### Speed Distance & Mass Metric System – Physics

This chapter covers speed distance and mass metric system of physics.

Newton

What is forced expressed as in the metric system

Parallelogram

To find the net result of two vectors we use the ___ rule

Resolution

The process of determining the components of a vector is called

Inertia

The tendency of objects to resist changes in motion

Mass

Is a measure of sluggishness of objects to resist changes in thEir motion

Kilogram

The metric system unit for this measurement of sluggishness

Mass, net force

The acceleration of an object is inversely proportional to the ___ of an

object and directly proportional to the ___ _____ acting on the object

G

When the net force acting on an object is the forc of gravity only the

acceleration of the object is

Constant

When an object falls through air, the net force is equal to th vector sum of

the force of gravity downward and the force of air resistance up ward. When

these forces are equal, objects falls at a ____ speed

Even

The total number of forces existing in the universe at any one time must be

( even or odd)

Mechanical equilibrium

the state of an object or system of objects for which any impressed forces

cancel to zero and no acceleration occurs

Static equilibrium

The type of equilibrium that exists when an object is not moving. Net force=

zero.

Dynamic equilibrium

A form of equilibrium where opposing forces balance each other out, and the

system as a whole does not change.

1/2at^2

D=

ViT+1/2at^2

D= (monster formula)

At

V=

Vi +at

Vf

Newton’s First Law

The Law of Inertia

Newton’s Second Law

Fnet = ma

Newton’s Third Law

For every action force there is an equal and opposite reaction force

Contact Forces

Forces that result from direct physical contact between objects

Field Forces

Forces that exist between objects in the absence of physical contact

Contact Force Examples

Friction force, Normal force, Tension force

Field Force Examples

Magnetic force, Gravity force, Electrical force

Inertia

Tendency of an object to maintain its state of motion

Equilibrium

The state of a car moving in constant velocity or at rest

Acceleration

The state of motion if a nonzero net force acting on the car

Force

Acceleration is directly proportionate to this quantity

Mass

Acceleration is inversely proportionate to this quantity

Weight

Measure of the force of gravity on an object

Newtons

Units used for the force of gravity of an object

Mass (measure)

measure of the quantity of matter of an object

Kg

Units used for the quantity of matter of an object

107,00 kilometers per hour

how we are moving relative to the sun

Galileo

credited with being the first to measure speed by considering the distance

covered and the time it takes

speed

defined as the distance covered per unit of time, how fast something moves

speed equation

distance/time

slash symbol (/)

is read as per and means divided by

instantaneous speed

is the speed at any instant

average speed equation

total distance covered/time interval

total distance covered equation

average speed x time

velocity

how fast an object is going and in what direction, we need to know both the

speed and the direction of an object for this

vector quantity

a quantity in physics that specifies a direction and a magnitude is called

this

constant speed

means steady speed

constant velocity

means motion in a straight line at a constant speed

acceleration

is how quickly velocity changes; the change in velocity, also is not just

the total change in velocity but also the time rate of change or the change per

second in velocity, and it applies to decreases as well as increases in

velocity (changes in both speed and direction

acceleration equation

change in velocity/time interval

change

the key idea that defines acceleration

deceleration

a large decrease per second in the velocity of a car

curved path

when we accelerate because our direction is changing

speed an velocity

are commonly used interchangeably when straight-line motion is being

considered

acceleration equation (along a straight line)

change in speed/time interval

Galileo

developed the concept of acceleration in his experiments on inclined planes,

and found greater accelerations for steeper inclines

velocity acquired equation

acceleration x time

instantaneous speed or velocity

are at any time simply equal to the acceleration multiplied by the number of

seconds it has been changing

no air resistance

all objects can fall with the same unchanging acceleration

free fall

when a falling object is free of all restraints- no friction, with the air

or otherwise- and falls under the influence of gravity alone, the object is in

this state

free fall equation

during each second of fall, the object gains a speed of 10 meters per

second, and the gain per second is its acceleration

velocity acquired in free fall from rest equation

v=gt

instantaneous speed is zero

at its highest point, when it is changing its direction of motion upward to

downward

the object slows as it rises

during the upward part of this motion

negative sign

downward velocities have this

distance traveled equation

1/2(acceleration x time x time), ?=1/2gt squared

unequal acceleration

is a common observation that many objects fall with

air resistance

is the fact that is responsible for these different accelerations, it also

appreciably alters the motion of things like feathers

speed or velocity

is how we specify on how fast something is falling, and it is expressed as

v=gt

a rate of a rate

is what makes acceleration so complex

0.6 meters

if you jump higher than this than you are exceptional

airborne

no amount of leg or arm pumping or other bodily motion can change your hang

time when you are this

when airborne

the jumpers horizontal speed remains constant while the vertical speed

undergoes acceleration

Motion is

described _____ to something

relative

True or

False: Speed is a measure of how fast something is moving

True

Speed is the

rate at which distance is covered, and it is measured in units of _____ divided

by time

distance

_________

speed is the speed at any instant

instantaneous

True or

False: Average speed is the total acceleration covered divided by the time

interval

False

True or

False: Velocity is speed together with direction

True

Velocity is

constant only when speed and _____ are both constant

direction

______ is

the rate at which velocity is changing with respect to time

acceleration

An object

accelerates when its speed is _____, when its speed is ______, and/ or when its

direction is changing

increasing;

decreasing

True or

False: Acceleration is measured in units of velocity divided by time

False

An object in

free fall has a constant acceleration of about ___m/s

10

Units

systems giving context to numbers

Length

meter (m)

Mass

kilogram (kg)

Force

newton (N)

Time

second (s)

Work

joule (J)

Energy

joule (J)

Power

watt (W)

giga

(G or B), 10^9

mega

(M), 10^6

kilo

(k), 10^3

centi

(c), 10^-2

milli

(m), 10^-3

micro

(µ), 10^-6

nano

(n), 10^-9

pico

(p), 10^-12

Scientific Notation

a method of writing very large or very small numbers by using powers of ten;

0.0000000004 = 4x 10^-10 or

500,000,000,000,000 = 5 x 10^14

Significand

the number before the power of 10 in scientific notation, such as the number

5 in the scientific notation 5 x 10^14

Scientific Notation Multiplications

multiply the significands and then add the exponents;

(4 x 10^-10)(5 x 10^14) = 2 x 10^5

– multiplying 4 by 5 = 20 (converted to 2)

– adding -10 and 14 = 4

Scientific Notation Divisions

divide the significand in the numerator (top) by the significand in the

denominator (bottom) and then subtract the exponent in the denominator from the

exponent in the numerator;

(4 x 10^-10) / (5 x 10^14) = 8 x 10^-25

– dividing 4 by 5 = 0.8 (convert to 8)

– subtracting 14 from -10 = -24

Scientific Notation Raised to a Power

raise the significand to that power and then multiply the exponent by that

number;

(6.0 x 10^4)^2 = 3.6 x 10^9

– squaring (^2) 6.0 = 36.0 (convert to 3.6)

– multiplying 4 by 2 (10^4 x 2) = 8

Scientific Notation Additions

exponents must always be the same (if not convert one), and then add the

significands together;

3.7 x 10^4 + 1.5 x 10^3 = 3.9 x 10^4

– converting 1.5 x 10^3 = 0.15 x 10^4

– adding 3.7 and 0.15 = 3.85 (round to 3.9)

Scientific Notation Subtractions

exponents must always be the same (if not convert one), and then subtract

the significands;

3.7 x 10^4 – 1.5 x 10^3 = 3.6 x 10^4

– converting 1.5 x 10^3 = 0.15 x 10^4

– subtracting 1.5 from 3.7 = 3.55 (round to 3.6)

sin θ

SOH

= opposite / hypotenuse

= y / h

cos θ

CAH

= adjacent / hypotenuse

= x / h

tan θ

TOA

= opposite / adjacent

= y / x

Trigonometric Functions

the ratio relationship between the sides of right triangles

Logarithm

the power to which a base such as 10 (log) or “e” (ln) must be

raised to get the desired number;

– log 45 = X (10^x = 45), so X = 1.6532

– ln 45 = Y (e^y = 45), so Y = 3.8067

Natural Log (“e”)

“e” = ln = 2.71828

Vectors

numbers that have both magnitude and direction, such as displacement,

velocity, acceleration, and force

Scalars

numbers that have magnitude only, such as disctance, speed, energy,

pressure, and mass

Resultant (R)

the sum or difference of two or more vectors

Pythagorean Theorem

X² + Y² = V² or, V = √X² + Y²

V = any vector (use V as the hypotenuse)

X = x component of vector V

Y = y component of vector V

Kinematics

branch of Newtonian mechanics that deals with the description of objects in

motion which allows us to describe an objects velocity, speed, acceleration,

and position with respect to time

Displacement (x)

an object in motions overall change in its position in space

Velocity (ν)

a vector quantity whose magnitude is speed and whose direction is the

direction of motion;

v = displacement (x) / time (t)

SI units = meters/second (m/s)

Average Velocity

average velocity (v, with a line over it) = Δx / Δt

Speed (s)

the rate of actual distance traveled in a given unit of time:

s = distance (d) / time (t)

Instantaneous Velocity

the average velocity as the change in time approaches zero;

v = limΔx / Δt

Acceleration (a)

a vector quantity of the rate of change of velocity over time;

a = Δv / Δt

Average Acceleration

average acceleration (a, with a line over it) = Δv / Δt

Instantaneous Acceleration

the average acceleration as the change in time approaches zero;

a = limΔv / Δt

Linear Motion

the objects velocity and acceleration are along the line of motion. The

pathway of the moving object is literally a straight line (one-dimensional

motion), but not limited to vertical or horizontal paths

Acceleration due to Gravity (g)

g = 9.8 m/s²

Constant Acceleration

an object in motion who’s velocity is changing due to a constant force being

applied

Kinematics Equations

the five equations applied to objects in motion with constant acceleration;

v = v0 + at

x – x0 = v0t + (at² / 2)

v² = v0² + 2a(x – x0)

average v = (v0 + v) / 2

Δx = (average v)(t) = [(v0 + v) / 2] t

Projectile Motion

an object in motion that follows a path along two dimensions and the

velocity and acceleration are in two directions (usually horizontal and

vertical) and separate from each other

Free Fall

objects in linear motion experiencing acceleration equal to that of gravity,

discounting air resistance

Momentum

the mass of an object multiplied by its velocity.

A moving object can have a large momentum if it has a large mass, a high speed,

or both.

It is harder to stop a large truck than a small car when both are moving at the

same speed.

The truck has more momentum than the car. By momentum, we mean inertia in

motion.

Momentum Equation

momentum = mass × velocity

momentum = mv

When direction is not an important factor,

momentum = mass × speed

Impulse

The quantity force × time interval is called impulse.

A force sustained for a long time produces more change in momentum than does

the same force applied briefly.

Both force and time are important in changing an object’s momentum.

When you push with the same force for twice the time, you impart twice the

impulse and produce twice the change in momentum.

Impulse Changes Momentum

The change in momentum depends on the force that acts and the length of time

it acts.

If the momentum of an object changes, either the mass or the velocity or both

change.

The greater the force acting on an object, the greater its change in velocity

and the greater its change in momentum.

A glass dish is more likely to survive if it is dropped on a carpet rather than

a sidewalk. The carpet has more “give.”

Since time is longer hitting the carpet than hitting the sidewalk, a smaller

force results.

The shorter time hitting the sidewalk results in a greater stopping force.

The safety net used by circus acrobats is a good example of how to achieve the

impulse needed for a safe landing.

The safety net reduces the stopping force on a fallen acrobat by substantially

increasing the time interval of the contact.

Impulse Equation

impulse = F × t

The greater the impulse exerted on something, the greater will be the change in

momentum.

impulse = change in momentum

Ft = ∆(mv)

Increasing Momentum

To increase the momentum of an object, apply the greatest force possible for

as long as possible.

A golfer teeing off and a baseball player trying for a home run do both of

these things when they swing as hard as possible and follow through with their

swing.

The force of impact on a golf ball varies throughout the duration of impact.

Decreasing Momentum

If you were in a car that was out of control and had to choose between

hitting a haystack or a concrete wall, you would choose the haystack.

Physics helps you to understand why hitting a soft object is entirely different

from hitting a hard one.

If the change in momentum occurs over a long time, the force of impact is

small.

If the change in momentum occurs over a short time, the force of impact is

large.

Bouncing

Cassy imparts a large impulse to the bricks in a short time and produces

considerable force. Her hand bounces back, yielding as much as twice the

impulse to the bricks.

The curved blades of the Pelton Wheel cause water to bounce and make a U-turn,

producing a large impulse that turns the wheel.

Conservation of Momentum

The momentum before firing a cannon is zero. After firing, the net momentum

is still zero because the momentum of the cannon is equal and opposite to the

momentum of the cannonball.

Law of Conservation of Momentum

Describes the momentum of a system

If a system undergoes changes wherein all forces are internal, the net momentum

of the system before and after the event is the same. Examples are:

atomic nuclei undergoing radioactive decay,

cars colliding, and

stars exploding.

Elastic Collisions

When a moving billiard ball collides head-on with a ball at rest, the first

ball comes to rest and the second ball moves away with a velocity equal to the

initial velocity of the first ball.

Momentum is transferred from the first ball to the second ball.

When objects collide without being permanently deformed and without generating

heat, the collision is an elastic collision.

Colliding objects bounce perfectly in perfect elastic collisions.

The sum of the momentum vectors is the same before and after each collision.

Terminal Velocity

the constant velocity of a falling object when the force (net force = 0) of

air resistance is equal in magnitude and opposite in direction to the force of

gravity

What change in momentum does the cart undergo?

25 kg x m/s Change in momentum is equal to impulse.

If a the mass of the cart is 2 kg and the cart is initially at rest,

calculate its final speed.

5 kg·m/s divided by 2kg = 12.5 m/s

Momentum is equal to mass multiplied by velocity. The change in momentum is 25

kg·m/s and since it started at rest, then this is equal to its final momentum.

To get velocity we divide momentum by mass.

A 2-kg blob of putty at 3 m/s slams into a 2 kg blob of putty at rest

Calculate the speed of the two stuck-together blobs of putty immediately after

colliding.

Momentum of the system before the

collision was 6 kg·m/s, and since momentum has to be conserved the momentum

after collision has to be 6 kg·m/s. The mass after

the collision is 4 kg, so the velocity after the collision is 1.5 m/s

Calculate the speed of the two blobs is the one at rest was 4 kg.

The momentum of the system before the collision was 6 kg·m/s, and since

momentum has to be conserved, the momentum after the collision has to be 6

kg·m/s. The total mass after the collision in this case would be 6 kg, making

the velocity 1 m/s.

When you ride a bicycle at full speed and the bike stops suddenly, why do

you have to push hard on the handlebars to keep from flying forward?

So that the reaction force of the handlebars on you will produce a

backward-acting impulse.

In terms of impulse and momentum, why are air bags in automobiles a good

idea?

In a crash you lose all momentum. Your change in momentum is equal to

impulse. Impulse is force multiplied by time. The air bag makes your collision

with the dashboard take longer so there is less force to hurt you.

Why is it difficult for a firefighter to hold a hose that ejects large

amounts of water at high speed?

The hose tends to recoil from the ejected water.

You can’t throw a raw egg against a wall without breaking it, but you can

throw it at the same speed into a sagging sheet without breaking it. Explain.

The sheet makes the collision take longer, and therefore there is a smaller

force on the egg. Remember that the impulse is equal to the change in momentum.

The change in momentum is defined by the mass and velocity, neither of which

are changed by how you stop the egg. So this means that the only way to

decrease the force on the egg is to increase the time it takes to change the

momentum, the sheet does this nicely.

Suppose you roll a bowling ball into a pillow and the ball stops. Now

suppose you roll it against a spring and it bounces back with an equal and

opposite momentum. Which object exerts a greater impulse, the pillow or the

spring?

The spring because the forward momentum is stopped and an equal and opposite

backward momentum is created, making the impulse twice as big because there is

twice as much change in momentum.

If the time it takes the pillow to stop the ball is the same as the time of

contact of the ball with the spring, how do the average forces on the ball

compare?

The force of the spring is twice as big. We know this because we found in

part a that the impulse is double. Impulse is time multiplied by force. If the

time is the same and the impulse is double that means that the force has to be

double.

If you topple from your tree house, you’ll continuously gain momentum as you

fall to the ground below. Doesn’t this violate the law of conservation of

momentum? Defend your answer.

If the system is you and the Earth, then your momentum toward Earth is equal

and opposite to Earth’s momentum toward you. There is no net change in momentum

because while you’re falling down, Earth is falling (much less noticeably) up.

A bug and the windshield of a fast-moving car collide. Indicate whether each

of the following statements is true or false.

The forces of impact on the bug and on the car are the same size. True

The impulses on the bug and on the car are the same size. True

The changes in speed of the bug and of the car are the same. False the changes

of speed are very different due to the different masses and resulting

accelerations.

The changes in momentum of the bug and of the car are the same size. True,

since the impulses are of the same size.