Transcript P221_2009_week1

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CALM system
P221 Lecture 1
• Welcome to P221;
– syllabus
• Question: What is Physics (science in general)?
– An attempt to understand the world around us in a
way that allows us to predict behariour and test our
observations quantitatively against those predictions.
• Any quantity in science has three elements:
– A number (3, or 2.56, or 6340.094 say).
– A unit (3 meters, 2.56 liters, 6240.094 seconds)
– An uncertainty (either explicit or implicit).
Adding numbers requires the
right UNITS!!
This sign makes no sense, you can’t add years and people!
Units and Uncertainty
• Always check your units!! You can’t have the correct
answer if your units are wrong or inconsistent!
• An informative website for the definition and meaning
of units can be found at:
– http://physics.nist.gov/cuu/Units/units.html
• Sometimes the uncertainty in a number is expressed
explicitly, sometimes implicitly:
– Explicit: 3.2265 +/- 0.0003
– Implicit: 3.23 or 0.674 (3 sig. figs. Uncertainty is
understood to be +/- 5 in the next digit, in these examples it
is +/- 0.005 and +/- 0.0005 respectively). UNCERTAINTY
is the way to look at it, not just the “number of significant
figures”. Note that the relative uncertainty in 1.00 is quite
different from that in 9.99.
Hints for solving problems
•
The text gives you a number of strategies for solving problems, pay
attention to them. Since it is often useful to have two views of such
important matters, here is my version of the key strategic points:
– RTFQ!!
– Draw a diagram (e.g. identify all forces here).
– Organize the data provided, ask yourself what the question is after
(explicit and implicit). Why was the question asked?
– Identify the crucial concept(s) and equation(s). What do you know
about the quantity that is being sought and what can you relate it to?
Can these be linked to the data provided?
– SIMPLIFY: can the problem be broken into smaller parts.
– SIMPLIFY: by doing some algebra before inserting numbers.
– Put numbers into the equation(s) (CHECK YOUR UNITS!!!)
– Round off to proper uncertainty (number of sig. figs.) ONLY at the
end of the calculation.
– Check to make sure that the answer makes sense (check units, is it
manifestly too large or too small, etc.) This may be easier if you can
make a rough guess for the size of the answer (see below).
Estimations
• If someone were to suggest to you that the
Earth “weighed” 1 billion billion tons (i.e.
109x109x103 = 1021 kg), would you say that
was about right, too small, or too big?
Newton’s Laws of Motion
• I: If no net force acts on an object, then that
object’s velocity (speed and direction of motion)
will not change.
• II: The net force on an object (F) is directly
proportional to its acceleration (a) ( i.e. the rate
of change of the object’s velocity); the
proportionality constant is the object’s mass, m:
–
F=ma
• III: When two objects interact, the force of one on
the other is precisely equal in size, but opposite
in direction as the force of the second on the first.
P221 Lecture 2
The horse pulls forward slightly harder on the buggy than the
buggy pulls backward on the horse, so they move forward.
(T: 28 F : 9 limited circum.: 7 Other: 2 No answ.: 7)
•
•
•
•
“The horse pulls forward with enough force to overcome the force of the
buggys mass” (think carefully about your answers, what does it mean to
“overcome an object’s mass”)
True. Since the force the of the horse pulling is greater than the cart it
would override the force of the cart. What is “the force of the cart”?
Ture, the buggy would move so long as the force acting in the the
positive x direction is greater than the force active in the negative x
directoins, or vice versa. Expl. Is correct, but is that the statement??
False. The buggy and the horse pull on one another with equal forces.
However, more than just those 2 forces are occuring. The reason the
buggy moves forward is that the force applied by the horse is greater
than the friction of the road. This is correct!!! Focus on the forces
acting on a given object, and identify each of them in terms of what
other object is producing that force. ALL FORCES COME FROM
SOMETHING AND ON SOMETHING ELSE.
P221 Lecture 2
The force on the buggy is as strong as the force on the horse,
but the horse is joined to the earth by its flat hoofs, while
the buggy is free to roll on its round wheels.
(T: 10




F : 21 limited circum.: 4 Other: 4
None: 6)
This statement is true only in limited circumstances. Only if the mass of the
buggy was perfectly larger than the mass of the horse to make up for the
difference in friction would this statement be true. Keep track of your concepts!
Mass has nothing to do with how much force is applied (except for gravity), it
tells you only how an object will react to a given force!!
If their forces are equal, making the net force zero, the buggy would not roll
freely on its wheels, making the statement false. (many answered this way,
anticipating the next question; see next slide for the explanation).
False, The horse has a stronger force then the force from the buggy because
the horse has more friction on its hooves compared to the buggy's wheels
The statement is true. The force from the tension in the connection between the
horse and buggy is equal on both objects. The force of friction between the
ground and the horse's hooves, however, is stronger than the force of friction
between the ground and the wheels. (This is the key. The motion of the
system is determined by the forces acting on it from the outside!! In this
case the size of those outside forces is indeed determined by the nature of
the interaction of the two bodies with the ground.)
P221 Lecture 2
Newton’s third law states clearly that the force of the horse on the
buggy is equal and opposite to the force of the buggy on the
horse. Hence the two forces cancel each other out and the
buggy cannot move forward. (T: 11+6 F : 23 Other: 4 None: 8)
•
•
•
The above statement is half correct concerning the situation. If the force
exerted by the bugy on the horse is equall in magnitude but opposite in
direction to the force exerted by the horse on the bugy, then there is no
movement if they are at rest or no acceleration if both are moving.
False. Although the interaction between the buggy and the horse are equal in
magnitude and opposite in direction, the net force of the system containing
the horse, the buggy, and the Earth is what truly matters when considering if
the buggy can move forward or not. This is true, but it misses a subtle point..
This is false because the horse and the buggy are two different [sub]systems
and therefore the forces cannot cancel so the [combined] system has a net
force [from the ground] that provides an acceleration, or in other words,
motion. THIS IS THE KEY HERE; these two forces act on different
objects, and you only add forces acting on the same object!!! YES,
they are equal and opposite; NO, they do not cancel!
Horse and Cart
Sample Warm-up (CALM) Q
• In the diagram below, what is the object
that provides the force to the weight
holding it up against the force of gravity?
Explain.
Ceiling
String
Wall 1
Wall 2
Weight
ground
•Answer:
Sample Warm-up (CALM) Q
• In the diagram below, what is the object
that provides the force to the weight
holding it up against the force of gravity?
Explain.
Ceiling
String
Wall 1
Wall 2
Weight
ground
•Answer: The string is supporting the weight against gravity. It is
the only object TOUCHING the weight. (of course, the ceiling is
holding up the string and the walls are holding up the ceiling, but
we are asked about the weight!
P221 Lecture 2
P221 Lecture 2
Newton’s Laws of Motion
• I: If no net force acts on an object, then that
object’s velocity (speed and direction of motion)
will not change.
• II: The net force on an object (F) is directly
proportional to its acceleration (a) ( i.e. the rate
of change of the object’s velocity); the
proportionality constant is the object’s mass, m:
–
F=ma
• III: When two objects interact, the force of one on
the other is precisely equal in size, but opposite
in direction as the force of the second on the first.
Explaining motion:
take-home lessons
• FORCES are the key: we need to develop
tools for identifying and quantifying forces.
• CONTACT, GRAVITY (for now) only!!
• Forces cause CHANGES in motion, they
DO NOT CAUSE motion itself!!
• Be careful with our (rather precise) use of
terminology in this course, it could differ in
subtle but important ways from your
previous experience.
• Watch your units!!
Terminology
•
•
•
The previous slide introduced a number of terms (in italics) that have
particular meaning to physicists. Please be careful in using the ideas
associated with these words.
Velocity (v): Gives the direction of an object’s motion as well as its speed
in that direction (our first example of a VECTOR).
Forces (F): clearly we need to get practice identifying forces, since they
play a key role in determining motion (though not necessarily the role your
intuition might lead you to believe). We consider:
– Contact (arise from physical contact between two objects, e.g. pushes, pulls,
spring forces, friction, etc.)
– Fundamental (gravity, nuclear (2 types), and electro-magnetic).
– For now we will only concern ourselves with contact forces and gravity. The other
fundamental forces we ignore for p221.
•
•
Acceleration (a): Time rate of change of an object’s velocity (more on this
later) NOTE: If a=0, then the velocity DOES NOT CHANGE.
Mass (m): measure of an object’s resistance to changes in its velocity (i.e. a
measurement of the object’s inertia).
The figure shows a displacement vs. time graph
for a ball rolling along the floor. During the
third second, what was the approximate the
speed of the ball? Please describe how you
obtained your answer.
The class did quite well on this one, no need to review
(39 correct; 2 incorrect; 12 no ans.)
•
“To figure this out I guess I really did not use
an equation or anything, I just viewed the
graph and put the displacement in place with
time and figured out their relationship to one
another.”
What is the average
velocity over the
time from 1 sec to 9
sec?
The figure shows a displacement vs. time graph
for a ball rolling along the floor. During the
third second, what was the approximate the
speed of the ball? Please describe how you
obtained your answer.
The class did quite well on this one, no need to review
(39 correct; 2 incorrect; 12 no ans.)
•
“To figure this out I guess I really did not use
an equation or anything, I just viewed the
graph and put the displacement in place with
time and figured out their relationship to one
another.”
What is the average
velocity over the
time from 1 sec to 9
sec? What is the
average speed?
The figure shows a displacement vs. time graph
for a ball rolling along the floor. During the
third second, what was the approximate the
speed of the ball? Please describe how you
obtained your answer.
• Average velocity: 0 m/s (displacement zero)
• Average speed: 2 m/s (it always moves at this
speed, first toward + x, then toward – x).
During aerobic exercising, people often suffer injuries
to knees and other joints due to HIGH
ACCELERATIONS. When do these high
accelerations occur? (13 impact on the ground; 19
Change in direction; 9 unclear; 12 no ans.)
•
•
•
•
•
The high accelerations occur when the person changes the
direction they move their joints very rappidly
High accelerations usually occur during the start of a run, or when
the person is changing directions.
During aerobic exercising, I think that those high accerlerations
occur when they are doing jumping steps. This could be a similar
thing to riding in a cab.
Virtually everyone figured that it is acceleration that is the key
(good), but a large number left it at that, or talked about changes
of velocity (concentrating on the size of the velocity change: i.e.
Large numerator). IN FACT it is the abrupt (small
denominator<<1sec) change in vertical motion when you impact
with the ground/floor that gives the greatest force (injury is slightly
more complicated as a smaller force in a direction in which the
joint is weaker, such as an awkward landing is more problematic).
Don't get trapped into thinking that velocity is ONLY along the
ground (more on this next week), and don’t forget that a large
ratio can come from either a large numerator or a small
denominator!