Download P202 Lecture 2

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CALM system
CALM system
P221 Lecture 1
• Welcome to P221; go over the syllabus
• Question: What is Physics (science in general)?
Why do the objects we observe in everyday life
come to rest when “left alone”?
• 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).
Note therefore, the relative uncertainty in 1.00 is quite
different from that of 9.99. UNCERTAINTY is the key,
not “number of significant figures”.
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: 26 F : 7 Other: 0 None: 12)
•

•
True. The force the horse is exerting on the buggy must be greater
than the force the buggy is exerting on the horse in order for the
buggy to move forward in the direction of the force provided by the
horse. *
This is true because the horse has to pull harder and provide more
force on the buggy for it to move forward. If the buggy pulled
backward with more force than the horse, then the horse and
buggy would more backwards.+
False; The horse moves forward because the ground exerts a force
on the horse in reaction to the horse's pushing against the road,
which results in a net force forward
This is correct!!!
•*BE CAREFUL OF WHAT FORCES YOU ARE TALKING ABOUT.RTFQ!!
•+The question is, HARDER THAN WHAT?
•DVB THE EXTERNAL FORCES PROVIDE THE KEY TO MOTION!!!
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: 16
•


F : 15 Other: 2
None: 12)
False because if the forces were equal, there would be no acceleration of
the horse and buggy. Even though the buggy is on round wheels, the force
vectors cancel each other out and provide the same necessary force to not
move. *
This is not true. Each body has a different mass. A different mass
results in a difference Force since force is dependent of mass.+
It is true that the force on the buggy is the same as the force on the horse.
But the difference between round wheels and flat hooves is not the reason
the buggy moves forward. The horse provides enough force to overcome
the friction between the street and the buggy so that the buggy can move
forward. (This is the key, and the hooves vs. wheels are in fact, the reason
for this difference in external forces!)
•* Several answers were like this, which anticipates the next question
•+Be careful of your concepts. Except for gravity, force is independent
•Of mass.
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: 9 F : 21 Other: 3 None: 12)
•
•
True, but is should be stated that the forces are equal because of the
absence of acceleration. If the horse and buggy are on a moving floor,
accelerating the horse and buggy in one direction, the magnitude of the
forces change.*
It's true that the two forces are equal and opposite, but it's false that the
two cancel out since the forces do not apply to the same object. The
buggy moves forward from the force of the horse if the horse
overcomes the force of the wagon by some other means such as using
the ground to propel itself forward.
THIS IS THE RIGHT
ANSWER!!!
• * NO! These two forces are equal irrespective of whether the horse and buggy
are accelerating or not!. DVB
Only 3 or 4 of you really nailed the reason for the statement being false.
Sample Warm-up (CALM) Q
• In the diagram below, what is the element
that provides the force holding the weight
up against the force of gravity? Why/How?
Ceiling
String
Wall 1
Wall 2
Weight
ground
•Answer:
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
(25 correct; 6 incorrect [sloppy with units, or
insufficient info to tell the mistake]; 17 no ans.)
• It could be approximated by the average speed.
The displacement/total time. 8m/4s = 2m/s (8=102, 4 = 5-1 to get the most accurate number).
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
(25 correct; 6 incorrect [sloppy with units, or
insufficient info to tell the mistake]; 17 no ans.)
• It could be approximated by the average speed.
The displacement/total time. 8m/4s = 2m/s (8=102, 4 = 5-1 to get the most accurate number).
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.
The class did quite well on this one, no need to review
(25 correct; 6 incorrect [sloppy with units, or
insufficient info to tell the mistake]; 17 no ans.)
• It could be approximated by the average speed.
The displacement/total time. 8m/4s = 2m/s (8=102, 4 = 5-1 to get the most accurate number).
During aerobic exercising, people often suffer injuries
to knees and other joints due to HIGH
ACCELERATIONS. When do these high
accelerations occur? (15 vertical; 12 lateral; 4
unclear; 17 no ans.)
•
•
•
•
•
These high acceleration occur when the athlete speeds up too
quickly. The speed needs to be increase slowly and gradually.
This can also happen when the motion suddenly comes a
complete stop.
These accelerations occur when the legs move up and down at
high speeds. (don't confuse speed an accel.)
High accelerations occur when one speeds up or jumps. Also,
high accelerations occur when one changes direction. (what do
you mean by changing direction here?)
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 (many with an explicit statement that the motion along
the ground was the key motion). IN FACT it is the abrupt (<<1sec)
change in vertical motion when you impact with the ground/floor.
Don't get trapped into thinking that velocity is ONLY along the
ground (more on this next week)!