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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