Dynamics

What is DynamicsWhere kinematics DESCRIBES motion ...

Dynamics studies the CAUSES of motion.

All motion can be explained by …

Force

Force is a VECTOR –

it has both ...

The magnitude of a force is measured in ...

NEWTONS, (N)

Four fundamental forcesThere are 4 fundamental forces:• Gravitation• Electromagnetism• Weak nuclear force• Strong nuclear forceAll forces that we experience in life

come either from gravitation or electromagnetism.

Types of forces

1. Applied2. Thrust3. Weight4. Normal5. Elastic

6. Tension7. Friction8. Air resistance9. Electric10. Magnetic

Some kinds of forces you will encounter include:

http://www.physicsclassroom.com/

class/newtlaws/u2l2c.cfmSummary and exercises on drawing free body diagrams.

Force and Newton’s First Law

Force and Newton’s First Law

An object will remain at rest or move with

constant velocity unless acted upon by

a net external force.

What does this mean?

A ball at rest will stay at rest unless someone kicks it.

… and …

An astronaut who is moving through space will continue to move with constant velocity unless acted upon by a force

(What kind of forces could alter the astronaut’s velocity?)

… so …

What causes this stone to stop after it leaves the athlete’s hand?

Net forcesRepulsion

Weight (mass x gravity)

There are forces on this ball.

What are they and why don’t they cause motion?

This is similar to a ‘tug of war’, which will experience no movement if both forces are equal

… similarly …Air resistance

Weight

(mass x gravity)

•As a sky diver accelerates during freefall …

•Air resistance increases

•When air resistance equals the sky diver’s weight …

•The sky diver will continue his fall at constant velocity

Task 1

• Draw graphs for• displacement and time, • velocity and time • acceleration and time

• for an object in freefall • under air resistance

Task 2

Magnetic forces are often at least as powerful as gravitational forces. Consider a 5 kg piece of iron suspended in mid-air by a powerful magnet above the piece of iron. How much force does the magnet exert on the iron?

Solution

•The iron does not move, implying a constant velocity ( v = 0 ). Thus, by Newton's First Law, the sum of the forces on the iron must be zero. In this case, there are two forces acting upon the iron: the gravitational force of the earth, and the magnetic force of the magnet. Thus F G + G M = 0 . We can calculate the gravitational force using the fact that the gravitational acceleration on earth is 9.8 m/s 2 : F G = ma = (5 kg)(9.8 m/s2) = 49 N, directed downward. the magnet must exert a force of 49 N in the upward direction.

Newton’s Second Law

Newton’s Second Law

F = ma Net Force = mass x acceleration

1N = 1kg x 1ms-2

1 Newton of force will cause a mass of 1 kg to accelerate at 1 metre/second every second

1. What does this mean?

A shuttle which applies a constant force in space will accelerate indefinitely at a constant rate

A constant force will cause a constant acceleration, NOT a constant velocity.

so why is it that a constant force …

…usually causes a constant VELOCITY, not a constant ACCELERATION?

Propulsion

V=VC

a = 0

Rolling Friction

… similarly …

If there is no net force (ie: F=0), then there is no acceleration (ie: a=0).This supports Newton’s first law…… in the absence of a net external force, (ie: F=0)

• Bodies at rest will remain at rest (since a=0)

• And bodies moving at velocity ‘v’ will continue to move at velocity ‘v’. (since a=0)

2 … also …Under the same force, larger masses will undergo

smaller accelerations …

… and vice versa

3. finally

If: F = ma, (and W = mg)Then: g = W/mSince: W is proportional to mThen: g is constant for all values

of m (and W).

W

m

What is the gradient?

What does this mean?

• It means that in a vacuum …

• All objects fall with the same acceleration

• (eg: a feather and a bowling ball).

• On earth, different accelerations are caused by air resistance.

Videohttp://article.wn.com/view/2014/11/04/Watch_a_feather_and_a_bowling_ball_fall_at_the_exact_same_sp/

Air resistance.• Air resistance is a force which

always opposes motion• It’s magnitude depends on …

• The size of the body• The velocity of the body• The viscosity of the fluid

• And is represented by the formulaF= 6[pi]Nrv

D = 6[pi]Nrv r

Drag

Weightv

N

Mass

Mass is a SCALAR.

Its magnitude is measured in kilograms, (kg)

It has no direction

Mass is the amount of matter, or ‘stuff’ that makes up a body

Weight •Mass is not weight

•Weight does not measure the matter (stuff) in your body

• It measures the FORCE that is exerted on your MASS due to GRAVITATIONAL acceleration (g)

•However, weight is used to calculate your mass

Weight (a force) is a VECTOR

–Weight’s magnitude is measured in …

–Weight’s direction is always …

From: F = ma

W = mgWeight = mass x gravitational acceleration

Weight will change in different locations due to different gravitational accelerations:

Location Earth Moon Space

g = 9.8 1.6 0

Weight80kg x 9.8 ms-2

= 784 N

80kg x1.6 ms-2

= 128 N

80kg x0 ms-2

= 0 N

In contrast …

Mass, whose matter (stuff) remains the same in all locations …

…also remains the same in all locations.

Mass and Inertia

• Mass has a property called INERTIA

• Inertia is the tendency to resist any change in motion (including direction).

• The tendency to keep moving in a straight line at constant linear velocity.

• The larger the mass, the larger its inertia.

Inertia is why …

…great effort is required to start something moving

… and less effort is required to keep it moving at the same speed

…you keep moving when your car stops

… and this happens

… (most) magicians are able to pull a table cloth from under things without pulling them all off the table.

… ships of great mass (and inertia) need to start braking at least half an hour before they want to stop.

Cars turning a corner will try to continue in its original direction (having the effect of leaning right when turning left, and vice versa)

Test on second law

Remember that Force is proportional to acceleration and not to velocity

Note also that Force and acceleration can be in opposite direction to velocity.

Try the following exercises to check whether you really understand this

Interactive:

http://www.physicsclassroom.com/Physics-Interactives/Newtons-Laws/Free-Body-Diagrams/Free-Body-Diagram-Interactive

Hard copy

http://www.physicsclassroom.com/Physics-Interactives/Newtons-Laws/Free-Body-Diagrams/Free-Body-Diagram-Exercise

Problem (part 1)

A 10 kg mass, initially at rest, experiences three forces: one North with magnitude 10 N, one East, with magnitude 20 N and one Northeast with magnitude 30 N. Find the resulting acceleration and direction of movement.

(Start by drawing a diagram)

Problem (part 2)

Assuming the forces continue to act while the object is in motion, after 10 seconds …

a) What is the object's velocity? b) How far has it traveled?

•

•

•

•

•

Solution (part 1)

•

θ

•

•

Solution (part 2)

Newton’s Third Law

Newton's third law

Every action has an equal and opposite

reaction

If object A exerts a force on object B, then

B exerts a force which is equal in size and

opposite in direction on A.

What are the action and reaction forces in the following pictures?

WARNING!

Balanced• Relates to 1st law• Is rarely the same

type of force• Relates to the

same object• Only applies during

constant velocity

Equal and opposite• Relates to 3rd law• Is always the same

type of force• Relates to 2

different objects• Applies in all kinds

of motion

Balanced forces are not the same as equal and opposite forces.

Practise1.

What are the equal and opposite forces related to this egg?

Practice

A plane is flying at constant velocity. Draw in all forces that act on the plane, together with their equal and opposite forces.

Task 1

Refer to the 12 questions on Newton’s second law. Add in all the equal and opposite forces

Summary of Newton’s Laws

Summary of Newton’s Laws

1. An object will remain at rest or move with

constant velocity unless acted upon by a

net force.

2. A constant force will cause a constant

acceleration, the magnitude of which is

inversely proportional to the body’s mass

3. Every action has an equal and opposite

reaction.

If F = 0

Then a = 0

v is constant

F = ma

FAB

= - FBA