26
AP Physics – B Midterm Review January 12, 2010
AP Physics – B Midterm Review
January 12, 2010
Before We Begin:
• You need to be confident in the basic skills of math before you can successfully approach physics problems. Refreshers for these topics are in your rainbow packet.
- Algebra - Basic trigonometry- Scientific Notation- Estimating
Mastering these skills takes PRACTICE, PRACTICE and more PRACTICE! If you are not getting the correct answers to physics problems, this is probably what you need to work on.
The Basic Concepts go a Long Way!• USE UNITS!
– If your units are not correct, your algebra is probably wrong – FIX IT!!
• Mass and Weight are NOT the same.• Weight is a Force and can be calculated using F = ma
where a is the acceleration due to gravity at that location. (often called g) Near Earth this is 9.8 m/s2, but we use 10m/s2 often to make the math quicker.
The force of gravity ALWAYS pulls straight down.And that is also the direction of the acceleration due to
gravity. <- even when something is flying in the air.
More Basics• An object in motion stays in motion unless a NET
force acts upon it. THEN it accelerates!!- A NET force is an unbalanced force.
- If an object is moving at CONSTANT VELOCITY, (or if the velocity in that direction is zero = “at rest”)
There is NO NET force acting on it.
DRAW free body diagrams any time you see forces acting on an object!!!
Linear Motion• The big d equation says it all:
d = di + vit + ½ a t2
If something is moving at CONSTANT VELOCITYThen a = 0So… d = di + vi t AKA: v = d/t
If something is “falling freely near the Earth”Then a = 10 m/s2 TOWARD EARTH.
**** if v is up (+) then acceleration due to gravity is down (- ) *** WATCH the signs!!!
PLC AP Physics 6
You MUST know these GRAPHS!!• Standing Still: (not really motion, but you’ll need it for mix-
n-match problems)
distance
time
veloci ty
time
accelerat ion
time
ZERO ZERO
PLC AP Physics 7
• Constant velocityThe slope of the distance vs. time graph IS velocity
The velocity graph has the same value for all time
Acceleration is ZERO.
distance
time
veloci ty
time
accelerat ion
time
ZERO
PLC AP Physics 8
• Constant acceleration
distance vs. time is quadratic ( the 1/2 at2 term)
velocity is linear (slope = a v = at)
acceleration is NOT ZERO!
distance
time
veloci ty
time
accelerat ion
time
Useful linear motion equations you should be prepared to use:
Constant velocity:
d = v t
t = d / v
v = (df-di) / t
a = 0
Constant acceleration:
df= di + vi t + ½ a t2
t = 2d / (vi+vf) vf
2 = vi2 + 2ad
vf = vi + at
a = (vf – vi) / t
Projectile Motion
ALWAYS assume there is no air frictionYou are working with two vectors vx and vy
use pathagorean theorem to find the resultantor if given v, use trigonometry to find vx and vy
• Horizontal velocity is CONSTANT v = d/t• Vertical motion is controlled by GRAVITY!!• When a projectile reaches the tippy top of its
path, its VERTICAL velocity is ZERO, but is STILL has the same horizontal velocity.
• Review the sheet (I think I gave you a copy of the famous Hewitt Concept Development sheet) with the boy throwing the ball off the cliff on one side and the boy throwing the ball in an arched path on the other.
Go TO YOUR NOTES!
Forces!
• We reviewed Free body diagrams and did several vector problems in class on Tuesday. Look at them again. Go to your homework book and try some homework problems from chapter 4.
• YOU MUST be comfortable with using trigonometry to find the x and y components of vectors!!!
Fnet = m a
• REMEMBER: For any system (group of objects moving together) the acceleration of the system = NET FORCE / TOTAL mass
• NET FORCE is the unbalanced force that acts on any part of the system that makes the ENTIRE system move.
• NET FORCE can also be the SUM of the forces acting on an object in either the x or y axis.
This is a good time to look at…• If you have the Hewitt Concept Development
sheet of the skydiver that we did at the library in November, read it again!
In your lab notebook:• In the Conservation of Energy lab we showed
how the problem could be solved using EITHER Newton’s Laws or Conservation of Energy. Take another look at that.
• The Atwood Machine is another good one to know.
ENERGY• Work is Energy
• ALL energy is measured in Joules
• Energy can NEVER be created nor destroyed, but it is constantly being transferred from one form to another.
• Power is the rate that energy is transferred (or work is done) P = w/t
Yes, it is a big equation!PEi + KEi + SEi = PEf + KEf + SEf + Work Lost
** The trick to these problems is to THINK and eliminate all factors that are zero before you go on.
PE = m g h (g = acceleration due to gravity = 10 m/s2)
KE = ½ m v2
SE = ½ k x2 Spring Energy k = force constant of the spring
Work lost = F d MUST be parallel (this F is often the frictional force in the problem)
Momentum• Momentum = m v
• Impulse = change in momentum = F t
• Momentum is ALWAYS conserved !!
The sum of the momentums of the individual objects before = the sum of the objects after
Its probably is a momentum problem if:
things collide, something explodes, a spring is released and it pushes or pulls things, a frictionless surface is involved
When energy is NOT conserved??
Elastic (ideal)collision = things bounce!
KE is the same before and after.
Inelastic collision = things crush, or stick together = energy is transferred (sound, friction…) and
KE is NOT the same before and after.
It can get a little messyIf two objects collide at a skew angle or if an
object explodes and pieces fly in various directions, momentum in x = m vx
The sum of the momentums in the x before = the sum of the momentums in the x after
The sum of the momentums in the y before = the sum of the momentums in the y after
Yes, momentum us a vector quantity. You may need to use some trig.
*** Watch the direction and +/- signs
Circular Motion• Velocity is tangential to the circular path• Acceleration is always toward the center of the
circular pathFc = m ac
ac = v2/rv = 2πr / T T = time for 1 rotation = periodf = 1/T f = frequency
Yes, you could need to use vectors, just as we did in the lab and the AP problem we did together in class
Qualitative Discussion• Don’t forget, if the force which holds an object in
circular motion suddenly stops, the object will fly off tangential to the circle!
• The object in circular motion is moving at constant speed, but since it is constantly changing direction, it is accelerating! And the direction of acceleration is inward.
• The greater the radius, the greater the tangential (also called linear) speed.
• All objects on a rotating object have the same rotational speed no matter where they are.
PLC AP Physics 22
Linear vs. AngularConstant velocity: v = d/ t ω = ∆θ / ∆ tConstant Acceleration:v = vo + at ω = ωo + α t
d = do + vot + ½ a t2 θ = θo+ ωo t + ½ α t2
V2 = vo2+ 2 ad ω2 = ωo
2 + 2 α θ
Hybrid equations:v = r ω a = r α f = ω / 2π
Don’t forget our Torque Trip!
When a force is applied at any location on an object other than its center of gravity it will cause the object to rotate.
Torque = d x F perpendicular (you may need trig.)
The weight (mass * gravity) of an object is considered to act at the center of gravity of the object.
Oh yeah, What’s CG?• When you have an object that has a simple symmetrical
shape, it is easy to see that the CG will be exactly in the center of the object, but when the shape is odd, you need to do more!
• Just like your grade in this course is a weighted average, the CG of an object is calculated the same way. – Cut the shape into simple shapes (rectangles and triangles)
– Find the center and area of each simple shape– Decide upon a datum point to measure from– X direction: for each shape:
multiply the distance (from its CG in the x direction to the datum point) by it’s area.
Sum the d x A for all the shapes and divide by the total area. The result is the x value (distance from the CG to the datum
point)- Do the same for the y direction.
PLC AP Physics 25
Newton’s Universal Law of Gravitation
• Every particle attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportion to the square of the distance between them.
F = G m1 m2 G = 6.67 x 10 -11 N*m2/kg2
d2
Back to little g • So why is the acceleration due to gravity the same for an ant as
it is for an elephant?
• Well, the F calculated using Newton’s universal gravitation is the same F that pulls the ant or elephant toward the Earth, also known as its weight (F = ma), where a is little g !!
m1 = the mass of Earth = 5.9737 × 1024 kgm2 = the mass of the ant or the elephant = make something up
d = the radius of the earth = 6,371,000 m
G m1 m2 = m2 g Does m2 matter? NO!!!d2 Feel free to calculate and find g!
