Week 3

 

Video č You are expected to view this material in a venue where you can concentrate. You may view the talk several times and you are allowed to take notes.

When you have finished, you must complete a short quiz. The quiz will ask a few questions about the material presented in the video. If there are aspects of the talk that are confusing the student should research the topic. However, the student is not expected to have a detailed knowledge of the subject but should be able to explain the video to a colleague.

Catherine Mohr: Surgery's past, present and robotic future http://www.ted.com/talks/catherine_mohr_surgery_s_past_present_and_robotic_future.html

 

 

Announcements:

First HW set is being posted.  I will place it in the HW1 folder and students will have till the end of September to complete it.

You have 10 tries.  This should be enough to get the answer but not enough to simply get the correct answer by guessing.

Yes, you get credit but HWs are also about mastering the important material.  I have held numerous HW sessions where students delight in getting the correct answer despite not understanding how they worked the problem.  This is a formula for a low grade.  With help from various sources most students should manage to receive a decent grade for this portion of the course.  The best students will be able to duplicate this level of work on the exams.

 

New video this week and I expect you to watch it and complete the quiz by Friday. While I will often leave the quizzes open longer so that students that encounter problems have time to resolve them, it is not my intention to add extra time.  In other words I have added a grace period to the due date to allow for busy schedules, unexpected assignments etc. so plan on completing assignments at least one day ahead of the due date.

 

We need to understand  how we describe motion.  There are some basic notions that are critical:

Average

Traveling to DC you clock 120 miles on your odometer and see that you arrive at your destination in 2 hours.  60 mph would be your average speed.  You are well aware of the fact that this doesn’t mean that your speedometer reads 60 mph at all points in the trip.  As a matter of fact an average value may be a value that your speedometer never really reads. For example,  I could travel part of my trip (20 minutes) at a constant speed of 50 mph and then travel another part (20 minutes) at 70 mph.  My average speed would be 60 mph even though no significant portion of the trip was driven at that speed.

Value which characterizes the entire process.

instantaneous

During my trip I could monitor and plot or record the value of my speedometer.  This would be my instantaneous velocity.

A value that characterizes a very short element or period of a process.

 

 

Position

Vector- Establish reference (origin-coordinate system x,y,z) – Find magnitude an direction to describe a location wrt the origin.  Given two positions you can find the change in position. This is the position of the second location but wrt the first position.

distance

Scalar – Number that describes how far irrelevant of the direction

 

 

Velocity

Vector – change in position / change in time

speed

Scalar Magnitude of the velocity (speedometer)

 

 

Acceleration

Vector –change in velocity / change in time

‘Amount”

Scalar- you can discuss simply the amount of acceleration without reference to the direction

 

 

Delta D

D is short hand notation for a difference or a change.

You can find the change in temperature, change in height, change in momentum, change in force, change in position.  The result of the calculation preserves the nature of the objects in that numbers remain numbers and vectors remain vectors. So that a change in velocity is a vector.

 

We need to know what these objects are and the relationship among them.  We need to be able to calculate values based on other information (word problems). We need to be able to represent these quantities on graphs (limit the problems to 1-d).

 

 

Lec6Week3

 

Newton’s Laws

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natural state of motion is rest or uniform motion

 

revisit inertia (discuss motion of earthč like sitting on a very fast moving train, 70,000 mph, speed of sound is 768 mph,  plane rocket 5000 mph, Saturn rocket 25,000, train few hundred mph)

 

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Force is a push or a pull.  We know what a force is but we probably do not know how forces change motion.  The problem is that there are usually several forces at play and we don’t break down motion so as to see the connections.  As a matter of fact,  it took two of the smartest people of all times to finally figure out motion, Galileo and Newton

 

Normally you relate the total force to the total acceleration.

total balance

total accleration

 

Consider the throwing and catching of a ball. [Work only with the horizontal motion and neglect falling motion and forces.  If necessary we can simply roll the ball along the foor so that the gravity force and the normal force cancel out.]  (One interesting thing about vectors is that the results of forces, accelerations, velocities can be analyzed in perpendicular directions separately. Break vectors into x,y,z components. Analyze the individual x,y,z motion. Combine these separate motions together for the total.)

 

Force of gravity on earth

 

 

We live in an environment where everything is being pulled downward in proportion to their mass.  This in combination with Newton’s 2nd law.

 

 

Although now we know that there is a relationship between space, time and gravity č General Relativity that explains the above equality for this class it is a mystery why these two fundamentally different definitions should have the same value.

 

 

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action interaction

 

key is defining the system

Recognize that different forces act on each system but some of these forces are related by Newton’s third law. The action reaction rule gives a relationship where one finds two forces.  The forces are the same magnitude and directed oppositely and , HERE IS THE KEY, each force acts on a DIFFERENT system.

 

Analysis of the motion of objects requires us to define what are the objects of interest.

Example:

Cars on the highwayč We don’t care what is happening to the objects that are considered part of the car.  So if two people are pushing each other (or the seat is pushing up on the driver and the driver due to gravity is pushing down) the forces are internal and though they may result in parts changing position we can define the position of the car, center of mass, in a way that is independent of the internal forces.  If we don’t allow anything in the car to move we can see that action and reaction between two parts cancel.  This may be one reason why there is so much difficulty understanding Newton’s third law.

 

Horse and buggy.

Flat surface

Analyze as two separate systems

Horse pushes on the ground ground pushes back:  1 force on the horse.

The horse pulls the buggy the buggy pulls back :   2nd force on the horse

Gravity pulls the horse down                                  3rd force

Horse pushes down on the the earth pushes up:     4th

For horizontal motion F3=-F4 sum is 0.

 

Buggy has the same forces 3,4 that will balance

Wheels (frictionless motion?  surface does allow for horizontal forces but the wheel eliminates frictional losses. Wheels on ice are useless. They don’t work because the smooth ice surface removes all horizontal surface forces. A wheel requires large horizontal surface forces but these forces are no longer able to retard the motion of the object so they may not be referred to as frictional forces. For uniform motion the part of the wheel that touches the surface comes to rest on the surface. For accelerated motion the wheel is at rest but pushing on the ground. Consider your foot as you take a step.  You push the ground back.  If you are running you are trying to touch the ground with a small relative speed.  If you don’t you slip or slide.)

 

when 1&2 balance and 3&4 balance No total force č constant motion

dealing with the cart and the horse separately we find that the horse pushes on the ground and the ground pushes on the horse.  The horse will then pull on the cart with the exact amount of force so that the buggy moves with the horse.  The buggy of course pulls back so that the total force on the horse is the ground force minus the buggy force and the total force on the buggy will be the force of the horse.  The other forces cancel.  If the buggy is very light then there is only a small force between the two.  If the buggy is very heavy (mass is the critical factor) then the forces will be large.