Announcements The book “A Tour of the Subatomic Zoo” is at the SU Bookstore,not the Orange bookstore. (The SU Bookstore is the one in Schine)

Frontiers of Science Lecture this Thursday at 7:30, Grant Auditorium. (Benefit of the doubt credits!)

“The Elegant Universe”Brian Greene, Columbia University

Lectures will be posted in the morning, so feel free to bring aprinted copy with you to class. Sometimes they will be availablethe night before.

FYI, When printing the PDF file for a lecture, you can print multiple slides to a sheet using the Printer Properties dialog box.

Introduction to Physical Quantities

Scalars

Scalar quantities are those which are described solely by their magnitude

Some examples are:

Mass e.g. 14 [kg], 36 [lbs], …Time e.g. 10 seconds, 40 minutes, …Volume e.g. 1000 cm3, 4 litres, 12 gallonsTemperature e.g 14 oF , 25 oC, …Voltage e.g. 9 Volts, etc

VectorsVector quantities are those which need to be described by BOTHmagnitude and direction

Some of the most common examples which we will encounter are:

Velocity e.g. 100 [mi/hr] NORTH

Acceleration e.g. 10 [m/sec2] at 35o with respect to EAST

Force e.g. 980 [Newtons] straight down (270o)

Momentum e.g. 200 [kg m/sec] at 90o.

Distance The separation between two locations.

Distance can be measured in many types of units. We will mostly use:MKS Units

millimeters [m]centimeters [cm]

meters [m]kilometers [km],

etc

You should be comfortable with converting from [cm] to [m], [mm] to [km], and so on.

We may use the symbolic notation d to mean a change in the position. The symbol should be read as “the change in”

FYI : 1 [km] = 0.6 [mi]

TimeIn physics, we are most often less interested in absolute time thanchanges in time, or a time interval.

Time can be expressed in several units as well:

seconds [sec]minutes [min]

hours [hr]daysyears

etc…

Example 1: How much time does it take for the earth to make one revolution?

Example 2: How long did it take for you to drive to the store today?

We usually refer to a time interval as : t

VelocityVelocity is a measure of the rate of change of the distance with respect to time.

v = d / t

It will usually be measured in [m/sec].

What does 5 [m/sec] mean? It means if an object passes by us at 5 [m/sec], it will advance itsposition by 5 [m] every second. So after 2 [sec], it will have advanced 10 [m], and 20 [m] in 4 [sec] and so on.

If a train moves at 50 [meters/sec], how far will it go in 50 seconds ?

a) 100 miles b) 2.5 [km] c) 250 [m] d) 2500 miles

Acceleration (I)Acceleration is the rate of change of velocity with respect to time

a = v / t [a] = [m/sec] / [sec] = [m/sec2]

What does a = 5 [m/sec2] mean? If an object starts at rest, its velocity increases by 5 [m/sec] every second.

Time (sec) Acceleration Velocity0 5 m/sec2 0 m/sec1 5 m/sec2 5 m/sec2 5 m/sec2 10 m/sec3 5 m/sec2 15 m/sec4 5 m/sec2 20 m/sec

Acceleration (II)

Acceleration can be negative also! We call this deceleration.

If the acceleration is in the same direction as the velocity, the object has positive acceleration (it speeds up).

If the acceleration is in the opposite direction as the velocity, the object has negative acceleration or deceleration (it slows down).

Deceleration: Animated GIF of car decelerating

What is a Force ?Force is simply:

A PUSH A PULLor

Forces have both magnitudeand direction

Force and Acceleration Experimentally, we find that if we apply a forceto an object, it accelerates.

We also find that the acceleration (a) is directlyproportional to the applied force (F) and inversely proportional to the mass (m) . That is:

a = F / m

This is Newton’s Law, and it is often written:

F = ma

This means: Increasing the force increases the acceleration; decreasing the force results in a lower acceleration.

Isaac Newton

Force (I) A force is generally a result of an interaction between two (or more) objects (Try and think of a scenario where a force is applied with only one object involved)?

Can you think of some examples of forces?

Gravitational Electric Magnetic Friction Wind drag Van der Waals forces Hydrogen bonds Forces in a compressed or stretched spring+…

Forces (II) Since two or more objects must be involved, a force intimately tied to the notion of an interaction.

Interactions are now believed to occur through the exchange of “force carriers”. This is a very important point, and we’ll come back to it later…

So far, we know only of four types of fundamental forces in nature:

Gravity, Electromagnetic, Weak, and Strong

We will come back to each of these

All other forces in nature are understood to be the residual effects of these fundamental forces

Particle Exchange and Force (use Explorer)

Momentum (I) What is momentum?

Momentum is simply the product of the mass and the velocity.Denoting momentum as p, it is simply:

The units of momentum are [kg][m/sec] == [kg m/sec]

Momentum is a very important subject in physics because it is what we call a conserved quantity. What does this mean?

We will come back to the idea of conserved quantities in physics. They play a very important role in understanding the world around us!

p = m*vm v

Momentum (Example I)If a 500 [kg] car is traveling west at 20 [m/sec], what is its momentum?

A) -1x104 [kg m/sec] B) -1x103 [kg m/sec] C) 25 [kg m/sec] D) 1x105 [kg m/sec]

p = mv = (500 [kg])(-20 [m/sec]) = -10,000 [kg m/sec] = -1x104 [kg m/sec]

-20 [m/sec] 500 [kg]

Momentum (Example II)If a 5000 [kg] truck is travelling east at 10 [m/sec], what is its momentum?

A) -5x104 [kg m/sec] B) 5x104 [kg m/sec] C) 500 [kg m/sec] D) 1x104 [kg m/sec]

10 [m/sec]5000 [kg]

p = m*v = (5000 [kg])(10 [m/sec]) = 50,000 [kg m/sec] = 5x104 [kg m/sec]

Momentum (Example III)If the car and the truck collide, what is the total momentum of the car and truck just before impact?

A) 6x104 [kg m/sec] B) -4x104 [kg m/sec] C) 4x104 [kg m/sec] D) 0 [kg m/sec]

Since their momenta are aligned in the same direction, we can just add them: PTOTAL = -1x104 [kg m/sec] + 5x104 [kg m/sec] = 4x104 [kg m/sec]

10 [m/sec]

5000 [kg]

-20 [m/sec]

500 [kg]

Energy

What is EnergyFrom Merriam Webster:

Energy: The capacity for doing work (or to produce heat)

What are some forms/types of energy?

1. Energy of motion (kinetic energy)

2. Heat

3. Electricity

4. Electromagnetic waves - like visible light, x-rays, UV rays, microwaves, etc

5. Mass

Energy

What do you mean mass is a form of energy?

We’ll get to this later….

The thing about energy is that it cannot be created or destroyed, it can only be transformed from one form into another

Yes, like momentum it is a “conserved” quantity. We willlearn that conserved quantities are a powerful tool in “predicting the future”!

Summary I

In nature, there are two types of quantities, scalars and vectors

Scalars have only magnitude, whereas vectors have both magnitude and direction.

The vectors we learned about are distance, velocity, acceleration, force, and momentum

The scalars we learned about are time, and Energy.

Summary II

Forces are the result of interactions between two or more objects.

If the net force on an object is not zero, it will accelerate. That is it will either speed up, slow down, or change direction.

Energy and momentum are conserved quantities. This has far-reaching consequences for predicting whether certain “events” or “processes” can occur.

There are many forms of energy. The topic of energy willbe discussed in greater detail in next lecture.