Motion
Student Learning Outcomes: Compare and contrast the terms used to describe
motion, and analyze circular and parabolic motion.
1. How do speed and velocity compare?
2. How are scalar and vector quantities different?
3. How is acceleration defined?
4. What causes vertical acceleration?
5. What is terminal velocity?
6. How are circular paths maintained?
7. Why does a projectile have a parabolic trajectory?
How do speed and velocity compare?
Speed and velocity are both words used to describe motion.
The basic difference is the inclusion of direction.
Average speed is the amount of distance covered in some amount of
time.
Velocity is speed in some direction.
The direction may be specified in many ways.
Up, Down
Left, Right
North, South, East, West
–, +
Question: If an Olympic runner completes the 100 meter dash in 11 seconds, what
is the average speed?
s = d
t
m/s
Motion C2 2
How are scalar and vector quantities different?
Scalars are quantities that indicate size, indicate the numerical value.
Vectors are quantities that indicate the size and direction.
The magnitude of a vector is a scalar; it is the size of the vector.
Questions: A car is traveling 65 mph north. Is the 65 mph north a scalar or
vector? What is the magnitude of this quantity?
How is acceleration defined?
Acceleration is the rate of change of velocity. It is a change in speed or
direction.
Deceleration is a change in velocity that is in the opposite direction as
compared to the motion of the car.
A calculated acceleration that is negative indicates deceleration.
Object is slowing
Velocity and acceleration are in opposite directions
The final velocity of an accelerating object can be found from the
acceleration equation.
A car that maintains a constant speed in a straight line has zero
acceleration.
Go To: http://www.physicsclassroom.com/mmedia/kinema/avd.cfm
http://www.physicsclassroom.com/mmedia/kinema/pvpa.cfm
http://www.physicsclassroom.com/mmedia/kinema/pvna.cfm
a = v
t
m/s2
vf = vi + at
Motion C2 3
Questions:
1) When driving through a curve at a constant rate of speed, is there acceleration?
2) On the freeway, you increase your speed from 15 mph (6.7 m/s) to 65 mph (29
m/s) which takes about 3 seconds. What is your average acceleration?
3) What would the final velocity of the car be if it continued to accelerate for
another 1.5 seconds?
What causes vertical acceleration?
Objects are accelerated downward because of gravity.
The gravitational force of Earth pulls objects toward the center of Earth.
The gravitational pull from the Earth is the same on all objects, so the
downward acceleration is the same on all objects, 9.8 m/s2.
Go To: http://www.youtube.com/watch?v=5C5_dOEyAfk
Any difference in the net acceleration is due to air resistance.
When there is acceleration, the distance traveled depends on how long the
object has been accelerating.
Questions:
1) I toss a ball upward and it returns to my hand. What is the ball’s rate of
acceleration if there is no air resistance?
a. Just after the ball leaves my hand?
b. At the top of the trajectory?
c. Just before the ball hits the ground?
2) Professional cliff divers fall from a cliff into the sea. If the dive takes 2.7
seconds, what is the distance they fall? What would be the speed of the diver as
the diver enters the water?
d = (1/2)at2
Motion C2 4
What is terminal velocity?
An object in free fall is only affected by gravity. We assume there is no air
resistance.
Air resistance provides acceleration upward.
Surface area increases air resistance.
Speed increases air resistance.
When air resistance balances gravity, a falling object will no longer
accelerate.
A constant speed is maintained for the rest of the fall, terminal
velocity. (125 mi/hr)
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http://www.physicsclassroom.com/mmedia/newtlaws/efar.cfm
http://www.physicsclassroom.com/mmedia/newtlaws/sd.cfm
How are circular paths maintained?
Objects move in a straight line unless there is an unbalanced force to change
motion.
In circular motion, a centripetal force (“center-seeking” force) causes a
constant change in motion, a constant change in direction.
An object in circular motion is constantly changing direction, resulting in
centripetal acceleration.
Acceleration is perpendicular to the instantaneous velocity
The change in velocity is toward the center of the circular path.
Go To: http://www.physicsclassroom.com/mmedia/circmot/ucm.cfm
ac = v2
r
Motion C2 5
Questions:
1) What are some examples of centripetal motion?
2) What is the circular velocity of an object traveling around a circle with a radius
of 8 cm if the object travels around the circle 2 times per second? What is the
centripetal acceleration?
Why does a projectile have a parabolic trajectory?
The addition of the horizontal velocity and the downward acceleration due to
gravity (9.8 m/s2) result in a curved path, a parabola.
A projectiles motion in x does not affect its motion in y!
Velocity in x is constant if there is no air resistance. Why?
Velocity in y changes. Why?
Go To: http://www.physicsclassroom.com/mmedia/vectors/hlp.cfm
http://www.physicsclassroom.com/mmedia/vectors/pap.cfm
A projectile will fall a vertical distance, y, each second after reaching
maximum height.
The range of a projectile relative to the horizontal plane depends on the
object’s horizontal velocity.
Projectiles launched at an angle are given a horizontal and vertical velocity.
The horizontal component of the velocity remains constant.
The vertical component of the velocity changes.
Objects launched at a 45o angle travel farthest.
y = (1/2)gt2
x = vt
Motion C2 6
Go To :
http://galileoandeinstein.physics.virginia.edu/more_stuff/Applets/ProjectileMotion/
jarapplet.html
Questions:
1) A player throws a baseball parallel to the ground with a horizontal velocity of 90
mph (40 m/s). Assume no air resistance.
a. What is the direction of the acceleration?
b. Does the horizontal speed change?
c. Does the vertical speed change?
d. What is the horizontal speed the instant before the ball hits the ground?
e. If there was no gravity, what would be the path of the ball? Why?
f. What is the maximum horizontal range of the baseball if it is released from a
height of 1.5 meters?
2) What are some examples of projectile motion that you have observed?