Physics- the study of the most fundamental interactions between time, space, energy and matter.

- is a mathematical science - that is, the underlying concepts and principles have a mathematical basis.

Introductory Physics

Major subdivisions:

• Mechanics – forces of motion

• Heat – temperature and its effect on the properties of matter

• Sound and Wave Motion – transfer of energy by means of periodic substances a medium

• Electricity and Magnetism- electric and magnetic fields and their interactions

• Optics – nature and behavior of light

• Modern Physics – recent development

Mechanics

- deals with the study of motion and the forces affecting the motion of bodies

Classification:

Kinematics

- the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations. (description of motion)

Dynamics

- study the forces affecting the state of motion of the bodies. (State of motion)

Mathematical Quantities

Kinematics in One Dimension

Department of Science and Mathematics Education

College of EducationMSU-IIT

MOTION ALONG A STRAIGHT LINE

Distance

- is a scalar quantity which refers to "how much ground an object has covered" during its motion.

Displacement

- is a vector quantity which refers to "how far out of place an object is"; it is the object's change in position.

Example:

A man walks 4 km

Example:

A man walks 4 km east

Distance and Displacement

Example 1:

Jam walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. What is Jam’s resulting distance and displacement?

Answer:

Distance = 12 m

Displacement = 0

Example 2:Oliver views football games from under the bleachers. He frequently paces back and forth to get the best view. The diagram below shows several of Oliver's positions at various times. At each marked position, Oliver makes a "U-turn" and moves in the opposite direction. In other words, Oliver moves from position A to B to C to D. What is Oliver's resulting displacement and distance of travel?

Answer:

Distance = 95 yards Displacement = 55 yards to the left

SPEED AND VELOCITY

- it is a scalar quantity which refers to "how fast an object is moving."

-fast-moving object has a high speed -slow-moving object has a low speed. -no movement at all has a zero speed.

Average speed – is a measure of the distance traveled in a given period of time; it is sometimes referred to as the distance per time ratio.

Instantaneous Speed- speed at a particular instant in time.

Average vs. Instantaneous Speed

Ave. speed = Distance Time

While on their vacation, Ellen, Jam and Phel traveled a total distance of 440 miles. Their trip took 8 hours. What was their average speed?

Example 3:

• Their car’s average speed is of 55 miles per hour.

• Probable instant speeds at 65 mi/hr and 45 mi/hr.

(65mi/hr + 45 mi/hr)/2 = 55 mi/hr ave. speed

Undoubtedly, they stopped at some instant in time (for a shopping galore and for a spa session along the way of their travel)

Constant Speed

- It is when an object covers the same distance every regular interval of time.

Data tables that depict objects with constant and changing speeds.

Velocity

- a vector measurement of the rate and direction of motion. The scalar absolute value (magnitude) of velocity is speed. Velocity can also

-defined as rate of change of displacement.

The average speed during the course of a motion is often computed using the following equation:

Meanwhile, the average velocity is often computed using the equation:

Speed versus Velocity

Average Velocity Defined 

 The standard international (SI) units of velocity are m / s.

Velocity is Speed with Direction

Velocity is "speed with direction".

Velocity is a vector quantity with a directional attribute.

"30 m/s due east" is a velocity; it has the two attributes, magnitude, and direction.

Car is moving at the constant speed of 30 m/s.  

Each second it travels 30 m.  

Its velocity is not constant.  

Why?

Speed is constant. Direction is changing.

    Average Velocity Example  

The directional attribute of each displacement vector is provided by either a plus, or a minus, sign

Displacements are positive if they are to the right, and negative if they are to the left

This sign convention is completely arbitrary and may be reversed

Example 4:

Jam walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the average speed and the average velocity.

Answer:

Ave. speed = 0.50m/s Ave. Velocity = 0

Average Velocity Calculation

Positive velocity indicates motion to the right.

Negative velocity indicates motion to the left

   Average Speed and Average Velocity

If the cheetah doesn't reverse direction,the distance traveled is the same as the displacement.

Average velocity  is equal to the average speed

Calculating Distance from Average Speed

Average speed = Distance Time

                                 _     vave = d / t     or    v  = d/t

                 Distance = Ave. speed x

Time                                         _      d = vave t     or      d =  v t

The average speed of the cheetah during a 50-second run is 65 m/s.

How far does it travel?

 Constant Velocity:  Equal Distances in Equal Times

This runner travels the same distance each second.

    d = v t

Constant Positive Velocity

Constant Negative Velocity

ACCELERATION

- is a vector quantity which is defined as "the rate at which an object changes its velocity." An object is accelerating if it is changing its velocity.

- the rate of change of velocity with time.

The Direction of the Acceleration Vector

Since acceleration is a vector quantity, it will always have a direction associated with it. The direction of the acceleration vector depends on two things:

• whether the object is moving in the + or - direction • whether the object is speeding up or slowing down

The general RULE OF THUMB is:

If an object is slowing down, then its acceleration is in the opposite direction of its motion.

-can be applied to determine whether the sign of the acceleration of an object is positive or negative, right or left, up or down, etc.

Acceleration

 a =  Average acceleration = (v - v0) / (t - t0)

           

Acceleration

Observe the animation of the three cars below. Which car or cars (red, green, and/or blue) are undergoing an acceleration? Study each car individually in order to determine the answer. If necessary, review the definition of acceleration.

     Average Acceleration

 The standard international units of acceleration are m / s2.

 Constant Acceleration

 _

 a = Average acceleration    = (v - v0) / (t - t0)                     (1) 

                                            _ If acceleration is constant, a  = a.

If t0 = 0, then

a = (v - v0) / t           (2)

v = v0 + at               (3)

*velocity is changing by a constant amount each second.

  Constant Acceleration:  v = v0 + a t

   Constant Acceleration

The slope of the velocity versus time curve is the acceleration.Equation of a straight line:

y = m x  + b

v = a t  + v0

or

v = v0 + a t

Average Velocity

If a = constant, the ave.velocity is the midpointvelocity.

vave = 1/2 ( v + v0 )

What distance is traveledbetween t = 1 s andt = 5 s?

Use d = vave t

Negative Acceleration:  Deceleration

           How far does the dragster travel during this time?

  Velocity and Acceleration Direction

Acceleration is negative:  velocitybecomes less positive.

Acceleration is positive: velocity becomes more positive.

Uniformly Accelerated Motion

A body is describing a uniformly accelerated motion if the change in velocity divided by the corresponding change in time is constant throughout the motion.

Example:

• A body sliding down a smooth inclined plane

• A car rolling downhill with its engine cut off and with no brakes

Constant Acceleration

Each second, a greater distance is traveled.

  Deriving a Motion Equation from Basic Ideas

Substitute eq. (1) into eq. (2)

d = v0 t + 1/2 a t2           (3)

Square both sides eq. (1)

v12= v0

2 + 2ad                    (4)

a= v1-v0/ t

v1= v0 + at (1)

______________________

vave = d/t

d= vavet

v1+v0

2d= t (2)

   Example Problem

What is the average speed of the jet during take-off? How long is the jet accelerating before it takes off? How much take-off room does this jet need?

v2 = v02 + 2 a d

Derivation of Motion Equation

Example Problem

Final speed is 50 m/s.

What average acceleration did the ball have?                  _v2 = v0

2 + 2a d

50 m/s is about 100 miles/hour.

Example:

Oliver is waiting at a stoplight in his car. When the light turns green, Oliver accelerates from rest at a rate of a 6.00 m/s2 for an interval of 4.10 seconds. Determine the displacement of Oliver's car during this time period.

Diagram

                Given:

vi = 0 m/s

t = 4.10 s a = 6.00 m/s2

Find:

d = ??

Solution:

d= (0m/s)(4.10s) + ½ (6.00 m/s2)(4.10 s)2

d= 50.43 m

Formula:

Quiz: ½ sheet of paper

A car starts from rest and is given a constant acceleration of 10 m/s for a total time of 5 s.

1. Find the velocity at the end of 5 seconds.

2. How far does it go during the first second?

3. What is the displacement after 5 s ?

Solution:

since the body starts from rest, v1= 0 in our equations,

1. a = v1-v2 /t

= (10 m/s2)*(5 s)

= 5 m/s

2. with t=1s

d = v0 t + 1/2 a t2  

= 1/2 (10 m/s2)*(1 s)2

= 5 m

3. with t = 5 s (use the same equation in # 2)

d= 125 m

Acceleration Due to Gravity  

Free-FallA free-falling object is an object which is falling under the sole influence of gravity.

Characteristics of a free-falling object:

• Free-falling objects do not encounter air resistance.

• All free-falling objects (on Earth) accelerate downwards at a rate of approximately 10 m/s2(to be exact, 9.8 m/s2).

Acceleration Due to Gravity v = a t

a = 9.8 m / s2

-----------------------

   t   (s)  

     v  (m/s)  

   0         0

   1      9.8

   2    19.6

   3    29.4

g = 9.8 m / s2

Assuming that the position of a free-falling ball dropped from a position of rest is shown every 1 second, the velocity of the ball will be shown to increase as depicted in the diagram at the right.

How Fast? and How Far?

Note: An object doesn't have to be falling to be in free fall - if you throw a ball upward its motion is still considered to be free fall, since it is moving under the influence of gravity. 

Distance which a Free-Falling Object

The distance which a free-falling object has fallen from a position of rest is also dependent upon the time of fall. The distance fallen after a time of t seconds is given by the formula below:

d = 1/2 * g * t2

Example:t = 1 s d = (0.5) * (10 m/s2) * (1 s)2 = 5 mt = 2 sd = (0.5) * (10 m/s2) * (2 s)2 = 20 mt = 5 sd = (0.5) * (10 m/s2) * (5 s)2 = 125 m

Velocity of a Free-Falling Object

The velocity of a free-falling object which has been dropped from a position of rest is dependent upon the length of time for which it has fallen. The formula for determining the velocity of a falling object after a time of t seconds is:

vf = g * t

g= is the acceleration of gravity

t = 5s

vf = (10 m/s2) * (5 s) = 50 m/s

Falling Object Example

What is the speed of the jumper when he strikes the net?

What average deceleration does he experience as the nets brings him to rest?

Rise Time

1.  After it leaves the hand, what is the direction of the coin's acceleration?Upward, or downward?

2.  What is the acceleration—magnitude and sign--of the coin?

3.  How long does it take the coin to lose all of its upward speed?

4.  What average speed did the coin have on the way up?

5.  How far did the coin travel upward?

  Objects Rising and Falling

Select the upwarddirection as positive. v0 = 40 m/s

What is the rise time?

How high does theball rise?

Objects Rising and Falling

v0 = 40 m/s

------------------------------Upward is positive:

a = - g   = - 9.8 m / s2.------------------------------How long is the ball inthe air?

y = y0 + v0 t + 1/2 a t2

  Alternative Method

v2 = v02 + 2 a d

v 0 = 40 m / s

a   = - 9.8 m / s2

d   = - 50 m----------------------Solve for v, then use

v = v0 + a t

t = (v - v0) / a

Sample Problem:

A bullet is fired directly upward from a rifle at ground level. Assuming a muzzle velocity of 490 m/s, and neglecting air resistance, find

1. Height of highest point reached

2. Time required to reach this point

3. Total time before the bullet returns to the ground

4. Speed of the bullet upon hitting the ground

Step 1: Identify the known quantities

v0 = 490 m/s

vf = 0 ( at highest point reached)

g = 10 m/s2

d = 0 (ground level)

Step 2 : Identify the unknown quantities

d = ? (highest point reached)t = ? (at highest point)ttotal = ? (as the bullet returns to the ground)v1 = ?

Step 3: Identify the basic equations

d = d = v0 t + 1/2 g t2

vf = v0 + a tv2 = v0

2 + 2 a d

Step 4: Calculation and substitution of values

Solution for # 1

0 = (490 m/s)2 + 2 (-10 m/s2) d

d = - (490 m/s2)

d = 12, 250 m

- 19.6 m/s2

-2vt = g

Solution # 2

vf = v0 + a t

0 = (490 m/s) + (-10 m/s2) t

t = - (490 m/s)

- 10 m/s2

Solution #3

d = v0 t + 1/2 g t2

0 = v0 t + 1/2 g t2

t = 98 s

Solution #4

t = 49 s

vf = v0 + a t

vf = 490 m/s + (-10m/s2) *100 s

Vf = - 490 m/s

Force and Its Representation

The Meaning of Force

- A force is a push or pull upon an object resulting from the object's interaction with another object.

- Forces only exist as a result of an interaction.

• contact forces, and • forces resulting from action-at-a-distance

two broad categories:

Contact forces

- are types of forces in which the two interacting objects are physically in contact with each other.

Examples:

frictional forces, tensional forces, normal forces, air resistance forces, and applied forces.

Action-at-a-distance forces

- are types of forces in which the two interacting objects are not in physical contact with each other, but are able to exert a push or pull despite the physical separation.

Examples:

gravitational forces, electric forces, and magnetic forces

Force

- is a quantity which is measured using a standard metric unit known as the Newton (N).

- is a vector quantityOne Newton is the amount of force required to give a 1-kg mass an

acceleration of 1 m/s2. A Newton is abbreviated by an "N."

1 Newton = 1 kg* ms2

Free-Body Diagrams

1. A book is at rest on a table top. Diagram the

forces acting on the book.

Examples:

2. A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance. A free-body diagram for this situation looks like this:

FBD 1

FBD 2

NEWTON’S THREE LAWS OF MOTION

Newton's First Law of Motion: Law of Inertia

“An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.’’

Pass the Water Exercise

Imagine that students participate in a relay race carrying a plastic container of water around a race track, the water will have a tendency to spill from the container at specific locations on the track. In general the water will spill when:

• the container is at rest and you attempt to move it • the container is in motion and you attempt to stop it • the container is moving in one direction and you attempt to change its

direction

Newton’s Second Law of Motion: Law of Acceleration- pertains to the behavior of objects for which all existing forces are not

balanced

- states that the “The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. .”

- mass of the object is inversely proportional with the object’s acceleration

Fnet = m * a

Example:

1. What acceleration will result when a 12-N net force applied to a 3-kg object? A 6-kg object?

Answer:

A 3-kg object experiences an acceleration of 4 m/s/s. A 6-kg object experiences an acceleration of 2 m/s/s.

2. A net force of 16 N causes a mass to accelerate at a rate of 5 m/s2. Determine the mass.

Answer:

m = 3.2 kg

Example 3:

A 10-kg body, initially at rest, is acted upon by a constant force of 20 Newtons for 4 seconds. What velocity is acquired at the end of the 4 seconds?

Solution:

F=ma

20 N = 10 kg * a

a = 2 N/kg or 2 m/s2

Next,

v2 = v1 + at

v2 = 2 m/s2 * 4 s

v2 = 8 m/s2

Newton’s Third Law of Motion: Law of Action and Reaction

- The direction of the force on the first object is opposite to the direction of the force on the second object.

- Forces always come in pairs - equal and opposite action-reaction force pairs.

“For every action there is an equal and opposite reaction.”

Examples:

a. Consider the flying motion of birds. A bird flies by use of its wings. The wings of a bird push air downwards. In turn, the air reacts by pushing the bird upwards.

b. Enclosed air particles push balloon wall outwards.

Check Your Understanding

1. While driving down the road, an unfortunate bug strikes the windshield of a bus. The bug hit the bus and the windshield hit the bus. Which of the two forces is greater: the force on the bug or the force on the bus?

Answer:

Each force is the same size. For every action, there is an equal and opposite reaction. The fact that the bug splatters only means that with its smaller mass, it is less able to withstand the larger acceleration resulting from the interaction.

2. Identify at least six pairs of action-reaction force pairs in the following diagram.

Possible Answers:

The elephant's feet push backward on the ground; the ground pushes forward on its feet.

The right end of the right rope pulls leftward on the elephant's body; its body pulls rightward on the right end of the right rope.

The left end of the right rope pulls rightward on the man; the man pulls leftward on the left end of the right rope.

The right end of the left rope pulls leftward on the man; the man pulls rightward on the right end of the left rope.

The tractor pulls leftward on the right end of the left rope; the left end of the left rope pulls rightward on the tractor.

Etc..etc.

WORK, POWER AND ENERGY

Workrefers to an activity involving a force and movement in the directon of the force. A force of 20 newtons pushing an object 5 meters in the direction of the force does 100 joules of work.

Energyis the capacity for doing work. You must have energy to accomplish work - it is like the "currency" for performing work. To do 100 joules of work, you must expend 100 joules of energy.

Poweris the rate of doing work or the rate of using energy, which are numerically the same. If you do 100 joules of work in one second (using 100 joules of energy), the power is 100 watts.

Work

- is defined as a force acting upon an object to cause a displacement.

- work must have a displacement and the force must cause the displacement

- standard metric unit is the Joule (abbreviated "J"). One Joule is equivalent to one Newton of force causing a displacement of one meter. In other words,

Examples:

• A carabao pulling a plow through the fields

• A father pushing a grocery cart down the aisle of a grocery store

Quick Quiz

1. A teacher applies a force to a wall and becomes exhausted.

2. A book falls off a table and free falls to the ground.

3. A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed.

4. A rocket accelerates through space.

Answers:

1. No. This is not an example of work. The wall is not displaced. A force must cause a displacement in order for work to be done.

2. Yes. This is an example of work. There is a force (gravity) which acts on the book which causes it to be displaced in a downward direction (i.e., "fall").

3. No. This is not an example of work. There is a force (the waiter pushes up on the tray) and there is a displacement (the tray is moved horizontally across the room). Yet the force does not cause the displacement. To cause a displacement, there must be a component of force in the direction of the displacement.

4. Yes. This is an example of work. There is a force (the expelled gases push on the rocket) which cause the rocket to be displaced through space.

 

Potential Energy

- is energy that is stored in an object.

Kinetic energy

- is energy of motion. A rubber band flying through the air has kinetic energy.

Potential Energy

Gravitational Potential Energy - is the energy stored in an object as the result of its vertical position. (i.e., height)

- It depends on the mass and height

PEgrav = mass * g * heightPEgrav = m * g * h

Elastic potential energy

- is the energy stored in elastic materials as the result of their stretching or compressing.

- It can be stored in rubber bands, bungee chords, trampolines, springs, an arrow drawn into a bow, etc.

Check your understanding:

1. A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

Answer:

PE=mgh

PE= 10 kg*10m/s/s*0.45m

PE= 13.7 J

Kinetic energy

- may be described as energy due to motion.

- defined as the amount of work it can do before being brought to rest.

- An object which has motion - whether it be vertical or horizontal motion - has kinetic energy.

Formulae for kinetic energy Let a body of mass m moving with speed v be brought to rest with uniform deceleration by a constant force F over a distance s.

vf2 = vi

2 + 2ad

0 = vi2 + 2ad

d = v2

a

W = F*dW = F* v2

a

Check your understanding:

1. Determine the kinetic energy of a 1000-kg roller coaster car that is moving with a speed of 20.0 m/s.

Answer: KE= 200 J

Conservation of Energy

The principle of conservation of energy state that the total energy of a system remains constant. Energy cannot be created or destroyed but may be converted from one form to another.

Example:

A body falling freely in air, neglecting air resistance, then mechanical energy is conserved, as potential energy is lost and equal amount of kinetic energy is gained as speed increases.

Friction- is the "evil" of all motion

- frictional resistance to the relative motion of two solid objects is usually proportional to the force which presses the surfaces together as well as the roughness of the surfaces.

POWER

- is the rate at which work is done

- the quantity work has to do with a force causing a displacement.

- the quantity which has to do with the rate at which a certain amount of work is done

- standard metric unit is watt (a unit of power is equivalent to a unit of work divided by a unit of time)

Mathematical equation:

Example:

A 60-kg man climbs a flight of stairs to the fourth floor of a building in 40 seconds. If the fourth floor is 12 meters above the ground, Find the man’s equivalent Power in

1. Watts

2. Horsepower

Solution:

Solve for Work done

W= weight*distance

= (60*9.8)N*(12m)

= 7, 056 J

1.

Power = 7, 056 J/40s

= 176.4 J/s or watts

2. 746 watt is approximately equal to 1 Hp

Hp = 176.4 W/746W/Hp

= 0.236 Hp