- Name 5 scalars
**“MaTe Speed TiDe”**

**Ma**ss**Te**mp**Sp**eed**Ti**me**De**nsity

- Name 8 vectors
**“VeDiAcFo MagMoImTo”**

**Ve**locity**Di**splacement**Ac**cel**Fo**rce**Mag**. Field**Mo**mentum**Im**pulse**To**rque

Think of force as…

- any
**influence**capable of:- causing a
**mass**to**accelerate**

- causing a

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

acceleration*CONSTANT*- therefore
velocity!!!*CHANGING*

- therefore

- 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.

change in direction*NO*- The object is in
*EQUILIBRIUM!!!*

- When you see a
, you’ll ask yourself*LINEAR MOTION GRAPH*:*these 6 things*

- What does the
represent?*SLOPE* - Is this slope
**(+)**or**(-)**? - It the slope….
**Constant**(straight line) or**Non-constant**(curved line)?

- What is the
?*value on the x-axis* - Is the y value
**(+)**or**(-)******aka are you**above or below**the*x-axis*?

- At
, do I expect the value on the*t=0**y-axis*to be:, or*LARGE**SMALL?*

- When I see the word “projectiles,” I will remember 7 things:

- Horizontal
*VELOCITY:*****never**changes

- Horizontal
*ACCELERATION:*is****always =0**

acceleration:*VERTICAL*- is
**always**10 m/s^{2}**downward**

- is
- Vertical
*BEHAVIOR*- is
**always symmetrical**- ex: upward trip=downward trip

- is
**Time in air**(T_{air}) depends on:of velocity*VERTICAL COMPONENT**ONLY!!*

- Range depends on both:
- vertical
horizontal components*AND*

- vertical
- Time is
**always the same**for both xy components of the motion*and*

Law of Universal Gravitation formula

*F _{g}=Gm_{1}m_{2}/r^{2}*

- F
_{g}=Gm_{1}m_{2}/r^{2}- gives
*WHAT?*

- gives

- the force
**DUE**to gravity**NOT**gravity itself!

- Formula for
**GRAVITY (***ITSELF*!)- aka “acceleration
*due*gravity”*to* - aka “
gravitational field”*strength of*

- aka “acceleration

**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
be used to calculate*ONLY**what?*

- this equation can

**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

- aka total time in air,V, must be

- At
**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 yousee on the MCAT?*MOST LIKELY*

**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**_{<strong>N</strong>) }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
equation solves for something DOWN an IP that you know of?*other*

- What

*a=gsinθ*

Derived from:

**F=mgsinθ**(Force__DOWN__an IP)

F=m**a**, ∴ “a”=gsinθ

Inclined Planes

- Why does
**V**work for either_{f}= √2gh__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”**

- and solving for “

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
value for*maximum***acceleration**down an inclined plane? - What is the
value for*minimum***acceleration**down an inclined plane?

- ) Because the
**acceleration**down a plane is directly related to the**SINE**of the angle

* (F=m**gsinθ**, where gsinθ=”**a**,” since F=m**a**)*

- the
**greater**the angle, the**closer**the sine of the angle will be to(1.0)*ONE* - 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**=mg_{n}**cosθ**…*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**

- ) 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 - ) The theoretical maximum incline is
**90 degrees**

*****where acceleration would be**exactly 9.8 m/s**^{2} - ) 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**experienceddue to the__by the ball__**spring** - The
**acceleration**of the**ball** - How
**both****change**with time

- The

- As the ball strikes the spring it experiences an
**ever**-**changing**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**per^{3}**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}= ?

- in other words,

***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 itsvolume*OWN*- …if
submerged*FULLY*

- …if

**…OR…**

- To the volume of whatever
**FRACTION**of the objectsubmerged (¾, ½, etc.)__IS__- …if
*FLOATING*

- …if

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!**

- volume of fluid

** NOT** the total volume

**of**the fluid itself!

- ρ
- density of the
**fluid**

- density of the

**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?

T*he 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)

- due to the

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

- Therefore, we can confidently conclude that depth does
- Whether the depth is shallow or very large, the
**pressure difference**between ρgh-**top**and ρgh-**bottom**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**