Transcript 4.1 The Concepts of Force and Mass

Free Write for 5 min:

What is the difference between speed and
velocity? Distance and Displacement?

What is the difference between distance and
displacement?

What does direction have to do with anything?
Chapter 2
Kinematics in One
Dimension
Distance and Displacement
Kinematics
Kinematics is the branch of mechanics that describes the
motion of objects without necessarily discussing what
causes the motion.
Dynamics deals with the effect that forces have on motion.
Together, kinematics and dynamics form the branch of
physics known as Mechanics.
How far have you gone if you
run around the track one time?
Distance vs Displacement


Distance ( d )
• Total length of the path travelled
• Measured in meters
• scalar
Displacement ( x )
• Change in position (x) regardless of path
• x = xf – xi
• Measured in meters
• vector
Distance vs Displacement
B
Displacement
A
Distance
Chapter 2
Kinematics in One
Dimension
Speed and Velocity
Average Speed
The total distance traveled divided by the time required to
cover the distance.
Distance
Average speed 
Elapsed time
d
s
t
SI units for speed: meters per second (m/s)
Example 1: Distance Run by a Jogger
How far does a jogger run in 1.5 hours (5400 s) if his
average speed is 2.22 m/s?
d
s
t
d  sΔt 
d  2.22 m s5400s  12000m
Average Velocity
The displacement divided by the elapsed time.
Displacement
Average velocity
Elapsed time
x  x o x
v

t  to
t
SI units for velocity: meters per second (m/s)
Example 2
The World’s Fastest Jet-Engine Car
Andy Green in the car ThrustSSC set
a world record of 341.1 m/s in 1997.
To establish such a record, the driver
makes two runs through the course,
one in each direction, to nullify wind
effects. From the data, determine the
average velocity for each run.
Example 2
v
x  1609 m

 339 .5 m s
t
4.740 s
x  1609 m
v

 342 .7 m s
t
4.695 s
What is the average velocity for
both runs? (combined)
What is the average speed for
both runs? (combined)
d
1609* 2 m
s

 341.1m s
t (4.740 4.695)s
Instantaneous Velocity & Speed
The instantaneous velocity indicates how fast the
car moves and the direction of motion at each
instant of time.
x

v  lim
t 0 t
The instantaneous speed is the magnitude of the
instantaneous velocity
Chapter 2
Kinematics in One
Dimension
Acceleration
Describe the motion of the ball
as it rolls down the ramp.


What happens to the displacement and velocity
as time goes by?
Draw a Position vs time and Velocity vs Time
graph of its motion
What if anything changes when the
ramp is facing in the opposite direction?
Acceleration
The difference between the final and initial velocity
divided by the elapsed time
 

 v  v o v
a

t  to
t
SI units for acceleration: meters per second per second (m/s2)
What does a negative acceleration
mean?
Scenario
Speeding up in the positive direction
Slowing down in the positive direction
Speeding up in the negative direction
Slowing down in the negative direction
Acceleration
Question #5
A ball is thrown toward a wall, bounces, and returns to the
thrower with the same speed as it had before it bounced.
Which one of the following statements correctly describes this
situation?
a) The ball was not accelerated during its contact with the wall
because its speed remained constant.
b) The instantaneous velocity of the ball from the time it left the
thrower’s hand was constant.
c) The only time that the ball had an acceleration was when the
ball started from rest and left the hand of the thrower and
again when the ball returned to the hand and was stopped.
d) During this situation, the ball was never accelerated.
e) The ball was accelerated during its contact with the wall
because its direction changed.
Question #6
a)
b)
c)
d)
e)
In an air race, two planes are traveling due east. Plane One
has a larger acceleration than Plane Two has. Both
accelerations are in the same direction. Which one of the
following statements is true concerning this situation?
In the same time interval, the change in the velocity of Plane
Two is greater than that of Plane One.
In the same time interval, the change in the velocity of Plane
One is greater than that of Plane Two.
Within the time interval, the velocity of Plane Two remains
greater than that of Plane One.
Within the time interval, the velocity of Plane One remains
greater than that of Plane Two.
Too little information is given to compare the velocities of the
planes or how the velocities are changing.
Question #7
Two cars travel along a level highway. An observer notices
that the distance between the cars is increasing. Which one of
the following statements concerning this situation is necessarily
true?
a) Both cars could be accelerating at the same rate.
b) The leading car has the greater acceleration.
c) The trailing car has the smaller acceleration.
d) The velocity of each car is increasing.
e) At least one of the cars has a non-zero acceleration.
Question #8
The drawing shows the position of a rolling ball at one
second intervals. Which one of the following phrases
best describes the motion of this ball?
a) constant position
b) constant velocity
c) increasing velocity
d) increasing acceleration
e) decreasing velocity
Question #9
At one particular moment, a subway train is moving with a
positive velocity and negative acceleration. Which of the
following phrases best describes the motion of this train?
Assume the front of the train is pointing in the positive x
direction.
a) The train is moving forward as it slows down.
b) The train is moving in reverse as it slows down.
c) The train is moving faster as it moves forward.
d) The train is moving faster as it moves in reverse.
e) There is no way to determine whether the train is moving
forward or in reverse.
Question #10
Which of the following velocity vs. time graphs
represents an object with a negative constant
acceleration?
Chapter 2
Kinematics in One
Dimension
Constant Acceleration
Equations
AP Kinematic Variables:
1. a = acceleration
2. t = time (elapsed)
3. v = final velocity (at time t),
4. vo = initial velocity (at time 0)
5. x = position (at time t)
6. xo = initial position (at time 0)
Equations of Kinematics for
Constant Acceleration
v  vo
a
t
at  v  vo
AP Equation
#1
v  vo  at
Equations of Kinematics for
Constant Acceleration
1
x  x0  v0  v t
2
v  vo
a
t
v  vo
t
a
 v  vo 
x  xo  vo  v 

 a 
1
2
v v
x  xo 
2a
2
2
o
AP Equation
#3
v  v  2ax  x0 
2
2
o
Equations of Kinematics for
Constant Acceleration
x  x0 1
 v0  v 
t
2
If, a is constant:
1
v  vo  v 
2
v
x  x0
t
v  vo  at
1
x  x0  v0  v t
1
2
x  xo  vo  vo  at t
2
AP Equation
#2
x  xo  vot  at
1
2
2
Question #11
Complete the following statement: For an object moving
at constant, positive acceleration, the distance traveled
a) increases for each second that the object moves.
b) is the same regardless of the time that the object moves.
c) is the same for each second that the object moves.
d) cannot be determined, even if the elapsed time is known.
e) decreases for each second that the object moves
Example 8
An Accelerating Spacecraft
A spacecraft is traveling with a velocity of +3250 m/s.
Suddenly the retrorockets are fired, and the spacecraft begins
to slow down with an acceleration whose magnitude is 10.0
m/s2. What is the velocity of the spacecraft when the
displacement of the craft is +215 km, relative to the point
where the retrorockets began firing?
d
a
v
vo
+215,000 m
-10.0 m/s2
?
+3250 m/s
v  v  2ax
2
t
v   v  2ax
2
o
2
o

v   3250m s   2 10.0 m s
2
v   2500 m
s
2
215000m
v   2500 m
s
Question #12
An object moves horizontally with a constant
acceleration. At time t = 0 s, the object is at x = 0 m.
For which of the following combinations of initial
velocity and acceleration will the object be at
x = 1.5 m at time t = 3 s?
a) v0 = +2 m/s, a = +2 m/s2
b) v0 = 2 m/s, a = +2 m/s2
c) v0 = +2 m/s, a = 2 m/s2
d) v0 = 2 m/s, a = 2 m/s2
e) v0 = +1 m/s, a = 1 m/s2
Question #13
An airplane starts from rest at the end of a
runway and accelerates at a constant rate. In
the first second, the airplane travels 1.11 m.
What is the speed of the airplane at the end of
the second second?
a) 1.11 m/s
b) 2.22 m/s
c) 3.33 m/s
d) 4.44 m/s
e) 5.55 m/s
Question #14
An airplane starts from rest at the end of a
runway and accelerates at a constant rate. In
the first second, the airplane travels 1.11 m.
How much additional distance will the airplane
travel during the second second of its motion?
a) 1.11 m
b) 2.22 m
c) 3.33 m
d) 4.44 m
e) 5.55 m
Chapter 2
Kinematics in One
Dimension
Section 6:
Freely Falling Bodies
Free Fall
In the absence of air resistance, it is found that all bodies
at the same location above the Earth fall vertically with
the same acceleration. If the distance of the fall is small
compared to the radius of the Earth, then the acceleration
remains essentially constant throughout the descent.
This idealized motion is called free-fall and the acceleration
of a freely falling body is called the acceleration due to
gravity.
g  9.80 m s
g  10 m s 2
2
or
or
32.2 ft s
30ft s 2
2
Freefalling bodies

I could give a boring
lecture on this and work
through some examples,
but I’d rather make it
more real…
Free fall problems
Use same kinematic equations just substitute g for a
Choose +/- carefully to make problem as easy as possible
Example 12
The referee tosses the coin up
with an initial speed of 5.00m/s.
In the absence if air resistance,
how high does the coin go above
its point of release?
h
a
v
vo
?
-9.80 m/s2
0 m/s
+5.00
m/s
t
h
a
v
vo
?
-9.80 m/s2
0 m/s
+5.00 m/s
v v
h
2a
2
v  v  2ah
2
2
o

0 m s  5.00 m s
h
2

2  9.80 m s
t
2
2

 1.28 m
2
o
Conceptual Example 14
Acceleration Versus Velocity
There are three parts to the motion of the coin. On the way
up, the coin has a vector velocity that is directed upward and
has decreasing magnitude. At the top of its path, the coin
momentarily has zero velocity. On the way down, the coin
has downward-pointing velocity with an increasing magnitude.
In the absence of air resistance, does the acceleration of the
coin, like the velocity, change from one part to another?
Conceptual Example 15 Taking
Advantage of Symmetry
Does the pellet in part b strike the ground beneath the cliff
with a smaller, greater, or the same speed as the pellet
in part a?
Question #19
a)
b)
c)
d)
e)
Two identical ping-pong balls are selected for a physics
demonstration. A tiny hole is drilled in one of the balls; and the
ball is filled with water. The hole is sealed so that no water can
escape. The two balls are then dropped from rest at the exact
same time from the roof of a building. Assuming there is no
wind, which one of the following statements is true?
The two balls reach the ground at the same time.
The heavier ball reaches the ground a long time before the
lighter ball.
The heavier ball reaches the ground just before the lighter ball.
The heavier ball has a much larger velocity when it strikes the
ground than the light ball.
The heavier ball has a slightly larger velocity when it strikes the
ground than the light ball.
Question #20
Two identical ping-pong balls are selected for a physics
demonstration. A tiny hole is drilled in one of the balls; and the ball is
filled with water. The hole is sealed so that no water can escape.
Each ball is shot horizontally from a gun with an initial velocity v0 from
the top of a building. The following drawing shows several trajectories
numbered 1 through 5. Which of the following statements is true?
a) Both balls would follow trajectory 5.
b) Both balls would follow trajectory 3.
c) The lighter ball would follow 4 and the heavier ball would follow 2.
d) The lighter ball would follow 4 and the heavier ball would follow 3.
e) The lighter ball would follow 4 or 3 and the heavier ball would follow 2
or 1, depending on the magnitude of v0.
Question #21
A cannon directed straight upward launches a ball with an
initial speed v. The ball reaches a maximum height h in a
time t. Then, the same cannon is used to launch a
second ball straight upward at a speed 2v. In terms of h
and t, what is the maximum height the second ball
reaches and how long does it take to reach that height?
Ignore any effects of air resistance.
a) 2h, t
b) 4h, 2t
c) 2h, 4t
d) 2h, 2t
e) h, t
Chapter 2
Kinematics in One
Dimension
Section 7:
Graphical Analysis of Velocity
and Acceleration
Calculus – the abridged addition
Slope of the line
(derivative)
Displacement
Velocity
Area under the curve
(integral)
acceleration
Finding velocity
x  8 m
Slope 

 4 m s
t
2s
Instantaneous Velocity
Finding acceleration
v  12 m s
Slope 

 6 m s 2
t
2s
Finding displacement
v
velocity
v – vo = at
1
area  l  w  b  h
2
vo
time
t
1
d  vot  t at 
2
1 2
d  v0t  at
2
Question #22
A dog is initially walking due east. He stops, noticing a cat behind him.
He runs due west and stops when the cat disappears into some bushes.
He starts walking due east again. Then, a motorcycle passes him and he
runs due east after it. The dog gets tired and stops running. Which of the
following graphs correctly represent the position versus time of the dog?
Question #23
The graph above represents the speed of a car traveling due
east for a portion of its travel along a horizontal road. Which
of the following statements concerning this graph is true?
a) The car initially increases its speed, but then the
speed decreases at a constant rate until the car stops.
b) The speed of the car is initially constant, but then
it has a variable positive acceleration before it stops.
c) The car initially has a positive acceleration, but then it has a
variable negative acceleration before it stops.
d) The car initially has a positive acceleration, but then it has a
variable positive acceleration before it stops.
e) No information about the acceleration of the car can be
determined from this graph.
Question #24
Consider the position versus time graph shown. Which curve
on the graph best represents a constantly accelerating car?
a) A
b) B
c) C
d) D
e) None of the curves represent a constantly accelerating car.
Question #25
Consider the position versus time graph shown. Which curve on
the graph best represents a car that is initially moving in one
direction and then reverses directions?
a) A
b) B
c) C
d) D
e) None of the curves represent a car moving in one direction then
reversing its direction.