Physics: What can it say?What can physics not say?

- Atoms and Molecules.

- Fundamental components and their interactions.

The LHC rap on Youtube.

http://www.youtube.com/watch?v=j50ZssEojtM

MOTION

1 Particle, 1D

Nothing else

Position

Velocity

Acceleration

Position

Velocity

Acceleration

Once again…

1. The average velocity of a particle moving in 1D has a positive value. (a) Is it possible for the instantaneous velocity to have

been negative at any time on the interval? (b) Suppose the particle started at the origin at x=0. If its average velocity is positive could it ever have been in the –x region of the axis?

2. Can the instantaneous velocity of an object ever be greater in magnitude than the average velocity over a time interval containing that instant?

Conceptual Questions on Motion

5. If the velocity of a particle is nonzero can its acceleration be zero?

6. If the velocity of a particle is zero can its acceleration be nonzero?

7. Consider the following combination of signs and values for velocity and acceleration with respect to a1D x-axis:

Velocity Accelerationa. + +b. + -c. + 0d. - +e. - -f. - 0g. 0 +h. 0 -

Describe what a particle is doing in each case.

Chapter 2 Conceptual Question

4. If an object’s average velocity is nonzero over some time interval does that mean that its instantaneous velocity is never zero during the interval?

In-Class Problems

t(s)

a(m/s2)

2

0

-3

A particle starts from rest and accelerates as shown. (a) Determine the particle’s speed at t =10sand t =20s. (b) The distance traveled in the first 20s.

10s

15s 20s

The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with an acceleration –5.6 m/s^2 for 4.2 s making straight skid marks 62.4m long ending at the tree. With what speed does the car then strike the tree?

In-Class Problems (cont’d)

Chapter 3: Motion in 2D !

- Position, Velocity and Acceleration- 2D Motion with constant Acceleration- Projectile Motion- Uniform Circular Motion- Tangential and Radial Acceleration- Relative Velocity

In- Class Problem

A ball is tossed from an upper-story window of a building.The ball is given an initial velocity of 8m/s at an angle 20 degrees below the horizontal. It strikes the ground 3s later. (a) How far horizontally from the base of the building does the ball strike the ground? (b) Find the height from which the ball was thrown? (c) How long does it take the ball to reach a point 10m below the launch level?

Projectile Motion

In- Class Problem

Uniform Circular Motion

A tire 0.5m in radius rotates at a constant rate of 200rev/min. Find the speed and acceleration of a small stone lodged in the outer tread of the tire.

In- Class Problem

A particle moves clockwise in a circle of radius 2.5m. Find (a) radial acceleration (b) tangential acceleration (c) speed

v

a

30

a = 15.0m/s^2

R = 2.5mR

In- Class Problem

(Problem 33 in the text) A river has a steady speed of ½ m/s. A student swims upstream a distance of 1km and swims back to the starting point. If the student can swim at a speed of 1.2m/s in still water, how long does the trip take? Compare this time interval with that in still water.

Relative Velocity

Chapter 3 Quick Questions

1. State which of the following quantities, if any, remain constant as a projectile moves through its parabolic trajectory:

(a) speed (b) acceleration (c) horizontal component of velocity (d) vertical component of velocity

2. A sailor drops a wrench from the top a sailboat’s mast while the boat is moving rapidly and steadily in a straight line. Where will the wrench hit the deck?

3. A spacecraft drifts through space at constant velocity. Suddenly a gas leak gives the craft a constant acceleration in a direction perpendicular to the initial velocity. What is the shape of the path of the spacecraft in this situation?

4. A projectile is launched at some angle to the horizontal with some initial speed and air resistance is negligible. Is the projectile a freely falling body? What is its acceleration in the vertical direction? horizontal direction?

5. Correct the following statement: “A racing car rounds the turn at a constant velocity of 90mi/h.”

Chapter 3 Quick Questions

Chapter 3 Quick Questions6. Explain whether or not the following particles have an acceleration:

(a) a particle moving in a straight line at constant speed.(b) a particle moving around a curve at constant speed.

7. An object moves in a circular path with constant speed v (a) Is the velocity of the object constant? (b) Is its acceleration constant?

8. A ball is thrown upward in the air by a passenger on a train that is moving at constant velocity. Describe the path as seen by the (a) the passenger (b) observer standing by the tracks outside the train. How would the observations change if the train were accelerating?

Chapter 4: Laws of Motion!

- Force- 1st Law (Inertia)- Mass - 2nd Law (Fnet = Ma)- Gravitational Force and Weight- 3rd Law (“Equal and Opposite”)- Applications

Concept of Force

- Fundamental (Field) and Effective Forces. - Forces, experimentally, behave as vectors.

Newton’s 1st Law An object retains its current state of motion (motion at constant velocity) unless it interacts with another object.

This defines Force (an interaction)! -Mass is a measure of the resistance of objects to changes in their motion.

Newton’s 2nd Law

• The acceleration of an object in a particular direction is directly proportional to the net force (the sum of all forces) on that object in that direction:

a ~ FNET

If you apply twice the force to an object the acceleration doubles.

•For a fixed force, the more massive the object is the less acceleration it acquires:

Together, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:

a = FNET/M

M

a

M

aa ~ 1/Mass

F F

In- Class Problem

A force F in the x-direction applied to an object of mass m1 produces an acceleration of 1m/s2 i. The same force applied to a second object of mass m2 produces an acceleration of 0.2 m/s2 i. (A) What is the ratio of the masses? (b) If m1 and m2 are combined what is their acceleration under the application of the same force F?

(Forces)

Quick Check

You push an object, initially at rest, across a frictionless floor with a constant force for a time interval t, resulting in a final speed v for the object. You repeat the experiment but with a force twice as large. What time interval is now required for the same final speed?

In- Class Problem

Problem (4)

Two Forces, F1 = -6i –4j and F2 = -3i +7j act on a particle of mass 2Kg that is initially at rest at the coordinates (-2,4)m. (a) What are the components of the particle’s velocity at t=10s? (b) In what direction is the particle moving at t =10s? (c) What displacement does the particle undergo in the 1st 10s? What are the coordinates at t=10s?

In- Class Problem

Problem (7)

Two Forces, F1 and F2 act on an object of mass M = 5Kg as shown. Find the accelerations in (a) and (b).

(a) (b)

60 degreesM

In- Class Problem

(30) Two objects are connected by a light string that passes over a frictionless pulley as shown. Draw free-body diagrams of both objects. The incline is frictionless and m1= 1Kg, m2 = 4Kg and = 30 degrees. Find (a) the acceleration of the objects (b) the tension in the string and (c) the speed of each object 2s after released from rest.

m1m2

Chapter 4 Quick Questions

• As you sit in a chair the chair pushes up on you with a normal force. The force is equal to your weight and in the opposite direction. Is this force the Newton’s 3rd Law reaction to your weight?

• A passenger sitting in the rear of a bus claims that she was injured as the driver slammed on the brakes, causing the suitcase to come flying toward her from the front of the bus. If you were the judge in the case, what disposition would you make?

• A weightlifter stands on a bathroom scale. He pumps a barbell up and down. What happens to the reading on the scale as he does so? What if he is strong enough to throw the barbell upward?

Chapter 4 Conceptual Questions (cont’d)

4. Suppose a truck loaded with sand accelerates along a highway. If the driving force of the truck remains constant, what happens to the truck’s acceleration if the trailer leaks sand at a constant rate through a hole in the bottom?

1. In the picture of the train which broke through the wall of the train station in the textbook, was the force exerted by the locomotive on the wall greater than the force the wall could exert on the locomotive?

1. If action and reaction forces are always equal in magnitude and opposite in direction, doesn’t the net force on any object add up to zero? How then are objects accelerated?

Chapter 5: Applications of Newton’s Laws

- Forces of Friction- Uniform Circular Motion (again)- Non-uniform circular motion (again)- Velocity-Dependent Resistive Forces- Fundamental Forces

Friction

- Friction generally provides the “reaction” force that allows objects to move.- Two Types: static and kinetic- We indicate the force of friction with an fs or fk.- Frictional force is proportional to the normal force.

fs

fk

FrictionalForce (N)

Applied Force

In- Class Problem

(8) A woman at the airport is towing her 20Kg suitcase at a constant speed by pulling on her suitcase as shown. She pulls on the strap with a 35N force, and the friction force on the suitcase is 20N.

(a) Draw a free-body diagram of the suitcase.

(b) What angle does the strap make with the horizontal?

(c) What normal force does the ground exert on the suitcase?

suitcase

In- Class Problem: Air Resistance

Calculate the terminal speed of a wooden sphere falling through air if its radius is 8cm and its drag coefficient is ½. From what height would a freely falling object reach this speed in the absence of air resistance?

FR

Mg

r = 8cmD= 1/2

1.What force causes an (a) automobile (b) propeller-driven airplane and (c) a rowboat to move?

2. Suppose you drive a classic car. Why should you avoid slamming on the brakes when you want to stop in the shortest possible distance (many cars have anti-lock brakes to solve this problem)?

3. A pail of water can whirled in a vertical path such that none is spilled. Why does the water stay in the pail even though the pail is upside down above your head?

Chapter 5 Quick Questions

4. Consider a small raindrop and a large raindrop falling through the atmosphere. Compare their terminal speeds. Whyich hits the ground first? What are their accelerations when they reach terminal speed?

Chapter 6: Energy and Energy Transfer

• Systems and Environments• Work Done by a Constant Force• The Scalar Product • Work Done by a Varying Force• Kinetic Energy and Work• Non-isolated Systems• Situations involving Kinetic Friction• Power

In- Class Problem:Work Done by a Constant Force

1. A block of mass 2.5Kg is pushed 2.5m along a frictionless horizontal table by a constant 16N force directed 25 degrees below the horizontal. Determine the work done on the block by (a) the applied force (b) the normal force exerted by the table (c) the gravitational force. (d) Determine the total Work done on the block.

In- Class Problem: Scalar (Dot) Product

1. A Force F = 6i – 2j N acts on a particle that undergoes a displacement r = (3 i + j) m. Find the work done by the force on the particle and (b) the angle between F and r.

In- Class Problem: Work Done by a Varying Force

1. A Force F(x,y) = (4x i + 3y j) N acts on a particle that moves in the x direction from the origin to x =5m. Find the work done on the object by this force.

Chapter 7: Potential Energy

• Potential Energy of a System• The Isolated System• Conservative and Non-conservative Forces• Non-isolated system in Steady-State• Potential Energy for Gravitational and Electric Field Forces• Energy Diagrams and Stability of Equilibrium• Potential Energy and Fuels

Potential Energy of a System

Gravitational potential energy of Earth-object system near surface(constant force = mg):

•The potential energy function depends on the force.•It is defined by the (negative of the) work done by the force.

Ug = mgy = mgy(t)

yi

Let U =Uf @ y=yf

Fg = mg

Drop the book!:Work done by Gravity: mg(yf –yi)

yf

yi

U =Uf @ y=yf

Fg = -mg

Work done by Gravity: -mg (yf –yi)

yf

= Ui – Uf

Ug = mgy = mgy(t)

Work-Energy Theorem:Work = KE = KEf - KEi

0

KEf – KEi = Ui – Uf = Work Done

xOR

Ui + KEi = Uf + KEf

Conservation of Total Mechanical Energy!

Ui + KEi = Uf + KEf

Conservation of Total Mechanical Energy!

Conservation of Mechanical energy for an isolated system is true whenever we can define a potential energy function (such as mgy) as we did above!

We can find such a function whenever we have forces which do not transfer mechanical energy into internal energy within the system = conservative forces.

Note that there is no energy being transferred into or out of the system (across the system boundary).

In- Class Problem: Conservation of Mechanical Energy

R

Ah

A bead slides without friction around the loop the loop. The bead is released from a height h =3.5R. What is its speed at point A? (b) How large is the normal force on the bead if m = 5g?

Ui + KEi = Uf + KEf

Conservation of Total Mechanical Energy!

Conservative forces: the work done by a conservative force does not depend on the path followed by the system, only their initial and final positions!

y

x

Path A

B

C

dW = F(x,y) ·dr

Examples: Constant force,Spring force,General Polynomial forces!

Example: Mechanical Energy of a Spring

F(x) = -k xU(x) = ½ k x2

http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html

Work-Energy Theorem:Work = KE = KEf - KEi

Work = Fdx

In- Class Problem:Conservative and Non-Conservative Forces

A force (in Newtons) acting on a particle moving in the xy plane is

F = 2y i + x2 j

Where x and y are in meters. The particle moves from (0,0) to (5,5). Calculate the work done along the three different paths. Is F conservative or Non-conservative?

0

B

A x

y(5,5)

Ui + KEi + Eint,i = Uf + KEf + Eint,f

Isolated System: Conservation of Total Energy!

(Isolated System)

Recall that with friction mechanical energy is converted to internal energy within a closed (an isolated) system.

Finding the Potential Energy Function from a given Force

Potential energy is defined so that Work = KE = - PE so that KE + PE = 0.

dU = -We define: dW =-F(x,y) ·dr

And integrate this along any path (for a conservative force) to find the actual function U(x,y) from F.

In 1D, F = - dU(x)/dxGoing backwards:

Finding the Force from a given Potential Energy Function

In- Class Problem:Conservative Forces and Potential Energy

1. For nonpolar molecules at large separation distances the forces between molecules are attractive and take the form: F = k/r7. Find the potential energy function. What happens when the molecules get too close?

2. If you are told a potential energy function is U(x,y) = 3x2y –7x, find the force that acts at any point (x,y).

Universal Law of Gravitation

mass1 mass2

distance2

Force ~

mass1

mass2

r- G m1 m2

r2

Force12 =

This force is always attractive and exists between every pair of masses in the universe!

If d is large we can approximate any object by a point particle at its center of mass. For a sphere we can do this at any distance (outside the sphere).

r

r(force on m2)

THE Universal constant “G”

Where does “G” come from?????

G = 6.67 10-11 N m2/kg2

G m1 m2

d2

Force =

This law has been verified from ~10-6 m to the largest distances probed with telescopes.

Extremely weak Force!

m1

m2

One Experimental Method(von Jolly) 6 TON lead sphere!

mercuryBalance – Measure F to restorethe balance!

Force (N)

distance from the surface of the Earth (in Earth Diameters)

1N

1 2 3 4 5

1/4N

Force on an apple as it moves away from the earth

0

d Rearth ~ 6400 KmMearth ~ 6 1024 Kg

G m1 Mearth

(Rearth + d)2

Force = - If you know G thiscan be used to measure the mass ofthe Earth!

Other influences also decrease as 1/R2 ! (sound, light from a star, etc.)

http://hubblesite.org/gallery/

Potential energy Functions for Gravitational and Electric Forces

Ug = -Gm1m2

r

Gravitational Potentialr

m1

m2

In- Class Problem: Gravitational Potential Energy

A satellite has a mass of 100Kg and orbits the Earth at an altitude of 2 106m. Find the potential energy of the satellite.

Potential energy Functions for Gravitational and Electric Forces

Ue = k q1q2

r

Electrostatic Potentialr

q1

q2

Conceptual Questions: Potential Energy

1. Explain why the total energy of a system can be either positive or negative, whereas the kinetic energy is always positive.

1. One person drops a ball from the top of a building while another person at the bottom observes its motion. Will these 2 people necessarily agree on the value of the gravitational potential energy of the ball-Earth system (at a given time)? On the change in potential energy? On the kinetic energy?

1. If 3 different conservative forces and 1 non-conservative force act within a system, how many potential energy terms appear in the equation that describes the system?

4. If only 1 external force acts on a particle (a) does it necessarily change the particle’s kinetic energy?(b) Does it change the particle’s velocity?

5. Our body muscles exert forces when we lift,push, run, jump, etc. Are these forces conservative?

6. What does the curve U(x) look like if a particle is in a region of neutral equilibrium?

7. A ball rolls on a horizontal surface. Is the ball in stable, unstable or neutral equilibrium?

Conceptual Questions (cont’d)

Chapter 8:Momentum and Collisions

• Linear Momentum and Its Conservation• Impulse and Momentum• Collisions• 2D Collisions• The Center of Mass• Motion of a System of Particles

In- Class Problems: Momentum

• A particle of mass 3Kg has a velocity (3 i – 4 j) m/s. Find its x and y components of momentum and the magnitude and direction.

• How fast can you get the Earth moving by jumping up in the air?

In- Class Problems: Impulse

1. A 1 kg steel ball strikes a wall at 5m/s at 60 degrees clockwise from the –y axis and bounces off at 60 degrees counterclockwise to the + y axis. The ball contacts the wall for 0.2s. What is the average force exerted on the ball by the wall?

• Angular Position, Speed and Acceleration ( ,, )• Rotational kinematics: constant angular acceleration (constant )• Relation between translational (linear) and rotational quantities• Rotational Kinetic Energy (KR = ½ I 2)• Torque ()• Rigid Object Under a Net Torque ( = I )• Angular Momentum and Its Conservation• Rolling Motion of Rigid Objects

Chapter 11: Rotational Motion

Rotational Motion- Circular Motion

Linear Speed and Rotational Speed

Tangential speed= distance rotational speed

d

A rotating “rigid” body (e.g., a turntable)

Rotational speed = angle you pass through in a certain amount of time. (How many revolutions per second?)

Rotational Motion- Rotational Inertia (the laziness of the rotational state of matter!)

Rotational Inertia (R.I.): the property of an object to resist changes in its state of rotation.

R.I. depends on the amount of mass and the distribution of that mass about an axis:

Lots of mass very far from the axis = high R.I.Small mass very close to axis of rotation = low R.I.

Axis of rotationAxis of rotation

M m

D

d

Rotational Inertia (also called “Moment of Inertia”)

Some Typical values:

PendulumI = mR2

m

r

Solid CylinderI = ½ mR2

- Depends on the axis (e.g., pencil)- Depends on how much massIs away from the axis!

Hoop about normal axisI = mR2

SphereI = 2/5 mR2

Stick about endI = 1/3mL2

Sample Problem: Rigid Object Under a Net Torque

Pivot

The rod is released from rest. What is the initial angular acceleration and tangential acceleration of the rigid rod?(I = 1/3ML2)

Sample Problem: Energy and Rotational Motion

The block falls 1m when released from rest. Given M, m and R. Find the final speed of the block.

M

m

When at rest on the launching pad, the force of gravity on the space shuttle is quite huge—the weight of the shuttle. When in orbit, some 200 km above Earth’s surface, the force of gravity on the shuttle is

1. nearly as much.2. about half as much.3. nearly zero (micro-gravity).4. zero.

(Neglect changes in the weight of the fuel carried by the shuttle.)

Answer: 1Discounting the changes in the fuel, the gravitational force on the shuttle in orbit is 94% as much as when on Earth’s surface—nearly the same!

Weight and Weightlessness

Weight = m”g”

More general definition of weight:

The weight of an object is the force the object exerts against a supporting surface (floor) or a weighing scale.

G Mearth m

Rearth2

Net Force = = m a = m “g”

a = g a = -g

What do the scales read in each case?

scale

Satellites

An Earth satellite is a projectile that falls around the Earth rather than into it!

Earth’s Surface

8000m (8Km ~5miles)

5m

Because the Earth is spherical, the earth’s surface drops ~5m for every 8000m tangent to the surface.

If you could throw a ball so that it only dropped 5m after traveling 8Km then the ball would follow the curvature of the Earth (we are not worried about mountains here)!

•Remember d = ½ gt2 ? It takes the ball about a second to drop 5m!So you have to throw it at 8 Km/s so that it orbits the Earth!

• The tangential velocity keeps satellites from colliding (the moon into the earth, the earth into the sun, etc.)

Satellites (cont’d)

Circular Orbits

Elliptical Orbits

- 8Km/s tangential speed!- Near surface, about 90minutes to orbit,

GPS satellites – about 12 hour orbits Geosynchronous – about 24 hour orbits. Moon – 27.3 days for orbit!

-Move faster than 8km/s(overshoots a circle)

-Kepler’s Laws!Real-time tracking @ http://www.n2yo.com/

Ocean Tides

Tides are caused by the rotation of the Earth combined with differences (about 6.7%)in the gravitational pull between the moon and the earth on the opposite sides of the earth!

Earth

Moon

Rotation axis

Pull on ocean fromMoon is larger here (not to scale!)

Pull on ocean fromMoon is smaller here • 2 high tides and 2 low tides per day!

• Spring tides/Neap tides

The ocean remain bulges are fixed while we rotate in and out of them!

Nasa

http://home.hiwaay.net/~krcool/Astro/moon/moontides/

Gravitational Fields

- We can imagine that any mass (even us!) sets up a gravitational field of force around is that attracts any “test” mass that is placed nearby.

We think of the mass as altering the space around it!

What is the gravitational field like INSIDE the Earth?

What is a “black” hole and should I be worried about particle accelerators creating them?

The Universal Law of Gravity

1. In what sense does the moon “fall”?

1. State Newton’s law of universal gravitation in words and in an equation!

3. What is the gravitational force between two 1Kg masses 1m apart?

4. What is the gravitational force between the Earth and a 1Kg mass?

5. What do we call the gravitational force between the Earth and your body?

The Inverse Square Law

6. If you travel four times further from the sun the amount of light to reach you is _________ as much.

For Review

Weight and Weightlessness

1. Give an example of when your weight is more than mg and another when your weight is less than mg. How about zero?

Tides

2. Why do both the sun and moon exert a greater gravitational force on one side than the other?

3. Gravitational force depends on the inverse _______ of distance. Tidal force, the difference in gravitational force per unit mass, depends on the inverse _________ of distance.

4. What’s the difference between spring tides and neap tides?

5. Do tides occur inside the Earth? Are they also greatest during a new or full moon?

6. Does the moon rotate (spin) on its axis? Does it spin and revolve about the Earth?

1. When the moon’s long axis is not aligned with the Earth there is a rotational force, or ________ about the Moon’s center.

Black Holes etc!

2. If the Earth shrank with no change in mass what would happen to the gravitational force on you if you stayed in the same place as before the earth started shrinking?

3. How can we detect black holes is they are invisible?

4. What percent of the universe is currently thought to be composed of an unknown form of matter (dark matter) and an unidentified form of energy (dark energy).