4. Physics 1 Flashcards
4 questions to test concept
- Can I visualize it?
- Can I draw a picture, graph, or diagram of it?
- Can I explain it to someone else in layman;s terms?
- Can I think of and describe real-life examples?
scalars
only magnitude, no direction
mass, temperature, speed, work, energy, charge, time, density
vectors
have magnitude AND direction
velocity, displacement, acceleration, force, weight, electric field, magnetic field, momentum, impulse, torque
a rock thrown into the air at an angle 30 degrees from the VERTICAL at a velocity of 40 m/s
normal equation would be x=Vcos(theta) w.r.t. to horizontal, but as it is w.r.t. vertical the eq would would be x=Vsin (theta)
force
any influence capable of causing a mass to accelerate
forces are vectors
measured in newtons (N = kg*m/s^2)
newton’s first law
an object as rest stays at rest, and an object in motion stays in motion, unless acted upon by an unbalanced external force
newton’s second law
Fnet=ma
newton’s third law
for every reaction, there is an equal and opposite reaction
inertia
the ability of an object to resist a change to its velocity
mass
a measure of an object’s inertia
center of mass (center of gravity)
Cmass = (r1m1 +r2m2 + . . . )/mtotal
a weighted average of mass distribution
opposite is center of buoyancy - the center of mass of the fluid displaced by the submerged object (not the center of mass of the submerged object itself )
Fnet = ma
- a constant force will NOT cause an object to accelerate faster, it will cause a constant acceleration
- a constant force can cause an object to move faster, so the displacement is changing nonlinearly, the velocity is changing linearly, and the acceleration is constant
- a constant net force will always cause a constant acceleration, therefore a changing velocity
4.you CANNOT accelerate a ball HORIZONTALLY across the room by throwing it, as the object MUST either 1) in contact with the object creating the force, or 2) be under the influence of a field force at that exact moment.
(it can accelerate vertically as there is always the force of gravity acting upon it )
track the velocity of a ball thrown by a pitcher - from the moment the pitcher begins his pitching motion until the ball hits the ground (no catcher, ignoring air resistance)
the ball experiences a force created by the pitcher that accelerates it forward, this acceleration only exists during the time that the pitcher’s hand is in actual contact with the ball. once the ball is released, it becomes a projectile in free fall. there is no acceleration in the horizontal, but there is in the vertical due to gravity. when the ball hits the ground it will have the vertical component of final velocity created by its fall from the height of release to the ground, plus the same constant horizontal velocity it had throughout the flight. (it would be in the air the same time as if it were simply dropped at the same height ex. bullet shot vs bullet dropped )
Think critically if there were to be air resistance as well.
displacement
shortest distance between two points
(think velocity)
going in a circle = no displacement
distance
total distance between two points
(think speed)
going in a circle = distance covered in circumference
velocity
displacement / time = V
speed
distance / time = V
constant velocity/ constant speed
- no acceleration
- no net force
- all forces sum to zero
- no change in direction
- the object is in equilibrium
acceleration
any change in velocity/second
(you accelerate when you walk around a corner because velocity is a vector with both changing magnitude and direction, thus constitutes in acceleration)
- if there is no net force, can there be acceleration?
- if the force increases, what happens to acceleration?
- if there is no acceleration is, or could there be, a force?
- if there is no net force, there can never be acceleration (2nd law)
- if forces inc. acceleration inc., if forces inc linearly, acceleration inc. linearly, if force inc. exponentially, acceleration increases exponentially.
- if there is no acceleration, there could be a force acting on that object, however if there is a force we would know that it must be exactly canceled out by other force vectors on that same object (the other object must be in equilibrium)
Linear Motion Graphs
- What does the slope represent?
- Is the slope (+) or (-)?, what does the sign of the slope tell you?
- Is the slope constant (straight line) or non-constant (curved line)? what does this observation tell you?
- What value is on the y-axis?
- Is the y value (+) or (-) (i.e. are you above or below the x-axis? What does this observation tell you
- Do you expect the value on the y-axis to be large or small at t=0
velocity vs. time graphs
1) Crossing the x-axis means velocity went from positive to negative; in other words, the particle turned around.;
2) A corner (where slope abruptly changes from positive to negative or vice versa) tells us that the direction of the acceleration vector abruptly reversed;
3) A horizontal line tells us that acceleration is zero (because slope is zero) and that velocity is constant.
displacement vs time graphs
1) Crossing the x-axis means that we passed the origin;
2) A corner tells us that the sign of velocity (which is the slope of a d vs. t graph) abruptly changed— in other words, the object turned around [NOTE to your students that this is entirely different from a velocity vs. time graph where the action of “turning around” is indicated by crossing the x-axis];
3) A flat line tells us that displacement is constant, which means the object is standing still. It also tells us that velocity is zero because the slope of the line is zero—another proof that the object is not in motion at that instant.
if a projectile has an initial vertical velocity of 30 m/s, how many seconds will it take to reach its max height?
3 m/s
if a projectile has an atoll velocity of 60 m/s at an angele 30 degrees from the horizontal, how many seconds will it be in the air?
find vertical component of velocity = 60sin(30) = 30 m/s
30m/s horizontal is 3 seconds to max height (halfway points) so = 6 seconds in the air total
Vavg
average velocity = Vavg = (V1+V2)/2
if a projectile has a vertical velocity of 100m/s, how many seconds will it be in the air?
it takes 10 seconds to reach max height,
so avg V will be 50 m/s
distance traveled
distance = rate * time
if a projectile has an initial V of 30m/s, how long will it be in the air, how high will it go, and what will be its avg velocity during the entire trip?
3 seconds for max height –> so 6 seconds in air total
avg velocity will be 15 m/s –> so max height is 45meters
avg velocity entire trip = displacement/ time = 0
projectiles
falling bodies in two dimensions
separate into x and y components
horizontal component = distance traveled = range = Vx *time
think:
- horizontal V never changes (w/ no air resistance)
- horizontal acceleration always = 0
- vertical acceleration always = 10m/s downward
- vertical behavior is exactly symmetrical (upward and downward trips are identical)
- time in air is dependent on the vertical component of velocity only
- range depends on both the vertical and horizontal components as vertical component dictates time and the horizontal component dictates range.
- time is always the same for both x and y components of the motion
compare a bullet was shot straight up from atop a cliff to a bullet shot straight down from a cliff, what is the final velocity of each bullet as it hits the ground?
the velocities are the same, as the bullet shot up will reach zero, where it then falls back down and should have the same velocity by the time it reaches back to the height it was shot at, thus giving the same initial velocity
two students throw identical balls into the air with identical initial total velocities of 40m/s. First student throws it at 50 degrees, and second student throws it at 40 decrees. what will happen?
first students ball will be in the air longer, but travel the same distance
the larger the vertical velocity, the larger the time in the air
max horizontal distance = at 45 degrees, both velocities varied by the same |5| magnitude so distance is the same
x = 1/2at^2
not relationship
V = sqrt(2gh)
will work for both Vi and Vf as projectiles go begin and end with the same velocity
tair = 2V/g (V= Vxi)
used only to calculate “round trip” times, or in other words, the total time in the air
air resistance
- cross section area: greater cross-section ara impacting the air = more are resistance
- shape: less aerodynamic - more air resistance
- velocity: increased velocity = more air resistance
note: always assume air resistance is being ignored, unless it specifically states otherwise in the question stem or passage.
terminal velocity
mg = Fair
object has stopped accelerating, and forces of gravity = force of air resistance
note: objects in vaccum do not have a terminal velocity as there is no air resistance
gravity
is a field that exists between any two objects with mass
universal law of gravitation
F= Gm1m2/r^2 –> simplified to F=mg as g = Gm1/r^2
G = gravitational constant = 6.67x10^-11 m^3/kg*s^2
note: all forces are equal and opposite in a stationary object (human put as much force on earth, as earth puts on human)
Potential energy
on earth PE = mgh
in space PE = -Gm1m2/r
note: (-) sign is needed as without it r inc, PE dec.
friction
opposes sliding, not motion
if there is sliding = kinetic friction, if not than static friction
kinetic friction
Ff = (mu)k Fn = (mu)k mgcos(theta)
static friction
Ff = (mu)s Fn = (mu)s mgcos(theta)
force down an incline plane, parallel to surface
F = m g sin(theta)
normaal force on an inclined plane
Fn = m g cos(theta)
velocity of a particle at the base of an inclined plane
Vf = sqrt(2gh)
acceleration down an inclined plane
a = g sin(theta)
what is the tension in a rope being pulled from opposite ends with identical 50N forces?
it is 50N. (same as rope attached to a wall or ceiling)
a 500 kg elevator is being accelerated upward by a cable with a tension of 6000N. what force does the elevator exert on the the cable?
according to newton’s third law
the elevator cable us pulling on the elevator with 6000N of force, the the elevator must be pulling on the rope with a force of 6000 newtons (same as tension on both sides of rope but vertically)
hooke’s law (springs)
F = k (delta)x
((delta)x is displacement of the spring from its equilibrium point, not length of the spring)
multiple springs use:
1/keffective = 1/k1 + 1/k2 + 1/k3
A student hangs a 4kg mass on a spring and it stretches 1m. What is the spring constant and how far will the spring stretch if he attaches a 2kg mass?
F=mg=k delta x
-> k=mg/delta x = 4kg*10m/s^2 / 1m
elastic potential energy
energy stored in a compressed spring
PE=1/2 k delta x^2
note: normally used with conservation of energy with a mass traveling at a certain velocity hitting a spring (1/2mv^2=1/2 k delta x^2)
spring compression and kinetic energy
a ball moving with twice the kinetic energy CANNOT compress a spring twice as far, but a ball moving with twice the Velocity CAN compress a spring twice as far
pendulum (energy)
PE is at maximum when at max height of arc and minimum is at the lowest of the arc
KE is at maximum when the pendulum is at the bottom of the arc and the minimum is at the max of the arc
note; gravitational potential energy is 0 at the lowest point of the arc (when h=0, PE = 0)
pendulum movement
one cycle is a movement from 1 side to another, and back to the original position
the reasons why pendulums slow down is due to non conservation of energy such as air resistance
simple harmonic motion
anything representing a sin wave, anything that socialites back and fourth
T = 2 pi sqrt(m/k) [mass on a spring] T = 2 pi sqrt(L/g) [pendulum]
mass-spring systems
inc mass = dec frequency, length of spring has no effect on frequency, the mass of the spring itself also has no effect on frequency, increasing gravity also has no effect, increasing the spring constant will also increase frequency
pendulum systems
decreasing mass will have no effect, decreasing long of pendulum will inc. frequency, dec. gravity will dec. frequency
density
D = m/v
water density: 1000kg/m^3 = 1g/cm^3
specific gravity
how dense something is compared to water
SG = Dsubstance/Dwater
note: for objects floating in liquids, the fraction of the object submerged = ratio of the density of the object to the density of the liquid
a ball is floating 3/4 submerged in a liquid with a density of 2g/cm^3. what is the specific gravity of the liquid and density of the ball?
Because the ball floats with 3⁄4 of its volume submerged it must be 3⁄4 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 DLiquid/DH2O=(2g/cm3)/(1g/cm3)=2.
archimedes principle
any object displaces an amount of fluid exactly equal to its own volume
note: the weight of the displaced fluid is exactly equal to the buoyant force pushing up on the object
buoyant force
Fbuoyant = rho v g
rho = p = density of the fluid, not the object
v= volume of the fluid displaced
note:depth and mass has no change in buoyant force
apparent weight
apparent weight of a submerged object is the actual weight minus the buoyant force
apparent weight = actual weight - Fbuoyant
AW = aW -Fbuoyant
general pressure formula
P = F/A units = Pa, mmHg, atm, Torr
atmospheric pressure = pressure do to atmosphere
fluid pressure = pressure of fluid on an area
gauge pressure = pressure measured with respect to atmospheric pressure, where atmospheric pressure is defined as zero gauge pressure (basically pressure in excess of ambient atmospheric pressure)
fluid pressure formula
P = rho g h
pascal’s law
pressure is transmitted in all directions, undiminished, through a contained, incompressible fluid (if you increase pressure in a confined incompressible fluid, it increases by that same amount in every other point within that fluid)
flow rate
Q = A V
A=total cross-section area
(cardiac output = stroke volume * heart rate)
cross sectional area decreases as you go from aorta to capillaries, thus velocity is slowest at capillaries
Bernoulli’s equation
K = P + rho g h + 1/2 rho v^2
if fluid velocity increases, pressure decreases
note: commonly used for velocity of water exiting a spigot
surface tension
intensity of intermolecular forces per unit length at the surface of a liquid
capillary action
cohesive vs. adhesive forces
cohesive forces
forces between the fluid molecules
adhesive forces
forces between the fluid and the container
a 20 kg block of unknown density has an apparent weight of 150 N when fully submerged in a liquid with a density of 8g/cm^3. what is the density of the unknown object?
the 20 kg block will create a 200N force outside of the liquid and 150N in the liquid. the 50N difference is due to the buoyant force acting up on the object. therefore the actual weight is 4 times as dense as the buoyant force. multiply density of the fluid by the factor of 4 to get 32 g/cm^3 as the density of the unknown object.
