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If something is moving, then something MUST be pushing on it. Things don’t move all by themselves!
Aristotle
Oh, baloney! Once an object is moving in a straight line, it’s going to keep right on moving, unless it runs into something. That is, of course, as long as there is NO friction! Friction is what slows things down.Galileo
Galileo…
Galileo found that, ignoring the effect of the air, all freely falling objects had the SAME acceleration, regardless of their mass or the height from which they were dropped.
The Law of Falling Bodies
Born in Pisa 1564
Galileo described HOW things moved, but not WHY they moved that way.
Galileo wrote, “the present does not seem to be the proper time to investigate the cause of the acceleration of natural motion….”
Galileo died in 1642.
When Isaac Newton, born Christmas day, 1642, began his studies of motion in the second half of the seventeenth century, that statement was no longer appropriate.
Because Galileo had been so effective in describing motion, Newton could turn his attention to dynamics.
Dynamics is the study of why an object moves the way it does- why it starts to move instead of remaining at rest, why it speeds up or moves on a curved path, and why it comes to a stop.
Newton’s most famous book was “Principia”, published in 1687. This book first listed what came to be known as
Newton’s Three Laws of Motion
ForcesForce: a push or a pullForces are vectors. ( you push or pull in a
direction!)There are Four Fundamental Forces in our
universe1. Gravitational Force2. Electromagnetic Force3. Strong Nuclear Force4. Weak Force
The strongest of these forces is….
The Strong Nuclear Force(it holds the nucleus of all atoms
together)
The weakest of these forces is….Gravity
The unit for Force is the Newton, N
If someone was pushing on you with one Newton of Force, it wouldn’t hurt much.
One Newton of Force is about the same as the weight of a quarter pound hamburger patty.
Inertia
Inertia: an object’s resistance to a change in its motion
Mass: how you measure inertia unit: kg
Newton’s First Law of Motion:“The Law of Inertia”
An object at rest remains at rest unless a net external force acts on it.
An object in motion continues that motion unless a net external force acts on it.
If there is a net external force acting on an object, it will accelerate.
(I call this “the granddaddy of all physics equations”!)
Second Law
maFormaForm
Fa net
net
Same Force on different mass….
Third Law
For every force, there is an equal but opposite force.
Action / Reaction forces
For every force, there is an equal but opposite force.
Action / Reaction forces
For every force, there is an equal but opposite force.
Action / Reaction forces
• The gun pushes on the bullet. The bullet pushes back on the gun!
The Action / Reaction forces do NOT act on the same object.
I kick the wall (Action)
The wall kicks me back (Reaction)
• While driving down the road, an unfortunate bug strikes the windshield of a bus.
• The bug hit the bus and the bus hit the bug.
• Which of the two forces is greater: the force on the bug or the force on the bus?
For every force, there is an EQUAL by opposite force!
A child pulls on a 5.0 kg wagon with a net force of 20.0 N. What is the wagon’s acceleration?
m = 5.0 kg
Fnet = 20.0 N
a = Fnet / m
a = 20.0 / 5.0 =
a = 4 m/s2
A dog pulling a man on a sled over ice can accelerate the sled at 2 m/s2. If the sled and man have a combined mass of 150.0 kg, what was the net force on the sled?
m = 150.0 kg
a = 2 m/s2
Fnet = ma
Fnet = 150.0 kg x 2 m/s2 = 300 N
When released, the lift provides a net force of 6 N on a 2 kg balloon. If it started at rest, how fast will it be moving in 4.0 s?
Fnet = 6 N m = 2 kg
vo = 0 t = 4 s
vf = ?
vf = vo + at, so we need “a”.
a = Fnet / m
a = 6 / 2= 3 m/s2
vf = 0 + 3 x 4
vf = 12 m/s
A 1500 kg. car starts from rest and is moving at 10 m/s after 5.0 s. What was the net force on the car?
m = 1500 kg
Vo = 0
Vf = 10 m/s
t = 5.0 s
Fnet = ?Fnet = ma, so we need to find the acceleration.
vf = vo + ata = ( vf – vo) / ta = (10 – 0) / 5 = 2 m/s2
Fnet = maFnet = 1500 kg x 2 m/s2
Fnet = 3000 N
More than one force can act on an object at the same time. For example, two people could push on a book at the same time. One person could push toward the left and the other could push toward the right. In this case the two forces would act against each other.
What is the NET force?
2 N towards the left
If the book had a mass of ½ kg, what would be its acceleration?
a = Fnet / m
a = 2 / .5
a = 4 m/s2 (left)
What if the opposing forces were equal?
What is the net Force?
What is the acceleration?
What if the forces were in the same direction?
What is the net force?
If the book had a mass of 2 kg, what is its acceleration?
a = Fnet / m
a = 14 / 2 = 7 m/s2
• What are the unknown forces for the given net force?
Forces on an AirplaneWhen Lift is larger than Weight, the plane will….When Weight is larger than Lift, the plane will…When Thrust is larger than Drag, the plan will….When Drag is larger than Thrust, the plane will….When Thrust = Drag, the plane will…When Lift = Weight, the plane will….
We usually label forces as negative or positive.
Forces upward are positive.
Forces downward are negative.
Forces to the right are positive.
Forces to the left are negative
+
-
-
+
What is the net Force?
- 6 N + 18 N = + 12 N
What is the acceleration?
a = Fnet / m
12 / 3 = 4 m/s2
3 kg 18N6N
What is the net Force?
- 6 N – 15 N + 18 N = - 3 N
What is the acceleration?
a = Fnet / m
a = - 3 N / 3 kg = - 1 m/s2
3 kg 18N6N
15N
Weight
Weight, Wt. is the gravitational force on an object
Weight = mass x gravity
W = mgSince weight is a force, it is measured in
Newtons, N
Remember, “g” on Earth is 9.8 m/s2(10 m/s2)
What is the weight of a 42 kg child on Earth?
W = mg m = 42 kg
W = 42 kg x 10 m/s2
W = 420 N
What is the mass of a 15000 N car?
W = mg
m = W / g
m = 15000 N / 10 m/s2
m = 1500 kg
Remember, one Newton is not a very big force (about the same as a ¼ pound).
So, your weight in Newtons is MUCH bigger than your weight in pounds!
In fact, you would have to multiply your weight in pounds by 4.45 to get your weight in Newtons.
How much do you weigh in Newton’s?
Even if you weigh 550 Newtons,
You still wouldn’t be much of a Sumo Wrestler!
(that’s only around 120 lbs)
A car weighs 1680 N on Earth. What is its mass?
W = mg
m = W / g
m = 1680 N / 10 m/s2
m = 16.80 kg
A parachute provides a lift force of 400 N on a parachutist that weighs 500 N. What is the net force on him?
-100 N
What is his acceleration?
a = Fnet / m
What is his mass?
a = -100 / 50
a = -2 m/s2
Tension
Tension, T, is the force that cables, ropes, and strings pull with.
A child pulls up on a string that is holding 2 fish of total mass 5 kg. If he is providing a tension of 60 N, what is the net force on the fish?
Fnet = + T – W
Fnet = 60 N – 50 N
Fnet = 10 NWhat is the acceleration of the
fish?
a = Fnet / ma = 10 / 5a = 2 m/s2
One child pulls up on a box with a force of 19 N. Another child pulls down on the box with a force of 5 N. What is the net Force?
Hold on, there’s another force not drawn!
The gravitational force of weight is pulling down!
Wt = mg, (g = 10 m/s2)Wt = 2 kg x 10 m/s2 = 20 NDraw the weight vector also!Now, what is the net Force?Net force = +19 N – 5 N – 20 N =Net Force = - 6 NWhat is the acceleration?a = Fnet / m =a = - 6 / 2a = -3 m/s2 It will accelerate downward.
2 kg
19 N
5 N
mg = 20 N
A child pulls a 5 kg bucket out of well with a rope. If the bucket accelerates upward at 1.2 m/s2, what is the tension in the rope?
m = 5 kg
a = 1.2 m/s2
T = ?
F = ma
T – mg = ma
T = ma + mg
T = 5 x 1.2 + 5 x 9.8
T = 55 N
T
mg
If the box is not moving up or down, then the Normal force must by equal to the Weight
Weight = mg
Normal force, N
But… what if you were moving up or down?
The Normal force would NOT be equal to your weight if you’re accelerating up or down. And… your weight seems to change!
A 50 kg woman steps on a scale in an elevator that accelerates upward at 1.5 m/s2.
What is her REAL weight?
mg = 500 N
What is her APPARENT weight?
F = ma
N – mg = ma
Her APPARENT weight is what she feels like she weighs, given by the Normal force, N.
N = ma + mg
N = 50 x 1.5 + 500
Apparent weight = 575 N
mg
N
Apparent Weight
When you ride an elevator, you “feel” heavier or lighter than you actually weigh because of the acceleration of the elevator.
Your “apparent weight” is found by taking your REAL weight, mg, and adding the term ma, where “a” is your acceleration
Apparent weight = mg + ma
Do falling objects REALLY accelerate toward the Earth at 9.8 m/s2?
No, because of air resistance.Air resistance is a force that
pushes up on an object as it falls.
The faster you fall…The greater the air resistance.Eventually, the air resistance
pushing up on you is just as large as your weight that is pulling down on you!!
The faster the man falls, the more air resistance pushes up on him. Eventually, there will be just as much air resistance pushing up on him as his weight pulling him down. What will be the NET force acting then?What will be his acceleration?
Once the air resistance pushing up is as large as the weight pushing down, the NET force acting on you is ZERO!
If the net force is zero, what is your acceleration?
ZERO!
This doesn’t mean you stop in mid air. But it does mean that you stop accelerating!
You still continue to fall towards the Earth, but you don’t pick up any more velocity- you continue to fall towards the Earth at the same velocity.
This speed is called your “terminal velocity”
You will reach your terminal velocity when
Air resistance = your weight
Which one will have a faster terminal velocity?You don’t reach terminal velocity until the air
resistance grows to as large a force as your weight.
The more massive skydiver will have a faster terminal velocity and hit the ground at a faster speed
The “Normal” Force, N
When an object is pressed against a surface, the surface pushes back. (That’s Newton’s 3rd Law)
This “push back” from the surface is called the Normal Force, N
The word “normal” in math terminology means “perpendicular”
The surface pushes back in a direction that is perpendicular to the surface.
If the box is not moving up or down, then the Normal force must by equal to the Weight
Weight = mg
Normal force, N
Friction, f
• A force that always opposes motion• Depends on two things: the roughness of
the surfaces and how hard they are pressed together.
f = N , mu- the “coefficient of friction” tells how
rough the surfaces are.N, the Normal force tells how hard the
surfaces are pressed together
Example: How large is the frictional force between 2 surfaces if the coefficient of friction is 0.2 and the Normal force is 80 N?
f = Nf = 0.2 x 80
f = 16 N
There are two kinds of friction:
“static friction” (not moving) must be overcome to initiate motion.
“kinetic friction” must be overcome while an object is moving
Static friction > Kinetic friction
Weight = mg
Normal force, N
FA = 30 N m = 2 kg = 0.4 a = ?
Fnet = ma f = NN = mg = 2 x 10 = 20Nf = N = 0.4(20) = 8N
Horizon: Fnet = FA - f 30N – 8N = 22N
a = Fnet / ma = 11 m/s2
FAf = N = 30 N
You pull on a box with an applied force of 30 N. The coefficient of friction is 0.4. If the mass of the box is 2 kg, what is its acceleration?
1. Draw the box and all FOUR forces acting on it.2. Write what you know and don’t know.3. Write the equations, Fnet = ma and f = N 4. Calculate the Normal force and the friction force.5. Calculate the value of the net Force and then the
acceleration.
