What is the main force acting on a projectile?
gravity
Projectile motion is always movement in _____ dimensions.
2
With projectile motion we usually ignore ___________________.
air resistance
With vertical motion, it is ___________.
accelerated
With horizontal motion, it has _______ velocity.
constant
shape of a projectile's path
parabola
curved path that an object makes in space or that a thrown object follows as it rises and falls to earth, path of a projectile
trajectory
horizontal distance traveled by a projectile
range
any object that moves through the air or through space under the influence of gravity only
projectile
highest point in the parabolic trajectory
apex
Projectiles are objects that are shot at some angle so they have both ____________ and vertical motion at the same time.
horizontal
Why do projectiles move forward?
due to their inertia given to them by initial force which launched the projectile
What path do projectiles follow?
parabolic
governed by the force of gravity, follows the same rules used in straight red fall
vertical component
The object in free fall will fall with _________ distance each time interval as it _____________ downward as it falls.
increasing, accelerates
constant, governed by the law of inertia, moves forward parallel to the ground the same distance in each successive time interval, motion in the forward direction is completely independent of the vertical, accelerated motion
horizontal component
A projectile is any object with an ________ non-zero horizontal velocity whose acceleration is due to _______ alone.
initial, gravity
acceleration due to gravity may be assumed constant in both magnitude and direction throughout its trajectory.
simple projectile
follows a closed path that never brings it in contact with a celestial body (like the earth).
satellite
no matter where its trajectory may take it.
general projectile
The kinematic equations for a simple projectile are those of an object traveling with...
constant _________ velocity and constant vertical acceleration
horizontal
horizontal distance traveled by a projectile
range
Give example of projectiles.
basketball, soccer ball, stone, arrow, human cannonball at a circle, frog hopping, kicked or thrown balls, jumping of animals
How can an object be thrown in the air? (what three ways)
launched at an angle, launched vertically, launched horizontally
line or point around which an object rotates
axis
spinning around an internal force; earth rotates around its axis once every 24 hours
rotation
moving around an external axis; Earth revolves around the sun once every 365.25 days
revolution
amount of time it takes for one revolution/ rotation
T= 1/f, unit is second, T= number of second/number of revolutions
period
number of rotations/revolutions per second
f= number of revolutions/number of seconds, f= 1/t, unit is Hertz
frequency
rate at which an object travels in a circular path, time=period (time for one revolution)
tangential (linear velocity)
What does tangential velocity depend on?
At center: tangential velocity= _____ m/s
As you move away from the center, your radius __________ so your tangential velocity ________.
radius of the path, 0, increase
not dependent on radius, number of rotations per unit time, how fast an object is spinning
rotational velocity
Is Hannah's tangential velocity greater than, less than, or same as Rebecca's linear speed. Why?
less than, smaller radius, standing closer to center so smaller radius
Is Hannah's rotational velocity greater than, less than, or the same as Rebecca's rotational speed?
same
rate at which an object moving in a circle changes direction
centripetal acceleration
The direction of centripetal acceleration is always ________ towards the center of the circle
inwards
net force causing circular motion, center seeking, like the normal force ,
centripetal force
The direction of centripetal force is always towards the ________ of the circle. (some fore pushing inward); not an additional vector
center
could be tension in a string or the wall of washing machine, or a seatbelt in a car
example of centripetal force
inertia of the object, fake force
centrifugal force
Centrifugal force is always directed toward _______ tangent to circular path
straight
driving toward a curve in a car (inertia makes slide across seat, moving in a straight line), seatbelt (centripetal) making move in a circle around a curve, washing machine (spin cycle)- holes in a wall
example of centrifugal force
Name characteristics of centripetal force.
actual force, can be calculated, towards center, tension in a string, causes circular motion
Name characteristics of centrifugal force.
can't be calculated, fake force, tangent to circular path, curve in car, just inertia of an object-straight linear motion
When an object moves in a vertical circle path, the _________ also factors into its centripetal force.
weight
net force into the center of the circular path
centripetal force
Name examples of vertical circles
twirling a whistle in a vertical circle, riding over a hill in car, going through roller coaster loop
Two people sit on a balanced seesaw. When one person leans toward the center of the seesaw, that person's end of the seesaw will
a. fall
b. rise
c. stay at the same level
B
When you carry a heavy load with one arm, why do you tend to hold your free arm away from your body?
a. change the mass of your body
b. be ready to grab something in case you fall
c. change the center of gravity of your body and load
d. change the weight
D
If you try to touch your toes while standing flat against a wall, you probably will fall over. The reason this happens is that
a. your center of gravity is not located directly above your support area
b. your center of gravity is outside your support area
A
Explain how an object moving at a constant speed can have a nonzero acceleration?
acceleration depends on the change in an object's velocity. an object moving at a constant speed can experience a nonzero acceleration if the direction of the object's motion changes
What provides the centripetal force for a car driving on a circular track?
friction between the car's tires and the track provides the centripetal force
Is there an outward force in circular motion? Explain.
no, only an inward force causing a deviation from a straight-line path. tendency to move in a straight line away from the circular path is inertia
Inertia wants to keep things moving in a __________ line.
straight
Suppose an airplane normally flying at 80 km/hr encounters wind at a right angle to its forward motion-crosswind. Will the airplane fly faster or slower than 80 km/hr. Explain.
faster, resultant velocity is the vector sum of its forward/sideways movement
At an instant, a horizontally pointed cannon is fired, a cannonball held at the cannon's side is released and rope to the ground. Which cannonball strikes the ground first, the one fired from the cannon or the one dropped explain
same time, only distance above ground influences time to hit and times are equal
A projectile is launched at an angle in the air. Neglecting air resistance, what is its vertical acceleration. Its horizontal acceleration.
ax= 0 m/s, ay= has number
At what point in its path does a projectile have minimum speed? Explain.
top of path, vy is only zero at this point, only has Vx
What does it mean when an object is moving in a horizontal circle.
object spins in a circle that is parallel to the ground
Give an example of a horizontal circle.
string with weight tied to end, rest on floor, starts to spin it around in a circle so that the weight is dragging along on the floor
What happens when something is spinning in a vertical circle?
gravity will have different effects on the object at different times
If you tie something and spin it in a vertical circle, what happens if you spin it too slowly?
tension in the sting disappears when it is at the top of its swing, weight may start to fall, never happens at the bottom of swing, relationship between the tension in the strong, centripetal force, force due to gravity
When the ball is moving a circle, there must be _______ force acting on the ball to keep it moving in a circle. That force always acts toward the center of the circle, pulling the ball towards there.
centripetal.
What happens at the bottom of the circle?
ball is pulled down by gravity, the string has to try to support this weight, the string will feel a force pulling it down (at the same time, the ball is also being pulled up towards the center of the circle by the centripetal force) (Newton's 3rd law sta
What is the miminum speed at which you could swing the ball so that the string won't go slack at the top of the swing?
minimum speed would happen when the centripetal force and the force due to gravity are exactly equal at the top of the swing; would make the tension exactly zero and the ball would be barely be able to keep moving in a circle
What happens at the top of the circle?
same sort of thing, gravity is still pointing down, centripetal force acting on the ball still points towards the center of the circle, centripetal force on the ball is now pointing down, Newton's 3d law means that the force acting on the string is up
A cannon fires a shell at a fixed angle above the horizontal. Which one of the following quantities is the same throughout the shell's flight?
a. its speed
b. its acceleration
c. its velocity
B
A projectile is fired at an angle of 45 degrees above the horizontal. Assume that air resistance is not significant. While the projectile is in flight, the horizontal component of the velocity remains constant.
True or False.
True
A projectile is fired at an angle of 45 degrees above the horizontal. Assume that air resistance is not significant. While the projectile is in flight, the acceleration remains constant.
True or False.
True
A machine launches a tennis ball at an angle of 25 degrees above the horizontal at a speed of 14 meters per second. Ball returns to level ground. Which combination of changes must produce an increase in time of flight of a second launch
a. increase the la
B
A .2 kg red ball is thrown horizontally at a speed of 4 m/s from a height of 3 m. A .4 kg green ball is thrown horizontally from the same height at a speed of 8 m/s. Compared to the time it takes the red ball to reach the ground, the time it takes the gre
C
A ball is thrown at an angle of 38 degrees to the horizontal. What happens to the magnitude of the ball's vertical acceleration during the total time interval that the ball is in the air
a. decreases then increases
b. decreases then remains the same
c. in
D
Explain the up motion of the projectile.
gravity is slowing projectile down
Explain the down motion of the projectile.
gravity is speeding projectile up, because gravity is causing the acceleration both up and down the two halves, are symmetrical
For the horizontal motion, what is happening to the projectile?
moving at constant speed
At the instant a ball is thrown horizontally with a larger force, an identical ball is dropped from the same height. Which ball hits the ground first?
same time, gravity is accelerating them both at the same rate downward
A ball is thrown into the air at some angle. At the very top of the ball's path, what is it velocity in the horizontal direction?
same as the velocity in the horizontal direction when it was launched
A ball is thrown into the air at some angle. At the very top of the ball's path, what is its velocity in the vertical direction?
O
At what angle should a ball be oriented for maximum height and range?
90, 45
continually falls around Earth
satellite
When an object is moving with uniform circular motion, the object's tangential sped is
a. circular
b. perpendicular to the plane of the motion
c. constant
d. directed toward the center of the motion
C
When the object is moving with uniform circular motion, the centripetal acceleration of the object
a. circular
b. perpendicular to the plane of the motion
c. constant
d. directed toward the center of the motion
D
net force directed toward the center of an object's circular path
centripetal force
The centripetal force on an object in circular motion is
a. same direction as tangential speed
b. direction opposite the tangential speed
c. same direction as the centripetal acceleration
d. direction opposite the centripetal acceleration
C
When a car makes a sharp left turn, what causes the passengers to move toward the right side of the car?
inertia
spinning around an internal axis; earth rotates around its axis once every 24 hours
rotation
moving around an external axis; earth revolves around the sun once every 365 days
revolution
amount of time it takes for one revolution or revolution
T= number of seconds/ number of revolutions
Unit: Seconds
period
number of rotations or revolutions per second
f= number of revs/number of seconds
unit is Hertz
frequency
Period and frequency are _________ (reciprocals)
T= 1/f
f= 1/T
inverse
distance moved per unit time
tangential (linea) velocity
Tangential velocity is always drawn ______ to the circular path.
Direction of the tangential velocity is the direction the object wants to move (_________ wants to move in a straight line)
tangent, inertia
distance, C= 2pir
Circumference
time for one revolution (period-T)
Time
V= circumference/T
tangential velocity formula
Tangential velocity depends on how far away the object is from the circle (its _______).
At the center, V= 0 m/s because r= 0
As you move away from the center, radius ________ so your tangential velocity _________.
radius, increases
number of rotations per unit time
rotational velocity
What does rotational velocity depend on?
number of degrees you turn in a given amount of time.
What does rotational velocity not depend on?
where you stand (radius) because the distance trave;ed (angle) will be the same
Rotational velocity is _________ proportional to its tangential velocity.
faster the object turns (rotational velocity), faster the tangential velocity can be
directly
Why is Hannah's tangential velocity less than Rebeccas?
standing closer to the center (smaller radius) covers less distance in the same amount of time, tangential velocity depends on radius
Why is Hannah's rotational velocity the same as Rebecca's?
turn through the same angle in the same amount of time, rotational velocity does not depend on radius
quantitative expression of the amount of rotation that a spinning object undergoes per unit tim
rotational velocity
When an object moves in a circle, direction is constantly changing so the object is accelerating.
The direction of centripetal acceleration is always __________ the center of the circle.
towards
acceleration due to an object moving in a circle path; constantly changing velocity
unit; m/s2
ac= v2/r
centripetal acceleration
net force causing circular motion
centripetal force
Centripetal force is always into the ________ of the circle. Fc is not an additional force, it is just the net force that is causing the object to keep changing direction. not a new velocity.
If the Fc is removed, the object will fly off in the direction
center, tangential
tension in string, wall of washing machine, seatbelt of a car friction between tires, road when driving around a curve
examples of centripetal force
inertia, not a real force, fake force that tries to make the objects move in a straight line; always directed tangent to the path of the circle.
centrifugal force
Explain the centrifugal force in a washing machine.
tiny holes in the walls of the machine always the water to fly out tangent to the circular path during the spin cycle; wall provides centripetal force for the clothing to keep it spinning in a circular path
When an object moves in a vertical circular, its _______ also factors into its centripetal force.
To Find Fc (net force), we take:
Fc= forces pulling into the circle- forces pulling out of the circle
(into the circle is always the positive direction)
Top:
weight.
dx= vixt
vix= vicostheta
vfx=vix
launched at an angle x direction equations
dy= viyt+ 1/2at2
viy=vi sin theta
vfy=viy+at
vfy2=viy2+2ady
launched at an angle y direction equations
When forces are launched at an angle, we have to break it down into _____ and __ components.
What degree is max range?
What degree is max height?
If angles are __________, ranges will be the same.
x, y, 45, 90, complimentary
Projectiles Launched at Angle
WAY UP
Vy _________
Ay constant (-9.81 m/s2)
Dy ________ each second
AT THE TOP:
Vy= _____
Ay is constant (-9.81 m/s2)
Vx= only velocity; ________
WAY DOWN
Vy _________
Ay constant (-9.81 m/s2)
Dy ______ each second.
decreases, 0, constant, increases
dx=vixt
vfx=vix
horizontally launched x direction equations
dy= 1/2ayt2
vfy=ayt
fy2=2ady
horizontally launched y direction equations
When the projectile is launched horizontally, all of its ______ velocity is in the _____ direction.
Vx is constant, so dx is the same every second
Vy is increasing due to the force of gravity, dy changes every second
initial, x
any object that is launched with an initial velocity and continues to move due its inertia and voce of gravity
projectile
path a projectile follows; parabolic
trajectory
horizontal distance covered by a projectile
range
vertical distance covered by a projectile
height
Motion in x direction:
Forces: none, _______ is the only thing that makes the projectile continue to move in the x direction
Velocity: ________
Acceleration: _______
Displacement: object will move equal distances every second in the horizontal direction b
inertia, constant, 0
Motion in y direction:
Forces: ________- only force in the y direction
Velocity: ______
Acceleration: -9.81 m/s2
Displacement: distance the object moves each second will change because it is accelerating
gravity, changes