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Physics
Force and motion
Image thanks to
www.wolvertonmountain.com
Objectives
• By the end of this lesson, you should be able to
• Explain how forces and motion are related
• Explain the differences between scalar and vector quantitites
• Explain the differences between distance and displacement
• Explain the differences between speed and velocity
• Explain acceleration
• Explain the difference between average velocity and instantaneous
velocity
• Using data, construct a distance-time graph
• Using data, construct a velocity-time graph
Objectives, continued
• Calculate distance or displacement when no acceleration is taking
place
• Calculate velocity or speed when no acceleration is taking place
• Calculate distance or displacement when acceleration is taking place
• Calculate velocity or speed when acceleration is taking place
• Use acceleration of gravity in 1-dimensional vertical movement
calculations
• Describe free fall
• Determine the resultant velocity of an object
• Calculate the instantaneous velocity from a distance-time graph
• Calculate the instantaneous acceleration from a velocity-time graph
Standards
• SP1.
Students will analyze the relationships between
force, mass, gravity, and the motion of
objects.
What is fast?
• How do you know if something is moving?
• You must compare its position to something else
• Frame of reference: the "something else " that you are comparing
So, how fast ARE you moving?
• A conceptual version
• https://www.youtube.com/watch?v=wIzvfki5ozU
• A more mathematical version
• https://www.youtube.com/watch?v=F77MBqpkul8
Types of motion
• There are three primary types of motion
• One-dimensional
• When an object only moves horizontally or only vertically through space
• Also known as 1D motion, straight line motion, or rectilinear motion
• Two dimensional motion
• When an object moves both vertically and horizontally through space
• Also called 2D motion
• Three dimensional motion
• We won’t cover this one….for that, we’d need calculus
Some more types of motion
• Rotational motion: when an object does not move through space.
Instead, it turns around a fixed point
• Periodic motion: when an object moves through space but returns to
its starting point over regular intervals
• Vibratory motion: when the interior components of an object move
back and forth within the object at regular intervals
Introductory vocabulary words
• Kinematics is the study of motion
• Motion is directly tied to forces
• Mechanics is the study of how forces affect objects
“An apple a day..”
• When Newton was 24, he was walking through a garden and noticed
an apple fall to the ground
• Newton realized that the apple falling was really caused by the Earth
pulling on the apple
• Most of the first half of the course is based on the mechanics and
dynamics partially developed by Newton
Forces
• A force is a push or pull on an object
• There are two main types of forces
• Contact forces
• Forces between two or more objects in direct contact
• Examples include: friction, tension, and applied forces
• Field forces
• Forces that act on an object from a distance
• Examples include: gravity, electrical and magnetic fields
Unbalancing the apple cart
• So, the apple fell. Why did it fall just then?
• Before then, something (say, the branch) was counteracting the pull of
gravity.
• This is an example of balanced forces
• Newton realized that nothing would change unless forces were
unbalanced
• Newton's 1st Law of Motion
• An object at rest stays at rest and an object in motion maintains its velocity
unless acted upon by an unbalanced force
Some vocabulary terms
• Distance: how far through space an object has moved
• Displacement: how far an object ends up from its starting point
• Speed: how much distance an object moves over time
• Velocity: how much displacement an object moves over time
• Acceleration: how rapidly velocity is changing
Scalars and vectors
• If a quantity has no direction, it is called a scalar quantity
• Examples of scalar quantities
• Distance
• Speed
• Examples of vector quantities
• Displacement
• Velocity
• Acceleration
Positive Attitude
• When giving directions , you could use
• Cardinal directions (north, south, northeast, etc)
• Angular direction (in degrees or radians")
• With positive meaning one direction and negative meaning the
opposite direction
• Commonly, up is positive and down is negative
• Commonly, to the right is positive and to the left is negative
• Technically, you can make any direction you want as positive (as long as you
are consistent)
Who's on first?
• A baseball player is on first base and plans to steal second base,
which is 90 feet away
• The player runs quickly, making it to second
• Distance ran is 90 feet
• Displacement is 90 feet
Who's on first, part 2
• Instead of making it, the first baseman throws the ball to second.
Being too far to slide, the runner quickly turns and makes it back to
first
• Distance ran: up to 180 feet ( depending on the place along the base
line that the turn was made)
• Displacement: 0 feet (ended up at the starting point)
• So, distance and displacement CAN be the same quantity but often
are not
“Feel the need for speed”
• Speed and velocity are often used interchangeably
• However, they are not necessarily the same quantity
• Speed is calculated by distance traveled divided by time
• Velocity is calculated by displacement traveled divided by time
•
•
•
•
Velocity must have a direction
v = Δ x /t
Δ x means “change in x (horizontal movement)”
Δ x = xfinal - xinitial
Road Trip!
• If you have ever taken a road trip, you know that the same speed is
not maintained throughout the entire trip
• You will have different legs of your journey that you traveled faster
than others or for longer periods of time than others
• Average speed is NOT adding up the individual speeds and dividing!
• Instead, it is the sum of the distances divided by the sum of the times
• Average velocity is similar (just replace the word distance with
displacement)
Gone in an instant
• Instantaneous speed or velocity is how fast something is going at one
particular time (in that instant, get it?)
• In the road trip example, a 300 mile trip completed in 6 hours would
have an average speed of 50 miles per hour
• The instantaneous speed might be 60 miles per hour, 25 miles per
hour, or even stopped, depending on which instant along the trip you
observe
Motion related graphs
• Several graphs that can be used to illustrate the straight line motion
of an object
• Distance-time graphs
• Displacement-time graphs
• Speed-time graphs
• Velocity-time graphs
Hike!
• Imagine a football team is running plays
•
•
•
•
The first play nets 4 yards
The second play nets 3 more
The third play nets 4 yards
The fourth play nets 5 yards
• For this example, we’ll pretend that each play took 10 seconds to
execute
• Let’s look at the difference between a distance-time graph and a
displacement-time graph
Distance-time graph
Trial 2
18
16
14
12
10
8
6
4
2
0
10s
20s
30s
Trial 2
40s
Additional notes on graph 1
• Remember, distance doesn’t matter the direction of travel – only the
amount of travel
• Notice, that the x-component and y-component are directly related
• Also notice that the distance increases
Displacement-Time graph
Trial 1
6
5
4
3
2
1
0
10s
20s
30s
Trial 1
40s
The other point of view
• From the opposing team’s perspective, they are moving backwards
with each play
• If we created a distance-time graph, it would like identical to that of
our home team
• If we created a displacement-time graph, you will notice that the line
falls under the x-axis
Displacement-time graph…from the other
team’s point of view
Trial 3
0
10s
20s
30s
-2
-4
-6
-8
-10
-12
-14
-16
-18
Trial 3
40s
Dry your eyes
• Think back to Algebra class (it’s ok, it’s over now)
• The steepness of a line was called its slope
• Recall that m=y/x (sometimes known as “rise over run”)
• Wait a minute!.....in a displacement-time graph, displacement is the
y-axis and time is the x-axis
• Displacement divided by time is……..velocity!
• The velocity found by slope is the instantaneous velocity of that time period
• So, the slope of the displacement-time graph is the velocity
Acceleration
• A change in velocity is known as an acceleration
• Accelerations can be changes in “speed”, changes in direction, or both
• Acceleration is calculated as: a = Δv / t
• Sometimes, negative acceleration is thought of as only “slowing down”
• In reality, it means accelerating in the opposite direction
• Huh?
• Imagine a sprinter running attached to a parachute when a strong breeze comes
along
• It is true that the sprinter will slow down, but eventually, he/she will start picking
up speed IN THE OPPOSITE DIRECTION
Acceleration on a graph
• On a velocity-time graph,
• Slope is velocity over time…..the same as acceleration
• So, slope of a velocity-time graph is the instantaneous acceleration for
that segment of the trip
• Note: if slope is zero, then there is no acceleration and the objects
maintains the same velocity
• Imagine a moving sidewalk at an airport that is moving 2 miles/hour
compared to the terminal floor
• One person gets on the moving sidewalk and another does not and
simply stands still
• How fast is the person on the moving sidewalk moving compared to
the moving sidewalk itself?
• How fast is the person on the moving sidewalk moving compared to
the observer?
• The answer?....It depends (of course, right?!)
2 Miles/Hour
overall
0 Miles/Hour
2 Miles/Hour
Scenario #1, the person on the moving sidewalk is standing still; the sidewalk is
moving
2 Miles/Hour
overall
2 Miles/Hour
0 Miles/Hour
Scenario #2, the person on the moving sidewalk is walking and the sidewalk
stopped moving
4 Miles/Hour
overall
2 Miles/Hour
2 Miles/Hour
Scenario #3, the person on the moving sidewalk is walking 2mph compared to the
sidewalk; the sidewalk is moving
0 Miles/Hour
overall
2 Miles/Hour
2 Miles/Hour
Scenario #4, the person on the moving sidewalk forgets something and walks the other
way at 2 mph; the sidewalk is moving
Resultant velocity
• In each scenario, there were two objects that had velocities
compared to two different things
• To get an overall velocity to the same thing, called a resultant
velocity, you must combine the velocities
Hurray!?!
• The velocity formula you have seen so far is when there is no
acceleration….the object has been travelling at a constant speed
• But what about when the object is accelerating while it is moving?
• Answer: Three new formulas!
Again, but with acceleration
• Position while accelerating
• xf = xi + vit + ½ at2
• Velocity while accelerating
• vf = vi + at
• If you don’t know the time travelled but you do know the distance
• vf2 = vi2 + 2ax
• Note: the “f” in the subscript means final and the “i” in the subscript
means initial
Acceleration and velocity; the different effects
• Note the difference in acceleration:
https://www.youtube.com/watch?v=apoeGMWF17c
• Another look; different race:
https://www.youtube.com/watch?v=7rVTIpS5zb4
• One car can attain a much higher speed
• The other car gets to its maximum speed sooner
• If the race would have continued
• The winning car would continue travelling at a constant, but fast velocity
• The losing car could continue to accelerate until reaching its much higher velocity;
Eventually, the losing car would have passed the winning car
Hints, tips, and tricks
• Physics problems are know for having many different number quantities
• It is suggested that you:
• Draw or sketch a picture and then label it with the information
• You might be surprised how it helps keep the problem organized
• Pick a frame of reference that makes it easiest on you
• Use the simplest formula that works for the information that you have and need
Vertical motion
• If we are talking about vertical (ie up and down) motion instead of
horizontal motion, we keep the same formulas but make some
changes
• First, we switch the letter x (for the x-axis) with the letter y (for the yaxis)
• Example: v=Δ x/t becomes v=Δ y/t
• Next, we’ll look at acceleration
“g, I didn’t know that”
• Gravity is always “pulling” on objects
• The average acceleration of gravity near the Earth’s surface is
9.81m/s2
• One of the most important numbers for you to memorize!
• Instead of writing agravity or ag, we just write g = 9.81m/s2
• If there is no air resistance or any other forces acting besides gravity
(like on the Moon, for example), an object is said to be in freefall
Choices
• When dealing with vertical motion, you need to decide which of the
following you want to do
• Treating the acceleration as positive in the up direction and negative
in the down position
• This is the traditional approach
• Treating the acceleration as positive if it is in the same direction as
the movement and negative if it is the opposite direction as the
movement
• The is the approach that I use
Engines OFF
• In the following example, a rocket lifts off from the launch pad
• After expending its fuel, it continues flying higher but at a slower and
slower rate (due to gravity)
• Eventually, it gets to its highest point (also known as apogee)
• It then falls towards the Earth at a faster and faster rate
• In these types of problems, you must break the motion down into three
parts:
• Engines are firing
• Engines are off and rocket keeps rising
• Engines are off and rocket is descending
UP Direction
Velocity is
positive;
acceleration
is negative
Velocity is
negative;
acceleration
is negative
Velocity is
positive;
acceleration
is negative
Velocity is
positive;
acceleration
is positive
DOWN Direction
Traditional
Frame of
Reference
Pros and Cons
• The advantage of the traditional system is consistency
• The positive and negative direction stays the same
• Zero is at the ground level
• The advantage of the frame of reference approach
• Easier (I think) to understand and use
• CAUTION: You have to make sure that the sign of your distances &
displacements match
Magic Kingdom
• In some ways, working out physics problems are like visiting a magical
land
• For example, in almost all problems, we pretend as if there is no air resistance
(which means no air!)
• Remember, that physics formulas describe idealized situations
• If you take further physics classes, you will use more detailed
calculations to more realistically model the real world