Download Notes for Unit 4

P _ Physics – Unit 4 – Newtons Laws
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Section 1:
MASS VS WEIGHT
Mass and Weight are two concepts easily confused. In this unit, we are going to be using BOTH mass and
weight. Therefore, we must clearly know the difference between them.
Mass (m) – The amount of matter in an object
Units – Kg (a gram is tiny, so the standard SI unit is Kg (1000 grams) )
The English system uses slugs (from sluggish) a more massive object is harder to move, or more
sluggish. For most of history, there wasn’t a unit for mass, since most people just used weight.
English units: Slug (for sluggish) – 1 slug = 14.6 kg
Mass doesn’t change, unless you physically add or take away pieces of the object.
Weight – The force pulling on an object. This is normally the Force of Gravity.
Fg = m ag
Fg = Force of Gravity (Weight)
M = Mass
ag = Acceleration of Gravity (ag = 10 m/s2 on Earth)
Sometimes you see Fg written as Fw for “Force Weight”. Fg and Fw are the same thing, they are the weight of
an object.
SI units: Newton (N) = 1 kg m/s2
English units – Pound. 1 pound = 4.5 N
On earth, a = 9.8 m/s2 ( we round it to 10 m/s2). However, on other planets acceleration of g is different, so
weight can change.
Also, in water, you are buoyant, so you weigh less.
Main Point: Weight can change, mass normally stays constant
The only way to change mass is to physically add or subtract matter from an object.
Where the confusion begins: On earth, gravity is always 9.8 (rounded to 10), so weight seems constant. Allot
of people confuse mass with weight. This is also compounded by the english system. The unit for mass is the
Slug (sluggish).
No one really uses a “slug” most people just equate pounds (weight) with mass.
On earth, 1 pound of weight = 2.2 kg
Examples:
1. A person has a mass of 70 kg. How much does this person weigh on Earth?
Solution:
Fg = m ag
Fg = (70kg) (10m/s2)
Fg = 700 N
2.
If that same person were on the Moon, where gravity is 6 times less, what would their mass be? What
would their weight be?
Solution:
Mass stays constant, so they would still weigh 70 kg.
Weight will Change: If ag is 6 times less than on Earth, ag = 10/6 = 1.7 m/s2
Fg = m ag
Fg = 70kg 1.67 m/s2
Fg = 116 N
(Notice this is 6 times less than their Fg on Earth)
3. A person weighs 1500N on Earth. What is this persons mass?
Fg = m ag
Solve for mass: m = Fg / ag
m = 1500 N / 10 m/s2
m = 150 Kg
4. A 50 kg person jumps into water and floats on the surface. What is their Mass and Weight in the water?
Solution:
Mass stays the same, so it’s still 50 kg.
Weight: They are floating! So they weigh nothing.
(The buoyant force of the water negates the force of gravity)
For example, if you put a bathroom scale under them in the water while they are floating, it would read 0 .
Section 2:
Newton’s 1St Law (Law of Inertia)
Newton’s 1st Law -- An object in motion will tend to stay in motion, an object at rest will tend to stay at
rest, unless acted upon by an unbalanced (external) force.
Examples:
A book sitting on a table has gravity pushing down, but the table stopping it. The forces are balanced. It will
stay there until some other force disturbes it, causing motion.
People in a car. If a car makes a sudden stop, the people still fly foreward. The people were in motion with the
car. When the car stopped, the people are still moving, so they still fly foreward.
A spacecraft launched to another planet: Once it leaves earth, the rockets shut off, and it simply coasts to the
other planet. Once in motion, it will stay in constant motion until it hits the other planet (in many cases years).
*** An object MUST have an unbalanced force acting on it in order to start its motion or stop its motion.
The 1st law is also called the Law of Inertia
Interia: The tendency for an object to resist a change in motion.
Inertia is directly related to Mass. Bigger Mass = More Inertia
This is an easy concept. For example, take two rocks, one boulder, and one pebble. Which one is harder to
kick? Obviously, the boubler is MUCH harder to kick, it has more mass, so it wants to stay are rest more than
the little pebble.
Again, lets say that boulder is rolling down the road. How hard would it be to stop? Very hard compared to the
pebble. Since it has such a large mass, once in motion it will stay in motion.
Another example: You have a brick and a styrofoam block sitting on a table. You give each one a quick flick
with your finger. Which one moves?
The brick doesn’t budge. It has MUCH more mass, and therefore more inertia, so it really
doesn’t want to move.
The styrofoam block flies off the table. It has MUCH less mass, and therefore hardly any inertia,
so even a tiny force will cause it to start moving.
Yet another Example: Sliding a book across a desk. You apply a force to start it in motion. According to the
1st law, it should stay in motion. Why doesn’t it? Because friction from the surface of the desk applies an
unbalanced force, which causes it to slow down. What if we slid it on ice? There is less friction, so it would
travel further.
 Wrap-up of 1st law: Law of Inertia
So, if an object is at rest, one must apply a force to overcome the objects inertia in order to get it to move.
If an object is moving, one must apply a force to overcome the objects inertia in order to stop it’s motion.
(demos: tablecloth pull, ball and cup, cart and flying doll, bowling ball vs pingpong ball)
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Section 3:
Newton’s 2nd Law (F=ma)
(demos: hovering globe, cart with increasing mass)
All three laws are closely related, when looking at the 2nd law, we have to consider the 1st law:
The 2nd law deals with unbalanced forces.
According to 1st law, if forces are balanced, there will not be any acceleration (no change in motion)
(do hovering globe demo)
Balanced forces:
A = 0 m/s2
Two cases:
If V = 0, the object will stay at rest
or if V ± 0, the object will stay in constant motion
(like a projectile in the X direction)
According to the 1st law, if forces are Unbalanced, the object will accelerate (change in motion)
Unbalanced forces:
A ± 0 m/s2
Newton experimented with unbalanced forces and found a relationship:
a is proportional to 1/m
and
a is proportional to Fnet
a is proportional to 1/m - makes common sense, a larger mass has more inertia, therefore it won’t change
motion as fast (a will be less)
a is proportional to F - makes common sense also, a larger force, larger disturbance, will cause a bigger change
in motion.
(do demo with cart varying masses)
Newton combined the two proportions: a is proportional to F/m - turn proportional sign to an = sign (add
constant) constant = 1.
a = F/m - Newton’s 2nd law. Often we see it written as F = ma
Weve already used this law (equation). Remember the force of gravity?
Fg = mag
Any force will equal mass times acceleration
Section 4:
Newton’s 3 Law and Freebody Diagrams
rd
Newton’s 3rd Law:
(rope “tug of war” with force readers demo)
3rd Law: For every action force there is an equal but opposite reaction force.
What this means is forces ALWAYS come in pairs.
This may sound counter intuative, but action/reaction pairs are easily seen in nature.
Swimmer in water – swimmer pushes arms back, water pushes person foreward
Birds – Wings push air down, air pushes bird up
Car – the wheels spin, pushing Backward on the road. Road pushes foreward on the car
Walking – You push backward on the ground, ground pushes you foreward.
Jumping – You push DOWN on ground, ground pushes you upward.
Student sitting on chair - Gravity pushes person down, chair pushes back up on person
Notice all of these reaction forces are OPPOSITE in direction. If measured, they are also EQUAL in
magnitude.
Just because the forces are equal, doesn’t mean the accelerations are equal:
Example:
Moon in orbit – Moon pulls on Earth, Earth pulls back on moon
The two forces are equal. However, the moons mass is MUCH smaller, so by newtons 2nd law, the acceleration
of the moon falling toward earth is MUCH grater. So the moon orbits the earth, not vice versa
(skateboard demo: raft/boat example)
This is a really important law, and the basis for constructing “FREE BODY DIAGRAMS” Diagrams used to
solve a variety of force/motion problems.
(Look at a horse and cart example:)
A FREEBODY DIAGRAM only shows the forces acting ON the object. They don’t show any forces that
are NOT acting on the object.
Example: (Fan Sail Demo)
Freebody Diagrams & problem solving
In order to sucessfully do “Newton’s laws “ problems, you should first construct a free body diagram of the
situation. This makes solving the problem much easier.
Steps:
1.
2.
3.
4.
5.
6.
Draw a freebody diagram of situation
Write a equations for total force in the X directoin and the Y direction.
Write down knowns and unknowns
Pick appropriate equation(s).
Substitute/ Sovle for appropriate variable
Plug in #’s and solve
By using freebody diagrams, we can do many applicatoins of newtons laws. Two notable ones are Friction and
Tension.
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