 Name 5 scalars
 "MaTe Speed TiDe"
 "MaTe Speed TiDe"

Mass

Temp

Speed

Time

Density
 Name 8 vectors
 "VeDiAcFo MagMoImTo"
 "VeDiAcFo MagMoImTo"

Velocity

Displacement

Accel

Force

Mag. Field

Momentum

Impulse

Torque
Think of force as...
 any influence capable of:
 causing a mass to accelerate
 causing a mass to accelerate
Center of Mass equation
 What should you remember to keep in mind with these problems?
C_{mass}=(r_{1}m_{1}+r_{2}m_{2}....)/m_{total}
 r=reference point
Hint: choose a reference point from which to measure each displacement vector
 Constant net force causes WHAT acceleration?
 and therefore WHAT velocity?
 and therefore WHAT velocity?

CONSTANT acceleration
 therefore CHANGING velocity!!!
 therefore CHANGING velocity!!!
 When you see "constant velocity" or "constant speed," think? (5)

NO acceleration

NO net force (F_{net}=0)
 All forces sum to zero
 up forces=down forces, left=right, etc.

NO change in direction
 The object is in EQUILIBRIUM!!!
 up forces=down forces, left=right, etc.
 When you see a LINEAR MOTION GRAPH, you'll ask yourself these 6 things:
 What does the SLOPE represent?
 Is this slope (+) or ()?
 It the slope....

Constant (straight line) or

Nonconstant (curved line)?
 What is the value on the xaxis?
 Is the y value (+) or ()

aka are you above or below the xaxis?
 At t=0, do I expect the value on the yaxis to be:

LARGE, or
 SMALL?
 Constant (straight line) or
 Nonconstant (curved line)?
 aka are you above or below the xaxis?
 LARGE, or
 SMALL?
 When I see the word "projectiles," I will remember 7 things:
 Horizontal VELOCITY:

never changes
 Horizontal ACCELERATION:

is always =0

VERTICAL acceleration:
 is always 10 m/s^{2} downward
 Vertical BEHAVIOR
 is always symmetrical
 ex: upward trip=downward trip

Time in air (T_{air}) depends on:

VERTICAL COMPONENT of velocity ONLY!!
 Range depends on both:
 vertical AND horizontal components
 Time is always the same for both x and y components of the motion
 never changes
 is always =0
 is always 10 m/s^{2} downward
 is always symmetrical
 ex: upward trip=downward trip
 VERTICAL COMPONENT of velocity ONLY!!
 vertical AND horizontal components
Law of Universal Gravitation formula
F_{g}=Gm_{1}m_{2}/r^{2}
 F_{g}=Gm_{1}m_{2}/r^{2}
 gives WHAT?
 gives WHAT?
 the force DUE to gravity
 NOT gravity itself!
 NOT gravity itself!
 Formula for GRAVITY (ITSELF!)
 aka "acceleration due to gravity"
 aka "strength of gravitational field"
 aka "acceleration due to gravity"
 aka "strength of gravitational field"
g=Gm/r^{2}
 What are the 2 physics equations that could be used FOR FALLING OBJECTS?
 x=½at^{2}
 V=√2gh
Time in air equation

T_{air}=?
 this equation can ONLY be used to calculate what?
T_{air}=2V/g
 can only be used to calculate "round trip" times
 aka total time in air,V, must be vertical component of INITIAL velocity
 At terminal velocity...
 What 2 things are happening?
 Give the formula for terminal velocity
 What 2 things are happening?
 Give the formula for terminal velocity
 object has stopped accelerating

forces of gravity and air resistance are BALANCED
F_{air}=mg
V_{avg}=?
V_{avg}=(V_{1}+V_{2})/2
 For PE_{grav}, which variation will you MOST LIKELY see on the MCAT?
PE_{grav}=mgh
 (At or near earth's surface; g=10m/s^{2})
Inclined Planes
 When is the equation when solving for:
Force down an IP PARALLEL to the surface?
F=mgsinθ
Inclined Planes
When is the equation when solving for:
Normal Force (F_{N) }down an IP
F_{N}=mgcosθ
Inclined Planes
 When is the equation when solving for:
Velocity of a particle at the base of an inclined plane
 What other kind of problem could this equation be used to help solve?
V_{final} = √2gh
Can also be used to help solve for
FALLING OBJECT problems
Inclined Planes
 When is the equation when solving for:
ACCELERATION DOWN an IP
 What other equation can you derive this from?
HINT:
 Notice you're solving for acceleration DOWN an IP.
 What other equation solves for something DOWN an IP that you know of?
a=gsinθ
Derived from:
 F=mgsinθ (Force DOWN an IP)
F=ma, ∴ "a"=gsinθ
Inclined Planes
 Why does V_{f} = √2gh work for either falling bodies OR a mass on an inclined plane?
HINT:
What is the above equation derived from?
What is happening to an object as it goes from the point where it is dropped until hitting the ground?
The formula V_{f} = √2gh is derived from CONSERVATION OF ENERGY
 by equating mgh to ½mv^{2}
 and solving for "v"
As long as friction, air resistance, etc. are ignored (which they are), energy will be conserved in an identical way...
WHETHER THE OBJECT FALLS DIRECTLY TO THE GROUND OR ROLLS DOWN A PLANE
Inclined Planes
As the angle of incline of a plane INCREASES:
 What happens to the value of a?
 What happens to the value of sinθ and cosθ?
 What happens to the normal force?
 What happens to the force down the plane?
 What is the maximum value for acceleration down an inclined plane?

What is the minimum value for acceleration down an inclined plane?
1.) Because the acceleration down a plane is directly related to the SINE of the angle
(F=mgsinθ, where gsinθ="a," since F=ma)
 the greater the angle, the closer the sine of the angle will be to ONE (1.0)
 Because increasing the angle of SIN:
 0 ⇒ 1.0
Therefore, the larger the angle, the closer the acceleration will be to 9.8m/s^{2}
2.) The normal force is related to the cosine of the angle (F_{n}=mgcosθ...OSD) , so as the angle increases, this value gets closer to zero
 Because increasing the angle of COS:
 1.0 ⇒ 0
 Therefore, as the angle increases the normal force decreases
3.) The force down an inclined plane is also related to the sine of the angle
 so it too will increase as the angle of incline increases
4.) The theoretical maximum incline is 90 degrees
 where acceleration would be exactly 9.8 m/s^{2}
5.) The minimum would be a plane with NO angle of incline
 where acceleration down the plane would be ZERO
Tension Forces
What is the tension in a rope being pulled from opposite ends with identical forces of 50N?
50N
Tension Forces
 A 500kg elevator is being accelerated upward by a cable with a tension of 6,000N
What force does the elevator exert on the cable?
TRICK QUESTION!
According to Newton’s 3^{rd} Law, if the elevator CABLE is pulling on the ELEVATOR with 6,000N of force...
...then the ELEVATOR must be pulling on the
CABLE with a force of 6,000N
Hooke's Law
 Give the equation
F=kΔx
 Δx is the displacement of the spring from its equilibrium point
Hooke's Law
F=kΔx
A ball rolls along a frictionless table and strikes a spring
 Describe:
 The force experienced by the ball due to the spring
 The acceleration of the ball
 How both change with time
 As the ball strikes the spring it experiences an everchanging force, F
As the spring compresses, however, that force increases according to Hooke’s Law
 Because the ball experiences an increasing force, it will also experience an increasing acceleration
The maximum force and acceleration will occur at the maximum compression of the spring
 As the ball is pushed backward by the spring these variables will change in a symmetrical way
such that their value is exactly the same at any given value of x on either the way in, or the way back out
QUICK!
What is the density of water?
 How many cm^{3} per mL?
 How many L of water in 1 kg?
 How many mL of water in 1 gram?
Density of water:
1000kg/m^{3} or 1.0g/cm^{3}
 1cm^{3} = 1mL
 1L of water = 1kg
 1mL of water = 1 gram
Define "SPECIFIC GRAVITY"
 HINT: It's a ratio that compares two things...
 Give the formula for Specific Gravity
SPECIFIC GRAVITY=
A ratio that describes how DENSE something is COMPARED TO WATER
SG = D_{substance }/ D_{water}
Specific Gravity
 For objects floating in liquids, the fraction of the object submerged = ?
 in other words, Fraction_{submerged}= ?
**If the liquid in which it is submerged is WATER, the fraction submerged is equal to ?
For objects floating in liquids:
 Fraction of the object submerged is equal to the ratio of the density of the object to the density of the liquid
Fraction_{submerged} = D_{object} / D_{liquid}
**If the liquid in which it is submerged is WATER, the fraction submerged is EQUAL to the specific gravity!
Specific Gravity
 A ball is floating ¾ submerged in a liquid with a density of 2.0 g/cm^{3}
What is the specific gravity of the liquid and the density of the ball?
Because the ball floats with ¾ of its volume submerged, it must be ¾ as dense as the liquid
 Therefore the density of the ball must be 1.5g/cm3
This is 1.5 times as dense as water, so the SG of the ball is 1.5, and the SG of the liquid is:
D_{Liquid}/D_{H2O }= 2g/cm^{3} / 1g/cm^{3}
=2
Define ARCHIMEDES' PRINCIPLE
 Differentiate b/t whether it's FULLY submerged or PARTIALLY (aka it's "floating")
Archimedes’ Principle
Any object displaces an amount of fluid.....
 Exactly EQUAL to its OWN volume
 ...if FULLY submerged
...OR...
 To the volume of whatever FRACTION of the object IS submerged (¾, ½, etc.)
 ...if FLOATING
The weight of the displaced fluid is exactly equal to the buoyant force pushing UP on the object
THE BUOYANT FORCE
 Give the equation
 Describe what each part means
HINT: PUG!
The Buoyant Force:
F_{buoyant} = ρvg

v
 volume of fluid that GETS displaced!
NOT the total volume of the fluid itself!
 ρ
 density of the fluid
NOT the object!
REMEMBER!
The buoyant force is always EXACTLY EQUAL to....?
... to the weight of the amount of fluid
that is getting DISPLACED BY the object
So, if an object is displacing 4 lb worth of fluid, then the buoyant force would be 4 N
The Buoyant Force
 What causes the buoyant force?
The best way to intuit buoyant force is to look at the pressure differential between the top and bottom of an object
 The fluid pressure, ρgh, will be larger at the object’s bottom surface than it is at the top surface
 due to the larger value of h (since it's at a deeper surface)
Let’s examine a submerged cube with the same surface area both top and bottom
The formula P = F/A tells us:
 If pressure is greater at the bottom, and area stays the same:
 there must be a greater force UP on the bottom surface than there is down on the top surface
This makes it logical that any submerged object will experience a net upward force
because of the PRESSURE DIFFERENTIAL!!
The Buoyant Force
 How does the buoyant force change with depth (h) ?
 How does the buoyant force change with the mass (m) of the object?
HINT: Think of the formula..."FB PUG" (facebook pug)
1.)
Buoyant force does NOT change with depth!
 Depth (h) is NOT in the formula ( F = ρvg )
 Therefore, we can confidently conclude that depth does NOT change buoyant force
 Whether the depth is shallow or very large, the pressure difference between ρghtop and ρghbottom will remain the SAME
2.)
Buoyant force does NOT change with depth!
Similarly, we can say that the mass of the object does NOT affect buoyant force
 Like depth, it is NOT in the formula
 Nor is it accounted for by our understanding of what causes the buoyant force
Remember: It's all about u