1. This Week Forces on an object Newtons laws
Relating force to acceleration
Mass and Weight
What’s the difference?
Friction good and bad
A necessary evil.
Reaction /action
What makes us walk or a car move
Riding in an elevator
What we feel going up and down
Sailing Up Wind
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2. What causes motion
In our everyday life we observe that objects change their state of motion. In fact everything that happens in the Universe results from a change in motion. That is a static inert object does not contribute to any of the things we consider to be useful. The functioning of our body depends on continual change throughout our bodies.
These changes are produced by forces and in our everyday life there are just two forces.
Gravity acts on mass
Electric charge
F = Gm1m2/r2
F = kq1q2/r2
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3. Newtons Second and First Law
Second Law
The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass. The acceleration is in the same direction as the force
F = ma F and a are vectors
unit is a Newton (or pound) 1lb = 4.448N
First Law
An object remains at rest or in uniform motion in a straight line unless it is acted on by an external force.
F = 0 a = 0 so v = constant
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4. Force at the earths surface
F = GMEm/rE2
But F = ma = mg so g = GME/rE2
Famous experiment by Cavendish
Measured F = Gm1m2/r2 using two known masses in the laboratory and so measured G
Then using g = GME/rE2 he determined the mass of the earth rE
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5. Mass and weight
Newtons second law enables us to measure relative mass. If we apply the same force to two objects and measure the accelerations then.
F = m1a1 and F = m2a2 so m1/m2 = a2/a1
We then need to have one mass as a calibration and a kilogram is the mass of a piece of platinum held in Paris.
Since gravity acts proportional to mass
then the force near the earths surface is
F = mg this is the weight of an object
so if we compare
F1 = m1g and F2 = m2g then
weight 1/weight 2 = m1/m2
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6. Inertia
Inertia = tendency of an object to resist changes in its velocity.
Since F = ma and a = Δv/t then Ft = mΔv
So if a force acts for a time t the change in velocity will be smaller for larger masses so it is mass that determines inertia.
In particular if t is very small and m is large then F can also be large but Δv can still be very small.
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7. How to remove the paper without toppling the rod ?
1F-04 Brass Rod (Inertia)
How to remove the paper without toppling the rod ?
One needs to remove the paper quickly so that the frictional force only lasts for a short time and the inertia of the rod prevents it from toppling over.
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8. 1F-05 Coin, Hoop & Milk Bottle (Inertia)
How can you get the coin into the bottle without touching it ?
Don’t know WHY??!!
This is actually a trick which depends on hitting the ring so that the top deflects down and the coin is free to drop
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9. 1F-06 Inertial Ball
Case 1: Place the aluminum rod in the
lower loop and pull SLOWLY downward.
Case 2: Use the wooden mallet to
strike a sharp blow to the aluminum rod.
Which string breaks first ?
IF IT IS DONE SLOWLY THE UPPER STRING BREAKS FIRST BECAUSE THE TENSION IN THAT STRING WILL BE THE WEIGHT OF THE BALL PLUS THE TENSION IN THE LOWER STRING.
IF THE LOWER STRING IS STRETCHED SUFFICIENTLY RAPIDLY, IT WILL REACH ITS BREAKING POINT BEFORE THE BALL HAS A CHANCE TO MOVE APPRECIABLY.
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10. Why does it work less well as the stack gets shorter ?
1F-02 Stack of Washers
This is a demonstration of Inertia where a washer can be removed from a stack if the blow is fast.
Why does it work less well as the stack gets shorter ?
Strike the stack quickly. So the friction will be very short-lived and the stack will not gain speed before the force is gone.
THIS TENDENCY TO RESIST CHANGES IN THEIR STATE OF MOTION IS DESCRIBED AS INERTIA. MASS IS A MEASURE OF THE AMOUNT OF INERTIA. SO FOR A FIXED FRICTIONAL FORCE ACTING FOR A SHORT TIME. THE BIGGER THE MASS, THE LESS IT WILL MOVE.
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11. Can the table cloth be removed without breaking any dishes ?
1F-07 Table Cloth Jerk
Can the table cloth be removed without breaking any dishes ?
THERE IS A FORCE ACTING ON THE DISHES, BUT IT LASTS FOR A VERY SHORT TIME. COMBINED WITH THE RELATIVELY LARGE MASS OF THE DISHES, THIS FORCE IS OVER SO QUICKLY AND IS SO SMALL THAT THE DISHES HARDLY MOVE.
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12. Is it possible to get the eggs in the beakers without touching them ?
1F-03 Egg drop
Is it possible to get the eggs in the beakers without touching them ?
IF THE PAN IS HIT SHARPLY A FORCE WILL ACT ON THE EGGS FOR A VERY SHORT TIME AND THEY WILL NOT MOVE HORIZONTALLY. THE PAN HAS TO BE HIT HARD ENOUGH SO THAT HAS MOVED OUT OF THE WAY BEFORE THE EGGS DROP ANY APPRECIABLE DISTANCE
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13. Friction
In our everyday world any object which is moving feels a force opposing the motion this is friction.
An object which is sliding
The air resistance on your car
These types of friction result in energy being lost and minimizing friction is very important. But:
Friction is also useful and essential since with no friction
a car would not move but just spin it’s wheels
a car would not be able to turn a corner
we would not be able to walk
objects would slide off surfaces unless perfectly horizontal
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14. Force diagrams When we are analyzing a particular object we
have to take into account all
the forces acting on the body both in magnitude and direction.
The acceleration of the object is equal to F/m in the direction of F where F is the net force acting.
As in the example above we know that if we want to move an object that there is a force called friction which opposes what we want to do.
In the case shown the 10N force is + and the 2N force - so the net force is 8N and 8 = 5a
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15. Terminal velocity Fair Ftire Freaction – Fair = ma Freaction v Ff
As an object moves through the atmosphere the air exerts a frictional retarding force which increases with velocity. So an object that is dropped from a great height first accelerates at 9.8m/s2 but this acceleration decreases until the retarding force = mg and at that point the acceleration is zero and the object has it’s terminal velocity.
Could a penny dropped from the top of the Empire State building Kill you? How about a pen?
When a car is moving at constant speed on the highway the forward force produced by the engine is balanced by the frictional force of the air. v mg
Mg – Ff =ma
Ftire
Freaction
Fair
Freaction – Fair = ma
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16. Reaction action: Newtons Third Law
For every force that acts on a body there is an equal and opposite reaction force.
You pull on the block the block pulls back on you
The floor exerts a frictional force holding the block back
The block exerts a frictional force on the floor trying to move the floor to the right.
The block accelerates providing F > Ff F Ff
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17. Force analysis
To analyze the motion of an object we need to draw a diagram and put in all the forces that are acting on the object.
We will only deal with problems that have an acceleration along a single axis. The net force along an axis perpendicular to this axis is zero
DRAW A FORCE DIAGRAM
We normally choose + in the direction of the acceleration. We now can use the equations
F = ma v = v0 + at d = v0t + ½ at2 v2 = v02 + 2ad F Ff
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18. Reaction action forcesmg N
For the book
Nt = mg
DRAW A FORCE DIAGRAM
For the table
Nearth = mg + mtableg mg Ne
mtableg
For a stack of plates or a brick wall and even a mountain each layer has to support the weight of everything higher. So for a stack of 48 plates the force on the second plate from the top is mg. For the bottom plate it is 47mg but of course each plate has a net force of mg to balance it’s own weight.
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19. 1H-02 Fan Cart (Action-Reaction)
Can a fan attached to a cart propel the cart?
What if the sail is removed?
Action
Reaction
In which direction will it move ?
What if the sail is canted at an angle ?
Someone is stranded in a boat but has a battery-operated fan. The stranded party decides to direct the fan toward the sail and propel the boat home. Will this work? What if the sail is canted at an angle so that the air strikes the sail at an angle rather than dead on?
INTERNAL FORCES IN A SYSTEM CANCEL EACH OTHER WHEN THE SYSTEM AS A WHOLE IS CONSIDERED. SO IF THE SAIL IS PERPENDICULAR THE FAN DOES NOT MOVE.
IF THE SAIL IS REMOVED THE FAN MOVES IN THE OPPOSITE DIRECTION TO WHICH IT BLOWS AIR. THE FAN WOULD NOT MOVE IN OUTER SPACE.
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20. 1H-03 CO2 Rocket ROCKET PROPULSION !
Imagine that you are sitting in a cart with a pile of bricks.
How could you use the bricks to get yourself and the cart to move ?
What would happen if you throw a brick out of the cart ?
Then you throw out another .
What if you throw smaller bricks faster and more frequently ?
Now, if the bricks were the size of molecules. . .
What happens when the fire extinguisher rapidly “throws” out CO 2 molecules ?
THIS IS DIFFERENT THAN THE FAN CART. CO2 IS EXPELLED AT HIGH VELOCITY AND IN TERMS OF FORCES THE REACTION FORCE CAUSES THE CART TO MOVE IN THE OPPOSITE DIRECTION. THE QUANTITY CALLED MOMENTUM IS CONSERVED AND THE MASS OF THE CO2 X AVERAGE SPEED = TOTAL MASS OF THE CART X AVERAGE VELOCITY. THIS IS HOW A ROCKET IS ACCELERATED AND IT WORKS IN OUTER SPACE.
Because the repulse
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21. 1H-04 Hero's Engine A glass bulb emits steam from small nozzles
Same Principle causes a Lawn Sprinkler to Turn.
A glass bulb emits steam from small nozzles
What happens when the Glass Bulb begins to emit steam ?
Reaction = Bulb Spins
Action = Ejects Steam
THE REACTION FORCE TO THE EJECTION OF MASS CAUSES THE OBJECT TO SPIN. THIS IS THE SAME AS THE CO2 ROCKET IN THAT MATERIAL IS EXPELLED AT HIGH VELOCITY
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22. mg WALL mg 1J-04 Scale Paradox 1 mg T = mg mg T = mg
A Scale Measures the Force acting on it
NOW, What is the reading on the scale ? mg
WALL
What is the reading on the scale ? mg mg
T = mg T T mg
T = mg mg
THE TENSION IN THE CORD IS THE SAME FOR BOTH CASES. THE SCALE MEASURES THE TENSION IN THE CORD. FOR EXAMPLE THE TENSION IN A ROPE IS THE SAME IF TWO PEOPLE PULL ON EACH END WITH FORCE F OR IF ONE PERSON PULLS WITH FORCE F TO A ROPE TIED TO A WALL. mg
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23. Forces in an elevator W = mg = true weight with no acceleration
N = apparent weight
N – mg is the net force taking + to be up
N – mg = ma is the equation of motion
If N > mg a is positive and the apparent
weight is > than the true weight
If N < mg a is negative and the apparent
weight is less than the true weight
IRRESPECTIVE OF THE DIRECTION OR MAGNITUDE OF THE VELOCITY mg N g +
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24. Connected objects T Both objects have the same acceleration
The coupling pulls back on the 4kg mass but accelerates the 2kg mass.
30 – 8 – T = 4a T – 6 = 2a
Or 30 – 8 – 6 = 6a a = 16/6 m/s2 T = 68/6N
If I have a freight train with 100 cars each of mass m then for the coupling between the engine and the first car
T1 = 100ma
And between the last two cars T99 = ma or 100 times less
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25. Connected objects 6mg 7mg F4 = 4ma F3 = 3ma F
In the example shown each brick has a net upward force = mg down.
But each brick has to support all the bricks above it. So the 7th brick has a downward force on it’s top surface of 6mg and an upward force of 7mg on it’s bottom surface.
In the example shown of 7 equal mass objects being accelerated
F = 7ma. The tension in each coupling pulls back on the mass ahead and accelerates the mass behind.
So F4 =4ma but the net force on block 4 is 4ma – 3ma = ma. So the net force on each block is ma but the tension in each coupling reduces by ma as one goes down the chain.
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26. Acceleration of a car Fair Freaction – Fair = ma Ftire Freaction
Generally Fair is proportional to v2 so the difference between 55mph and 80mph is a factor of This means you use 2.16 more gasoline to cover the same distance
Travel from Indianapolis to Lafayette a distance of 60 miles
Car does 30miles/gallon at 55mph gas costs $4/gallon
At 55mph use 2 gallons cost 8$ time = minutes
At 80 mph use 4.32 gallons cost $ time = 45 minutes
Cost of saving minutes = $9.28
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27. Summary of Chapter 4 Forces are responsible for all physical phenomena
Gravitation and the electromagnetic force are responsible for all the phenomena we normally observe in our everyday life.
Newton’s laws F = ma where F is net force
v = v0 + at d = v0t + ½ at d = ½(v + v0)t v2 = v02 + 2ad
Every force produces an equal and opposite reaction
Weight = mg where g = 9.8m/s2 locally
Apparent weight in an elevator depends on the acceleration
a up weight is higher a down weight is lower
If your weight becomes zero it’s time to worry because you are in free fall!!
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28. Sailing Up Wind The force on the sail
balances out the force on the keel and leaves a component of force “against the wind”. Then F = ma and the boat will increase speed until the component of the wind force equals the drag force
The sail and keel forces are like lift forces on an airplane wing
An example is when the boat is moving perpendicular to the wind the force of the winds on the sails remains constant. The sails are set at about 450 to the direction of motion and the wind. The boats equilibrium speed is determined by the resistance to the motion. If the resistance can be made small the boat speed can be very high. Sail iceboats have very little resistance and reach speeds in excess of 90mph with wind speeds of 30mph
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29. Questions Chapter 4
Q8 A 3-kg block is observed to accelerate at a rate twice that of a 6-kg block. Is the net force acting on the 3-kg block therefore twice as large as that acting on the 6-kg block? Explain.
The net force is the same
Q9 Two equal-magnitude horizontal forces act on a box as shown in the diagram. Is the object accelerated horizontally? Explain. -F F
No the net force is zero
Q10 Is it possible that the object pictured in question 9 is moving, given the fact that the two forces acting on it are equal in size but opposite in direction? Explain.
Yes, constant velocity
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30. Q18 The acceleration due to gravity on the moon is approximately one-sixth the gravitational acceleration near the earth’s surface. If a rock is transported from the earth to the moon, will either its mass or its weight change in the process? Explain.
It’s mass will not change but it’s weight wil be 6 times less
Q22 The engine of a car is part of the car and cannot push directly on the car in order to accelerate it. What external force acting on the car is responsible for the acceleration of the car on a level road surface? Explain.
Ftire
Freaction
Fair
It’s the reaction force between the tires and the road
Q23 It is difficult to stop a car on icy road surface. It is also difficult to accelerate a car on this same icy road? Explain.
Because of a lack of friction the wheels will skid or spin
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31. Q25 When a magician performs the tablecloth trick, the objects on the table do not move very far. Is there a horizontal force acting on these objects while the tablecloth is being pulled off the table? Why do the objects not move very far? Explain.
Yes but the force acts for a very short time and the objects start to move, then when the cloth is gone friction stops them. • m2 m1
Q30 Two masses, m1 and m2, connected by a string, are placed upon a fixed frictionless pulley as shown in the diagram. If m2 is larger than m1, will the two masses accelerate? Explain.
Yes m2 will fall and m1 will rise
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32. Q31 Two blocks with the same mass are connected by a string and are pulled across a frictionless surface by a constant force, F, exerted by a string (see diagram).
A. Will the two blocks move with constant velocity? Explain.
B. Will the tension in the connecting string be greater than, less than, or equal to the force F? Explain. F
A. They will accelerate F = ma
B. The tension will be less
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33. Q33 If you get into an elevator on the top floor of a large building and the elevator begins to accelerate downward, will the normal force pushing up on your feet be greater than, equal to, or less than the force of gravity pulling downward on you? Explain. mg N g + a
N – mg = ma but a is negative so N is smaller than mg
The only force pulling you down is gravity so if you are accelerating down the force due to gravity must be larger than the reaction force N ( N is apparent weight)
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34. Ch 4 E4 Net force = 75 N a = 75/2.5 = 30 m/s2
A 2.5kg block is pulled with a force of 80N and friction is 5N
a) What is the acceleration?
5 N
2.5 kg
80 N
Net force = 75 N a = 75/2.5 = 30 m/s2
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35. Ch 4 E6 a) F = ma = 6 x 3 = 18 N b) F = P – Ff Ff = 2N
A 6kg block is being pushed with a force P and has an acceleration of 3.0m/s2
What is the net force?
If P is 20N what is Ff?
6 kg P
a = 3m/s2 Ff
a) F = ma = 6 x 3 = 18 N
b) F = P – Ff Ff = 2N
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36. Ch 4 E14 F = 4 x 9.8 – 15 F = ma = 24.2 N a = 24.2/4 = 6.05m/s2
A 4kg rock is dropped and experiences
air resistance of 15N
a) What is the acceleration?
4 kg Mg
15 N
F = 4 x 9.8 – 15
F = ma = 24.2 N
a = 24.2/4 = 6.05m/s2
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37. Ch 4 E16 a) Gravitational Force = mg = 3.92 N
0.4 kg N
6 N g
A vertical force of 6N presses on a book.
What is the gravitational force?
What is the normal force ?
a) Gravitational Force = mg = 3.92 N
b) Upward Force = = 9.92 N
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38. Ch 4 E18 a) Net Force F = Ma = 60 x 1.2 = 72 N
m = 60 KG
a = 1.2 m/s2 mg
A 60kg person is in an elevator
With an upward acceleration of
1.2m/s2
a) What is the net force?
b) What is the gravitational force?
c) What is the normal force?
a) Net Force
F = Ma = 60 x 1.2
= 72 N
b) mg = 60 x 9.8 = 588 N
c) N = = 660 N
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39. Ch 4 CP4 a) Net Force = 60 x 9.8 – 500 = 588 – 500 = 88 N
A 60kg crate is lowered from a height of 1.4m
and the tension is 500N
Will the crate accelerate?
What is the acceleration?
How long to reach the floor?
How fast does the crate hit the floor?
500 N
60 kg g
a) Net Force
= 60 x 9.8 – 500
= 588 – 500
= 88 N
b) Will accelerate down
a = 88/60 = 1.47 m/s2
c) d = 1/2 at t = 1.38s
d) v = v0 + at v = 2.03 m/s
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40. Ch 4 CP6 a) True weight = mg = 60 x 9.8 = 588 N
A 60kg person accelerating down at 1.4m/s2
What is the true weight?
What is the net force?
What is N?
What is the apparent weight?
a, b, c, d with 1.4m/s2 up? Mg
1.4 m/s2 N
a) True weight = mg
= 60 x 9.8 = 588 N
b) Net Force = Ma = 84 N
c) N = 588 – 84 = 504 N
d) 504 N
e) ↑1.4 m/s2
Net Force = 84 N↑
N = = 672 N
W = 672 N
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41. Review Chapters 1 - 4 - + x d
Units----Length, mass, time SI units m, kg, second
Coordinate systems
Average speed = distance/time = d/t
Instantaneous speed = d/Δt
Vector quantities---magnitude and direction
Magnitude is always positive
Velocity----magnitude is speed
Acceleration = change in velocity/time =Δv/Δt
Force = ma Newtons
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42. Conversions, prefixes and scientific notation
giga
1,000,000,000
109
billion
mega
1,000,000
106
million
kilo
1,000
103
thousand
centi
1/100
0.01
10-2
hundredth
milli
1/1000
0.001
10-3
thousandth
micro
1/1,000,000
1/106
10-6
millionth
nano
1/1,000,000,000
1/109
10-9
billionth
1 in
2.54cm
1cm
0.394in
1ft
30.5cm 1m
39.4in
3.281ft
1km
0.621mi
1mi
5280ft
1.609km
1lb
0.4536kg
g =9.8
1kg
2.205lbs
g=9.8
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43. Speed, velocity and acceleration
v = Δd/Δt a = Δv/Δt
The magnitude of a is not related to the magnitude of v
the direction of a is not related to the direction of v 1 2 3 4
v = v0 + at constant acceleration
d = v0t + 1/2at d,v0 v,a can be + or -
d = 1/2(v + v0) t v2 = v02 + 2ad
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44. One dimensional motion and gravity
v = v0 + at d = v0t + 1/2at d = ½(v + v0)t
v2 = v02 + 2ad +
g = -9.8m/s2 +
At the top v = 0 and t = v0/9.8
At the bottom t = 2v0/9.8
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45. Equations
v = v0 + at d = v0t + 1/2at d = ½(v + v0)t v2 = v02 + 2ad
Sometimes you have to use two equations.
v0 = 15m/s v = 50m/s What is h?
v = v0 + at
50 = t t = 3.57 s ` h = v0t + 1/2at2
h = 15 x /2x9.8x3.572
= 116m
h = ½( ) x 3.57 = 116m v0 h g v
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46. Projectile Motion axis 1 v1 = constant and d1 = v1t
axis vv = v0v + at and d = v0vt + 1/2at2 v1 g h v R
9.8m/s2
Use + down so g is + and h is h = v0vt + 1/2at2
v0v = 0, t2 = 2h/a R = v1t v = v0v + at
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47. Complete Projectile highest point the vertical velocity is zero
v0v
9.8m/s2
v0v
highest point the vertical velocity is zero
vv = v0v + at so t = v0v/9.8 h = v0vt + 1/2at2
end t = 2v0v/9.8 and R = v1 x 2v0v/9.8
and the vertical velocity is minus v0v
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48. Newton’s Second and First Law
Second Law F = ma unit is a Newton (or pound)
First Law F = 0 a = 0 so v = constant
Third law For every force there is an equal and opposite reaction force mg N
Weight = mg F Ff
F = ma v = v0 + at d = v0t + ½ at2 d = ½(v + v0)t v2 = v02 + 2ad
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49. Examples + T N 30 – 8 – T = 4a T – 6 = 2a g 30 – 8 – 6 = 6a mg
N – mg = ma
a N > mg
a – N < mg
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