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Level 35

2D Motion


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projectile
An object in the air that is only subject to the force of gravity and wind resistance after it leaves the ground.
trajectory
Path of a projectile
range
distance a projectile travels horizontally along the ground
height
displacement in the y-axis; dy
parabola
A U-shaped curve characteristic of the graphs of quadratic equations
acceleration
(physics) a rate of change of velocity
Velocity
a speed in a particular direction.
time
A measure of change between two events or moments.
v0
The initial velocity of a projectile at an angle (m/s)
θ
Angular Displacement (rads)
v0y
The initial velocity of a projectile in the y-direction (m/s)
vx
The velocity of a projectile in the x-direction (m/s)
vfy
The final velocity of a projectile in the y-direction (m/s)
dx
The displacement in the x-direction (m)
T
1/f
a
acceleration (m/s2)
components
parts of a vector, one is parallel to the x-axis and the other one is parallel to the y-axis
horizontal acceleration
Acceleration is zero in the horizontal direction.
dx = vxt
The one equation we can use in the horizontal direction.
vertical acceleration
Acceleration is -9.8 m/s2 in the vertical direction.
vertical direction equations
dy = v0yt + ½at2
viy = 0 m/s
3 assumptions about vertical component
Projectile Motion
2D Motion in which the object moves at a constant velocity in one direction and accelerates in another
period
What is T?
Frequency
#cycles/second
h= (.5)+(g)(t)^2
Horizontal Projectile Motion from a height
r= V cos(o)sin(0)/4.9
Angular Projectile Motion starting and ending from the same height
2(3.14)(r)/T
Circular motion with a known speed and radius
-m(4)(3.14)^2(r)/T^2 or
Circular motion with a known time and radius (FC)
Accelerating
Even at a constant speed, an object moving in a circle is _______.
Magnitude...
... of a vector is always a positive quantity
centripetal acceleration
a = centripetal acceleration
circumference
2pi x r
-v^2/r
Two Equations for AC
Centripetal Force
A force directed towards the center of a circle that causes an object to follow a circular path
Frequency (F)
If you are given revolution per second or minute
H2
H2= s^-1, Hertz
f
1/T
If given revolutions/minute
Divide by 60 to get revolutions per second, then take the reciprocal to get T in seconds.
Vy
SIN
Galilean Transformation Formula for Velocities
An object's velocity relative to the ground is the vector sum of it's velocity relative to a moving reference frame plus the reference frame's velocity relative to the ground.
Galilean Transformation Formula for Position
(This one doesn't get used very often. The velocity formula is much more useful.)
a component vector
The projection of a vector along the axes of a coordinate system is called
Perpendicular
A wave in which the vibration of the medium is _______ to the direction in which the wave travels is called a transverse wave.
90<A<180
A vector that has components that lie along the -xaxis and the +yaxis is oriented at angle A measured counterclockwise from the +xaxis. Which of the following ranges give the values of angle A?
By equals 0
If the x-component of B equals the magnitude of B, them
scalar
a physical quantity that has magnitude but no direction
II
In the figure above, which diagram represents the vector addition, C=A+B?
IV
In the figure above, which diagram represents vector subtraction, C=A-B?
Vectors
have a magnitude and a direction e.g. velocity, displacement
cos 0 (theta)
The x component of the vector equals the vector's magnitude multiplied by which trigonometric function?
4
How many displacement vectors shown in the figure above have horizontal components?
d1 and d3
Which displacement vectors shown in the figure above have vertical components that are equal?
-d5,x; -d5,y
A hiker undergoes a displacement of d5 as shown in the figure above. A single displacement that would return the hiker to his starting point would have which of the following sets of components?
a baseball being thrown
Which of the following is an example of projectile motion?
a parabola
what does the center of mass follow when in projectile motion
a stone thrown into a lake
Which of the following exhibits parabolic motion?
Which of the following does not exhibit parabolic motion?
a flat piece of paper released from a window
B
At what point of the ball's path shown in the figure above is the vertical component of the ball's velocity zero?
move west at a speed that is equal to the bus's speed
A passenger on a bus moving east sees a man standing on a curb. From the passenger's perspective, the man appears to
straight down
Piece of chalk is dropped by a teacher walking at a speed of 1.5 m/s. From the teacher's perspective, the chalk appears to fall
scalar, scalar, vector
Identify the following quantities as scalar or vector: the mass of an object, the number of leaves on a tree, wind velocity
-3Vstudent
A student walks from the door of the house to the end of the driveway and realizes that he missed the bus. The student runs back to the house, traveling three times as fast. W…
29cm
An ant on a picnic table travels 3.0 x 10^1 cm eastward, then 25 cm northward, and finally 15 cm westward. What is the magnitude of the ant's displacement relative to its original position?
divided by the cosine of 0 (theta)
In a coordinate system, the magnitude of the x component of a vector and theta, the angle between the vector and xaxis, are known. The magnitude of the vector equals the x component
248 units 53.9 north of west
Find the resultant of these two vectors: 2.00 x10 ^2 units due east and 4.00 x 10^2 units 30.0 degrees north of west
equal to the horizontal component of its initial velocity
In the figure at the right, the horizontal component of the ball's velocity at A is
9.2 m
A track star in the long jump goes into the jump at 12 m/s and launches herself at 20.0 degrees above the horizontal. What is the magnitude of her horizontal displacement?
one component is perpendicular to v; the other component equals -v.
A boat travels directly across a river that has a downstream current, v. What is true about the perpendicular components of the boat's velocity?
606.9 km/h
A jet moving at 5000 km/h due east is in a region where the wind is moving at 120 km/h in a direction 30.00 degrees north of east. What is the speed of the aircraft relative to the ground?
7.5 m/s
A duck flying south for the winter has a velocity of 10.0m/s. If the duck is flying against a gust of wind with a velocity of 2.5 m/s, what is the resultant velocity of the duck?
(1/2)Vcar
A car travels down a road at a certain velocity, Vcar. The driver slows down so that the car is traveling only half as fast as before. Which of the following is the correct expression for the resultant velocity?
vecotrs
Multiplying or dividing vectors by scalars results in
vector
a displacement distinguished by magnitude and direction but not by location.
Vplayer, -2Vplayer
A football player runs in one direction to catch a pass, then turns and runs twice as fast in the opposite direction toward the goal line. Which of the following is a correct expression…
x axis: horizontal along the ground y axis: up and down
Which of the following is the best coordinate system to analyze a painter climbing a ladder at an angle of 60 degrees to the ground?
sin 0 (theta)
In a coordinate system, the y component of the vector equals the vector's magnitude multiplied by which trigonometric function?
d
Displacement (variable)
C
Light travels as fast as it can possibly go in air. This speed is 300 million m/s, and is labeled _______.
frame of reference
assists one in physics in which one chooses a place (point) a measure it against changes in position.
faster and faster
Objects that are falling toward Earth in free fall move
positive x axis pointing east; positive y axis pointing north
Which of the following is the best coordinate system to use to analyze the motion of
a bullet being fired from a gun
Which of the following is an example of projectile motion
Which of the following exhibits parabolic motion?
a person driving into a pool from a diving board
13 blocks
A jogger runs 10.0 blocks due east, 5 blocks due south and another 2 blocks due east. find the magnitude
12 m
A cave explorer travels 3.0 m east then 2.5 north finally 15m west. find magnitude
43m
A quaterback takes the ball from the line of scrimmage and runs back for 10 m then sideways for 15 m how far is the football displaced?
south of east
vector A points north and vector B points east, then vector C points
vx= constant and ay= -9.81
The motion of a projectile in free fall is characterized by
have a horizontal component
For an object to be a projectile, it must be in free fall and its initial velocity must
I only
A baby drops a ball from her hand resting on the serving tray of her high char. She knocks another ball from the same tray. Which of the following statements are true?
The horizontal displacement of a projectile depends on the
vertical component and horizontal component of its initial velocity
at the highest point of its path
A volleyball player taps a volleyball well above the net. The ball's speed is at least
magnitude of the vector
In a diagram, the length of a vector arrow represents the
axis
straight line which rotation takes place
rotataion
spinning around an internal axis
earth rotates around axis every 24 hours
what is an example of a rotation
Revolution
1 cycle = 1 year, 365 days; earths orbit around sun
earth orbiting around sun
what is an example of a revolution
directly proportional
when quantities change in the same direction
rotational velocity
rotations per time, depends on how fast you change DEGREES or angles
Tangential velocity
A velocity parallel to the Earth's surface
remains constant, increases
how does your rotational and tangential speed change when you walk from the center of the merry go round to the outer edge
gets increased
how is your tangential velocity affected if you cover greater distance
centripetal (towards the center)
when you twirl a can at the end of a string in a circular path, what is the direction of the force that acts on the can
does an object undergoing uniform circular motion accelerate? why?
yes, it changes direction (it has same speed but constantly changing direction)
centripetal
center seeking
lack of a force, 1st law (inertia)
if a string that holds a whirling can in its circular path breaks, what causes the can to movie in a straight line path, centripetal force, centrifugal force, or lack of a force? whic…
why is a centrifugal force called a fictitious force?
it does not result from a push or pull, it is an effect of rotation and inertia
increases (direct, quad)
a stopper is twirled in a horizontal circle. If you vary the following quantities, how will the velocity change:
decreases (direct, quad)
a stopper is twirled in a horizontal circle. If you vary the following quantities, how will the velocity change:
decrease (inverse, square)
a stopper is twirled in a horizontal circle. If you vary the following quantities, how will the velocity change:
tension, friction, gravity
name 3 forces that can act as a centripetal force
increase lever arm
if the amount of torque required remained constant, what can you do to decrease the amount force required to rotate the object
increase angle (90 degrees), increase lever arm, increase force
what can you do to achieve max torque exerted on an object
length, acceleration due to gravity
what 2 factors affect the period of a pendulum
increase, decrease
what happens to velocity as a pendulum swings downwards towards equilibrium? upwards away from equilibrium?
stays the same
if you changed the mass of the pendulum bob, how would the period be affected
does not
rotation velocity _______ depend on where you stand because the angle will be the same
rotational speed
at the center, tangential speed = o m's but you do have _______
simple harmonic motion
motion that is repeated because displacement and restoring force are proportional
equilibrium
1)starting point of SHM, object is in _______, fnet equals zero
Period (T)
the time for an object to complete one revolution
amplitude
The maxiumum displacement
bob
the object attached to a length of a string or rod (L)
inertia
_______ is the property of an object that leads it to resist any change in motion
length (L) and acceleration due to gravity (g)
what does the period of the pendulum depend on
what are the 2 forces exerted on the block (mass on a spring)
gravity (down) upward force of tension (directly proportional to the amount the string is stretched)
weight
A force that comes from gravity pulling down on any object with mass
Increases
As temperature increases, the vapor pressure of a liquid _______.
Decreases
A freight car moves along a frictionless level railroad
increased
If the pressure of a gas is increased, what must have happened to the volume?
force
(interactions between two objects)
Torque
A "force" that causes rotation because it is exerted at a distance from the axis of rotation.
lever arm
distance from the axis of rotation
increase torque
what happens when you increase the lever arm
Small
A force with a big mass has a _______ acceleration
Large
An object with a _______ heat capacity can absorb a lot of heat without undergoing much of a change in temperature.
move (linearly)
if you have a net torque, it will cause an object to _______