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Review
http://astro.temple.edu/~elenab/
Describing Motion:
Kinematics in one dimension
Kinematics is a part of mechanics, which is the
description of how objects move.
Speed
Speed is a measure of how fast object moves,
measured by a unit of distance divided by a unit
of time.
Instantaneous Speed
Average speed doesn’t indicate the different
speeds that may have taken place during
shorter time intervals.
Average Speed
average speed = total distance traveled/ time elapsed
Total distance traveled = average speed X time
1. What is the average speed of a cheetah that sprints 100 m in 4 s?
How about if it sprints 50 m in 2 s?
2. If a car moves with an average speed of 60 km/h for an hour, it
will travel a distance of 60 km.
(a) how far would it travel if it moved at this rate for 4 h?
(b) for 10 h?
3. In addition to speedometer on the dashboard of every car is an
odometer, which records the distance traveled. If the initial
reading is set at zero at the beginning of a trip and the reading is
40 km one half hour later, what has been your average speed?
4. Would it be possible to attain the average speed in previous
example and never go faster than 80 km/h?
Velocity
When we describe speed and the direction of
motion, we are specifying velocity
1. With what two physical values is the race-car driver
concerned? Speed or velocity?
2. The speedometer of a car moving to the east reads 100
km/h. It passes another car that moves to the west at 100
km/h. Do both cars have the same speed? Do they have the
same velocity?
3. During certain period of time, the speedometer of a car
reads a constant 60 km/h. Does this indicate a constant
speed or a constant velocity?
1. How might you estimate your speed if the speedometer in
your car is broken?
2. Which of the following can be used to measure an average
speed: stopwatch, odometer, or speedometer? An
instantaneous speed?
Acceleration
We can change the velocity of something
by changing its speed; by changing its
direction or by changing its speed and its
direction.
Motion at Constant Acceleration
Acceleration is a rate of
change , or change per
second of velocity.
v= at
1. Which has the greater acceleration, an airplane that goes
from 1000 km/h to 1005 km/h in 10 s, or a skateboard that
goes from 0 to 5 km/h in 1 sec?
2. What is the acceleration of a race car that whizzes past you at
a constant velocity 400 km/h?
Acceleration on Galileo Inclined Planes
Galileo found greater accelerations for
steeper inclines. The ball attains max
acceleration when the incline is tipped
vertically.
-a ball rolling down an inclined plane is moving with constant
acceleration
- greater accelerations for steeper planes, max acceleration when
incline is tipped vertically
- regardless of weight and size, when air resistance is small
enough to be neglected, all objects fall with the same unchanging
acceleration.
We call this acceleration the acceleration due to gravity
on the Earth, and we give it the symbol g.
g = 9.80 m/ s2 ~ 10 m/ s2
How Far?
With his inclined planes Galileo found that the distance a
uniformly accelerating object travels is proportional to the
square of the time
Distance = acceleration x time x time /2.
At a given location on the Earth and in the
absence of air resistance, all objects fall with the
same constant acceleration
1. Which of the following (if any) could not be considered an
“accelerator” in an automobile: gas pedal, brake pedal,
steering wheel?
2. A sports car accelerates from 65 mph to 75 mph in 2 seconds
while a minivan accelerates from 20 mph to 35 mph in 2
seconds. Which one has the larger acceleration?
3. You are standing on a high cliff above the ocean. You drop a
pebble, and it strikes the water 4 seconds later. Ignoring the
effects of air resistance, how fast was the pebble traveling
just before striking the water? What is the height of the cliff?
Explaining Motion
Galileo’s inclined planes revisited
Slope upward –
speed decreases
Slope downward – speed
increases
No slope. Does speed
change?
Initial
Final position
Where is the final
position?
Newton’s first law of motion
The first law incorporates Galileo’s idea of
inertia and introduces a new concept, force.
Every object continues in its state of
rest, or of uniform motion in a straight
line, unless it is compelled to change the
state by forces impressed upon it.
Examples
1. Assume that you are pushing car across a level parking lot.
When you are stop pushing, the car comes to stop. Does this
violate Newton’s first law? Why?
2. Why does a tassel hanging from the rearview mirror appear
to swing forward as you apply the brakes?
If you were traveling toward a distant
star and you ran out of fuel, would your
spaceship slow down and stop? Explain.
Addition of Vectors – Graphical
Methods
Examples
1. In everyday use, inertia means that something is hard to get
moving. Is this the only meaning it has in physics? If not,
what other meaning does it have?
2. How would you determine that two objects have the same
inertia?
3. When a number of different forces act on an object, is the net
force necessarily in the same direction as one of the
individual forces? Why?
4. Modern cars are required to have headrests to protect your
neck during collisions. For what type of collision are these
headrests most effective?
Newton’s Second Law
The net force on an object is equal to its mass times its
acceleration and points in the direction of acceleration
Fnet = ma
Examples
1. Forces of 4 N and 6 N act on the object. What is the
minimum value for the sum of these two forces?
2. Two ropes are being used to pull a car out of a ditch. Each
rope exerts a force of 700 N on the car. Is it possible for
the sum of these two forces to have a magnitude of
1000N? Explain your reasoning.
3. If the net force on a boat is directed due east, what is the
direction of the acceleration of the boat? Would your
answer change if the boat had a velocity due north but the
net force still acted to the east?
Examples
1. Describe the force(s) that allow you to walk across the
room.
2. You are analyzing a problem in which two forces act on an
object. A 200 N force pulls to the right, and a 40 N force
pulls to the left. Your classmate asserts that the net force is
200 N because that is the dominant force that is acting.
What is wrong with that assertion?
Net Force
The combination of forces that act
on the object is the net force
Units of Force
1 newton (N) = 1 Kg *m/s2
1. You push on a crate that sits on a smooth
floor and it accelerates. If you apply four
times the pushing force, how much greater
will be the acceleration?
2. Same for a rough surface.
Friction
If you apply a force to an object, a force of friction
usually reduces the net force and resulting acceleration.
The direction of friction force is always in the direction
opposing motion.
The force of dry friction between solid surfaces doesn’t
depend on speed or area of contact.
Question
A jumbo jet cruises at constant velocity of 1000 km/h
when the thrusting force of its engines is constant
100000 N.
1. What is the acceleration of the jet?
2. What is the force resistance on the jet?
Mass and Force of Gravity
Mass: The quantity of matter in an object. It is also the
measure of the inertia or sluggishness, that an object
exhibits in response to any effort made to start it, stop
it, or change its state of motion in any way.
Force of Gravity= mg
Newton’s Second Law
The net force on an object is equal to its mass times its
acceleration and points in the direction of acceleration
Fnet = ma
Important: acceleration of a body is
always in the direction of net force!!!!
Free-body diagrams
Free fall revisited
When Acceleration is Less Than
g – Nonfree Fall
Examples
1. Forces of 4 N and 6 N act on the object. What is the
minimum value for the sum of these two forces?
2. Two ropes are being used to pull a car out of a ditch. Each
rope exerts a force of 700 N on the car. Is it possible for
the sum of these two forces to have a magnitude of
1000N? Explain your reasoning.
3. If the net force on a boat is directed due east, what is the
direction of the acceleration of the boat? Would your
answer change if the boat had a velocity due north but the
net force still acted to the east?
Newton’s Third Law of Motion
Forces and Interactions
In a broader sense, a force is not a thing in
itself but makes up an interaction
between one thing and another.
Newton’s Third Law of Motion
Whenever one object exerts a force on a second object, the
second exerts equal and opposite force on the first.
“On every action there is equal and opposite reaction”…
Which force we call action and which we
call reaction doesn’t matter. The point is that
neither exists without the other.
Action and Reaction on Different
Masses
1. A car accelerates along a road. Identify the
force that moves the car.
2. A high speed bus and an innocent bug have a
head-on collision. The force of impact
splatters the poor bug over the windshield. Is
the corresponding force that bug exerts
against the windshield greater, less or the
same? Is the resulting acceleration of the bus
greater than, less than or the same as that of
the bug?
1. A skier is skiing down a steep slope, traveling at constant
speed (that is, the skier has reached terminal velocity). What
are the size and direction of the net force on the skier?
2. A car can accelerate at 2 meters per second per second when
towing an identical car. What will its acceleration be if the
towrope breaks?
3. If the number of different forces act on the object, is the net
force necessarily in the same direction as one of the
individual forces?
1. You apply a 75 N force to pull a child’s wagon across
the floor at constant speed. If you increase your pull to
80 N, will the wagon speed up to some new constant
speed, or will it continue to speed up indefinitely?
Explain your reasoning.
2. You are riding an elevator from your tenth-floor
apartment to the parking garage in the basement. As
you approach the garage, the elevator begins to slow.
What is the direction of the net force on you?
1. If the force exerted by a horse on a cart is equal and
opposite to the force exerted by a cart on the horse, as
required by Newton’s third law, how does the horse
manage to move a cart?
2. A soft-drink sits at rest on a table. Which of the
Newton’s laws explains why the upward force of the
table acting on the can is equal and opposite to Earth’s
gravitational force pulling down on the can?
3. A book sits at rest on a table. Which force does
Newton’s third law tell us is equal and opposite to the
gravitational force acting on the book?
Circular Motion
An object moving along a circular path at
a constant speed must have a net force
acting on it.
It is important to distinguish between
adjectives centripetal (center-seeking) and
centrifugal (center-fleeing).
The force, we are discussing , the centripetal
force, is directed toward the center of the
circle.
A Car, Rounding a Curve
Velocity and acceleration are perpendicular each other at each
point of this circle.
Dynamics of Uniform Circular
Motion
S F = ma = m
2
V /R
Centripetal force is just a term, which means that there is the
acceleration pointed to the center.
Projectile Motion
When something is thrown or launched
near the Earth surface,
it experiences a constant vertical gravitational
force. Motion under these conditions is called
projectile motion.
Important: The study of projectile motion is
simplified because the motion can be treated as
two mutually independent, perpendicular motions,
one horizontal and the other vertical.
Question
Suppose a bullet is fired horizontally from a
pistol and simultaneously another bullet is
dropped from the same height.
Which bullet hits the ground first?
Important:The object projected horizontally
will reach the ground in the same time as
the object released vertically from the rest.
Fast Moving Projectiles: Satellites
The Earth satellite is simply a projectile that
falls around the Earth rather than into it.
Question
A newspaper report reads in part, “ The space shuttle orbits Earth
at an altitude of nearly 200 miles and is traveling at a speed of
18,000 mph. The shuttle remains in orbit because the
gravitational force pulling it toward Earth is balanced by the
centrifugal force (the force of inertia) that is pulling it away from
Earth”. Explain why this newspaper should hire a new reporter.
Questions
1. What is the force that allows a person on roller-blades to turn a
corner? What happens if this force is not strong enough?
2. A child rides on a carousel at constant speed. In which direction
does each of the following vectors point?
a. velocity
b. change in velocity
c. acceleration
d. net force.
Questions
A vine is just strong to support Tarzan when he is
hanging straight down. However, when he tries to
swing from tree to tree, the same vine breaks at the
bottom of the swing. How could it happen?