1. Mechanics – the study of Motion
Chapters 2 & 3
Mechanics – the study of Motion
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2. What is Mechanics
The study of how and why objects move is called Mechanics.
Mechanics is customarily divided into 2 parts kinematics and dynamics.
We will begin with the simplest part of kinematics – motion in a straight line. This is known as linear or translational motion.
We will begin by discussing Newton’s First Law of Motion.
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3. Frame of Reference
In physics, Motion is relative. This means that in order to describe motion, you have to pick a “frame of reference”
Frame of reference is always decided by the observer
In physics we often use a coordinate axis to denote our frame of reference.
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4. Frame of Reference Y -x x
This is a familiar coordinate axis, but in physics it has a slightly different meaning. -Y
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5. Frame of Reference
In this frame of reference, up is positive, right is positive
Down is negative, as is left
Hence in physics a negative has no value, it merely denotes direction
This is necessary because direction has a special distinction in physics; it separates vector quantities from scalar quantities
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6. Chapter 2
Newton’s First Law
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7. Newton’s First Law The Law of Inertia
An object at rest tends to stay at rest.
An object in motion tends to stay in motion.
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8. Inertia: A resistance to change, a property of all matter.
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9. Mass: A Measure of Inertia
Mass is measured in kilograms
Mass is not Weight
Mass is a “built in” property of matter
Just because you leave earth, you don’t change your mass, but you do change your weight
Weight is a force caused by the acceleration due to gravity on the mass
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10. Net Force and Equilibrium
Net force is the sum of all the forces acting on an object
When the net force on an object equals zero – the object is said to be in equilibrium.
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11. Net Force and Equilibrium
When a statue sits on the ground, the weight of the statue pushes downward and a support force* from the ground pushes upward, so the statue is in equilibrium
* The support force is also called the Normal Force Fw FN
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12. Sample Problem
If a box with a weight of 20 Newton sits on a table, with what normal force does the table push back?
A second, 10 Newton force is added to the top of the first box. Now what is the normal force exerted by the table on the 20 Newton box? What normal force is exerted by the 20 Newton box on the 10 Newton box?
20 N
10 N
20 N
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15. Chapter 3
Linear Motion
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16. Frame of Reference
Earlier we said that in physics, Motion is relative. We talked about “frame of reference” and the fact that frame of reference is always decided by the observer
So if you are standing still on the sidewalk and a car passes you at 60 m/s how fast is it going with respect to you?
If that same car passes you at 60 m/s when you are riding in your car, traveling in the same direction at 30 m/s, how fast is it going with respect to you?
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17. Vector vs. Scalar
A Scalar Quantity is one that has only magnitude – distance is a scalar
Example: If you travel 500 miles that is a distance
A Vector Quantity is one that has magnitude and direction – displacement is a vector
Example: If you travel 500 miles North this is displacement
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18. Vector vs. Scalar If you divide distance by time you get average speed
Example: S = D/t = 500 miles/2 hours =250 mph
If you divide displacement by time you get average velocity
Example: Vavg = x/t = 500 miles North/2 hours = 250 mph North
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19. Acceleration
Acceleration is defined as the change in velocity with respect to time
a = Δv/t = (v2 – v1)/t
Δ – the greek symbol delta represents change
Example: If a car is traveling at 10 m/s and speeds up to 20 m/s in 2 seconds, acceleration is:
a = (20 m/s – 10 m/s)/2 seconds = 5 m/s2
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20. Gravity & Free Fall Things fall because of the force of gravity.
Gravity is an acceleration
Near earth gravity has been experimentally calculated to be 9.8 m/s2
This means that the velocity of an object changes by almost 10 m/s each second.
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21. Important Variables x – displacement – measured in meters
v0 (Vnaught) – Initial Velocity – in m/s
vf (Vfinal) – Final Velocity – in m/s
a – acceleration – in m/s2
t – time – in seconds
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22. Motion with Constant Acceleration
Since a = (vf – v0)/t we can rearrange this to:
vf = v0 + at
and
since x = vavgt and
since vavg = (vf + v0)/2
A new equation is derrived:
x = v0t + ½ at2
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23. Motion with Constant Acceleration
Using this equation:
x = v0t + ½ at2
and since we can rearrange a previous equation:
vf = v0 + at
to solve for time which gives us: t = (vf – v0)/a
Substituting the second into the first we get:
vf2 = v02 + 2ax
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24. Summary of the Kinematic Equations
Just a hint – Your “A” truly depends upon memorizing these and knowing how to use them!
Vavg = x/t
vavg = (vf + v0)/2
vf = v0 + at
x = v0t + ½ at2
vf2 = v02 + 2ax
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25. Recognizing Motion Graphs
Graph A: No motion
Graph B: Constant Velocity
Graph C: Accelerated motion B
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