Download PES 1110 Fall 2013, Spendier Lecture 9/Page 1 Today

PES 1110 Fall 2013, Spendier
Lecture 9/Page 1
Today:
- Introduction to forces
- Newton’s 1st Law
- This week Friday, Quiz 2
- online you have the cover sheet of the quiz with the equations I will give you
- make sure you know how to the HW problems on 2D motion (applying
equations of motion) and projectile examples – even ground, uneven ground,
launching objects at an angle.
Enough of kinematics – we are now moving on to dynamics. Why do things move? What
causes motion?
Dynamics - Why objects move.
In 1687 Sir Isaac Newton published the Philosophiæ Naturalis Principia Mathematica.
The Principia details how all motion can be explained by one of three simple statements
= Newton’s Three Laws of Motion.
Sir Isaac Newton (1642-1727)
British Physicist, one of the
most famous Physicists we
know.
Exceptions
These three laws are still in use but today we know that they don’t correctly predict
everything. They need modification in two situations:
– if something goes really fast – order of speed of light – Newton’s Three Laws of
Motion don’t work.
– For really small things atomic sized objects, they don’t work either .
Einstein’s theory of relativity: When an object’s velocity approaches the speed of light Quantum Mechanics: Motion of atomic-sized objects - (Also started by Einstein).
What we are learning in this class this semester is classical mechanics. Unless you want
to become a Physicist or Chemist, you will spend your entire life doing classical
mechanics, so it is not a waste of time to learn classical mechanics since you will be
using it – and there are only two cases when Newton’s laws don’t work.
PES 1110 Fall 2013, Spendier
Lecture 9/Page 2
Force
Underlying all three of Newton’s Laws is the concept of force.
If I want to move a table, what do I have to do to it? I have to push it, I have to apply a
force. I have to either push it or pull it. That’s it. Because it is simple it makes it profound
Force, F - push or pull exerted by some agent, Force is a vector
Two types of forces:
Contact Forces - Two objects in physically in contact (grap a cart, pull something).
Long-range Forces - Act at a distance. Examples = gravity,
Contact force is not the only type of force we have in nature. What happens if I release
this eraser? It falls. Why does it fall? Gravity pulls it down. So gravity is a pull. Hence
there is a force of gravity. What is pulling the eraser? It for sure is not a contact force. In
this example, the earth is pulling resulting in a long range force. You could say that the
earth is reaching out with invisible fingers and is pulling the eraser down.
This term gravity is the only long range force we will be using this semester. Next
semester in Physics II, you will work with two other long range forces: Electric force
(two charged particles push and pull each other) and Magnetism (two magnets push and
pull on each other)
Weight - w , Force on an object due to gravity.
When we use the term weight, we mean something particular. When you weigh yourself,
you step on a scale. You push down on it. Really gravity is pulling down on you and you
exert a force on the scale. This downward pull is the gravitational force. We will see that
weight and mass are not the same things.
So weight is a force, hence weight is a vector
Unit of Force (weight):
U. S. Customary: Pound (lb)
S. I. : Newton (N),
This is how we honor great Physicists – we name units after them.
1N = 0.22 lb (on Earth) if you go some place else your weight is different
Just for fun, go to burger king and you ask for “one Newton Burger” and see what they
will do
In can only think of one problem in this term were there is only a single force acting
on an object. Every other problem will be more than one. Right now there are at
least two individual forces acting on me, there are at least two individual forces
acting on you. So how do we deal with the situations when there are multiple forces?
This is will be used on every thing HW problem
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Superposition:
You will see a lot of boxes this semester, so if I exert a single force on it F1 it moves. If I
exert three forces on it simultaneously – how do I figure out how it moves? I will draw a
force diagram and then apply the principle of superposition. This states that to find the
net result of two or more forces, I add the forces together.
Superposition, is the net result of two or more forces and is given by a vector sum
For three forces the net force is: ∑ F = F1 + F2 + F3
When I push on the table, I push with a certain magnitude given in Newtons and I also
can push in different direction. To add forces, I add them vectorially by components.
We replace here the three forces wit a single force - ∑ F - the vector sum. For now until
chapter 9 or 10 we always assume that the net sum of forces will be applied at the center.
This is because there can be two effects when force is applied to an object:
1) Force can make something slide
2) Force can make something spin/ rotate
At the moment, we don’t want to deal with rotating object, only with objects that slide on
a surface or hang. So we have to apply the force at the center to make it slide back and
forth up and down and any combination – no rotation
Superposition Exercise
A box is subjected to the two forces, F1 and F2 shown. Which of the following correctly
shows the net force, ∑ F , acting on the box?
Notice at I drew the arrows from the center of the box – what is the net force using
pictorial vector addition?
PES 1110 Fall 2013, Spendier
More Superposition Exercises:
Lecture 9/Page 4
PES 1110 Fall 2013, Spendier
Lecture 9/Page 5
Forces you will be expected to identify:
You will be expected to identify these on every HW and every problem from here on out.
Weight: W - downward force exerted by gravity (long range force)
Weight = W = mass times g = mg
We still use the particle model by replacing the object with a dot.
When we stop using the particle model and assuming forces applied at the center will be
locate the weight at a point called center of gravity,
Draw downwards weight vector from the center. Later on when we stop using this
particle model, we will then locate the weight at a very famous point what is called the
center of gravity. For nice symmetric objects it will be at the center, like boxes. For nonsymmetrical objects, the center of gravity is elsewhere, where we will locate the weight
of an object.
Normal Force: Fn , the perpendicular force exerted by one solid object onto another solid
object.
I put a block on the incline. The incline pushes up on the block. Does the incline push
straight up? Not in the case shown below. It pushes at 90 degrees to the surface
(perpendicular, normal, 90 degrees). Normal force gives you a chance to play around
with calculus because the direction is 90 degrees to the tangent line to the surface and the
slope of the tangent line can be computed from calculus. We will do simple stuff – our
normal force will be obvious. The normal force only exists between solid objects. If this
is jelly it does not work that way.
Whether object is being pushed or pulled we always draw the forces going away from the
dot. Notice, the normal force is not drawn from the surface; it is drawn from the dot. The
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Lecture 9/Page 6
normal force looks so simple, but it is tricky and students have sometimes a hard time
identifying it.
For example, what are the two forces acting on me, or you, I have mentioned earlier?
Gravity is always there and it pulls me down. But I am not falling since the floor pushes
up on me. What type of force is this? It is a normal force. I am solid, the floor is solid,
and hence the floor pushing up on me is a normal force. How does the normal force in
size compare to my weight? They are equal. But his is only because I am standing. Please
be aware that the size of the normal force is not always equal to the size of the weight of
the object. What if I jumped? The size of the normal force is NOT equal to my weight.
Friction: f - force which slows a moving object, always opposed to the motion, i.e.
opposite to velocity.
Why is it that a block is slide down the incline? It is because of friction. When things
slide across a surface friction is opposed to the motion, meaning that it is opposite to the
velocity. It has to be exactly 180 degrees from the velocity - we will get into detail why
this must be the case later.
For a stationary box, there is obviously no velocity, it is sitting still. Later, we’ll be more
precise and distinguish sliding friction = kinetic friction from friction on a stationary
object = static friction. There is more, there is also rolling friction which is between the
wheels on the ground – tend to ignore this one – since it is difficult.
Tension: T - pulling force exerted by a thin rope, chain, string.
Each of these two ropes exerts a tension on the block, a pulling force. Which way does
the horizontal force pull on the block? To the right, horizontally. That is the tension
exerted by the first rope. Which way does the second rope pull on the block? Up and to
the left. Here we use the geometric information of the rope; the angle of the rope
determines the angle of the tension force. The angle you get for the rope is also the angle
for the tension force.
PES 1110 Fall 2013, Spendier
Lecture 9/Page 7
Identifying Forces
We need to learn how to identify the forces acting on an object. It helps to do the
following:
To identify what forces are acting on an object, draw a circle around the object and
remember that only things that touch the object at the boundary can exert contact forces.
The wall does not pull on the block – it is the rope. The rope is at the contact point for the
boundary.
Here we also need to identify our long range force: Gravity - w
Long range forces you need to throw in and say that one is special
Newton’s First Law: The Law of Inertia
An object at rest stays at rest, an object in uniform motion stays in uniform motion if (and
only if) the net force acting on the object is zero.
∑ Fnet = 0
Demo:
Pull table cloth out of dishes very fast – something at rest stays as rest
Uniform motion - Straight line and constant speed, i.e, constant velocity.
Inertia - The property of all matter to stay in motion if already in motion; to stay at rest if
already at rest.
Inertial Reference Frames
Reference frames in which Newtonian mechanics holds are called inertial reference
frames or inertial frames. These are reference frames that move with constant velocity ,
including v = 0. We typically say that the ground is an inertial frame. But we know from
last lecture that the earth’s rotation causes a small centripetal acceleration. We calculated
it to be 0.3% of g and hence we will ignore it and treat the earth surface as an inertial
frame.
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Inertia Example
You are the driver of a car. You are foolishly not wearing a seat belt. You slam the breaks
– what do you do? You move forward, why? Are you pushed forward? In order to slow
down there has to be a force on you. Something in motion wants to stay in motion. Why
does the car slow down? There is a force acting on the car – you pushed the breaks. There
is no push on you, so you will go forward in a straight line until there is something which
will push on you. If you are lucky, it will just be the dash board.
It goes the other way too, as you might have suspected.
You are lying on the couch, somebody asks you to get up – it is hard to get up isn’t. That
is inertia. It is harder to get off the couch than it is to keep going after you are of the
couch – this is physics! Since an object at rest likes to stay at rest.
Free-Body Diagram - f. b. d. sketch of all the forces acting on an object using a
convenient coordinate system.
First Law Example 1)
A 6860N car (that is the weight of the car, it is a force since it is given in Newton) is
traveling with a constant 30m/s speed on a straight road. If the ground is exerting a
forward 350N force*, what is the magnitude and direction of all forces acting on the car?
(* We’ll learn later that this is due to the car’s engine.)
This picture is very busy. We need to simplify by drawing a free body diagram which
only shows the forces acting on the car. Now we can get rid of the velocity vector.
Drawing the velocity vector initially is helpful since it helps us find the direction of the
friction force.
Next we need to compute the magnitude and direction of the net force acting on the car:
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First Law Example 2)
A 5 kg mass is hung from the ceiling using a "massless" rope. What is the magnitude of
the tension force exerted by the rope on the mass? Hint: A 5 kg mass has a weight of 49N
on earth where this problem is taking place.
Answer: 49 N
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Lecture 9/Page 10
First Law Exercise 3)
Two 5 kg masses are connected to each over pulleys using a rope. What is the tension
force that the rope exerts on the right-hand mass if they are both at rest?
Answer: 49 N