PhysicsForce and motion

Image thanks to www.wolverton-mountain.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 betweenforce, mass, gravity, and the motion ofobjects.

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

10s 20s 30s 40s0

2

4

6

8

10

12

14

16

18

Trial 2

Trial 2

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

10s 20s 30s 40s0

1

2

3

4

5

6

Trial 1

Trial 1

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

10s 20s 30s 40s

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Trial 3

Trial 3

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

0 Miles/Hour

2 Miles/Hour overall

Scenario #1, the person on the moving sidewalk is standing still; the sidewalk is moving

0 Miles/Hour

2 Miles/Hour

2 Miles/Hour overall

Scenario #2, the person on the moving sidewalk is walking and the sidewalk stopped moving

2 Miles/Hour

2 Miles/Hour

4 Miles/Hour overall

Scenario #3, the person on the moving sidewalk is walking 2mph compared to the sidewalk; the sidewalk is moving

2 Miles/Hour

2 Miles/Hour

0 Miles/Hour overall

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• vf

2 = 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 y-

axis)• 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

Traditional

Frame of Reference

UP Direction

DOWN Direction

Velocity is positive; acceleration is negative

Velocity is negative; acceleration is negative

Velocity is positive; acceleration is positive

Velocity is positive; acceleration is negative

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