300 000 x aa = 180 000 = 0.14 m/s2

1 300 000

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The NewtonThe newton (symbol: N) is the SI unit of force,

named after Sir Isaac Newton.

It is defined as the amount of force requiredto accelerate a mass of one kilogram at a rate of one metreper second per second.

The newton is a derived unit, comprising kg m s-2.

Since weight is the force acting between two objects due to

gravity, the newton is also the unit of weight. A mass of onekilogram near the Earth's surface has a weight ofapproximately 9.81 newtons.

Rather fittingly, given the story about Newton's discovery ofgravity, one newton is about the mass of a small apple.

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Whatis

Weight ?This astronaut is weightless.

However he is still in the Earths gravitational field.

He is orbiting the Earth and is continuously fallingtowards it.

He does not feel weight because there is nothing holding

him up from the Earth.You feel your weight when you sit on a seat that holds

you up against the pull of the Earth.

Weight is experienced when an object is prevented fromfalling to the Earth.

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Weight

The weight of an object (measured in Newtons) will varyaccording to where in the universe the object is.

Weight depends upon which planet is exerting the forceand the distance the object is from the planet. Weightis dependent upon the value of g (acceleration ofgravity).

On Earth's surface, g is 9.81 m/s2. On the moon'ssurface, g is 1.7 m/s2. Go to another planet, and there

will be another g value.Also g decreases with the distance from the center ofthe planet. If g were measured at a distance of 400 kmabove the earth's surface, you would find the value of g

to be less than 9.8 m/s2.

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Complete the following table showing the relationshipbetween mass and weight.

Object Mass (kg) Weight (N)

Melon 1

Apple 0.98Pat Eatladee 25

Fred 980

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Complete the following table showing the relationshipbetween mass and weight.

Object Mass (kg) Weight (N)

Melon 1 9.8

Apple 0.1 0.98Pat Eatladee 25 245

Fred 100 980

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The weight of an object is defined as the force ofgravity on the object and may be calculated as the

mass times the acceleration due to gravity,w = mg.

At the Earth's surface, g=9.81 m/s2

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How to feel Weightless

F F ll G lil th l h t d th f th

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Free FallGalileo, the elephant and the feather.

(Actually he used a large and a small object.)

Assume there is no air resistance.TRUE or FALSE:The elephant and the feather each have the same force ofgravity.

The elelphant has more mass, yet both elephant and featherexperience the same force of gravity.

The elephant experiences a greater force of gravity, yetboth the elephant and the feather have the same mass.

On earth, all objects (whether an elephant or a feather)have the same force of gravity.

The elephant weighs more than the feather, yet they each

have the same mass.The elephant clearly has more mass than the feather, yetthey each weigh the same.

The elephant clearly has more mass than the feather, yetthe amount of gravity (force) is the same for each.

The elephant has the greatest acceleration, yet the amountof gravity is the same for each.

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All objects (regardless of their mass)experience the same acceleration when in astate of free fall. When the only force isgravity, the acceleration is the same value forall objects.

What about air resistance? Isn't itnon-realistice to ignore the influence of airresistance upon the two object? In thepresence of air resistance, the elephant is sureto fall faster.

TRUE or FALSE:

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TRUE or FALSE

The elephant encounters a smaller force of air resistance than the

feather and therefore falls faster.

The elephant has a greater acceleration of gravity than the feather

and therefore falls faster.

Both elephant and feather have the same force of gravity, yet the acceleration ofgravity is greatest for the elephant.

Both elephant and feather have the same force of gravity, yet the

feather experiences a greater air resistance.

Each object experiences the same amount of air resistance, yet

the elephant experiences the greatest force of gravity. Each object experiences the same amount of air resistance, yet the feather

experiences the greatest force of gravity.

The feather weighs more than the elephant, and therefore will not accelerate asrapidly as the elephant.

Both elephant and feather weigh the same amount, yet the greater mass of the

feather leads to a smaller acceleration. The elephant experiences less air resistance and than the feather and thus reaches

a larger terminal velocity.

The feather experiences more air resistance than the elephant and thus reaches asmaller terminal velocity.

The elephant and the feather encounter the same amount of air resistance, yet theelephant has a greater terminal velocity.

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Watch the animation of a skydiver below.

Look at what happens at different stages.

Write an explanation of what is happening,ensuring you describe all the forces and theacceleration and how they change.