Objectives: The students will be able to: Identify frames of reference and describe how they are used to measure motion. Identify appropriate SI units

Objectives: The students will be able to:

• Identify frames of reference and describe how they are used to measure motion.

• Identify appropriate SI units for measuring distances.

• Distinguish between distance and displacement.

• Calculate displacement using vector addition.

Engagement / Exploration Activity

• How does a Ramp Affect a Rolling Marble?

Engagement Activity

• What did you learn about motion from this activity?

• Kinematics

Kinematics

• Describes motion while ignoring the agents that caused the motion

11.1 Distance and Displacement

How fast is the butterfly moving? What direction is it moving?

To describe motion, you must state the direction the object is moving as well as how fast the object is moving. You must also tell its location at a certain time.


What is needed to describe motion completely?

A frame of reference is a system of objects that are not moving with respect to one another.

To describe motion accurately and completely, a frame of reference is necessary.

Introduction to Frame of Reference

Choosing a Frame of Reference


How Fast Are You Moving?

How fast the passengers on a train are moving depends on the frame of reference chosen to measure their motion.

Relative motion is movement in relation to a frame of reference.

• As the train moves past a platform, people standing on the platform will see those on the train speeding by.

• When the people on the train look at one another, they don’t seem to be moving at all.

Choosing a Frame of Reference (Period 4A starts)

Reference Frames and DisplacementAny measurement of position, distance, or speed must be made with respect to a reference frame.

For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher.


To someone riding on a speeding train, others on the train don’t seem to be moving.


Myth Busters Clip


Which Frame Should You Choose?• When you sit on a train and look out a window, a

treetop may help you see how fast you are moving relative to the ground.

• If you get up and walk toward the rear of the train, looking at a seat or the floor shows how fast you are walking relative to the train.

• Choosing a meaningful frame of reference allows you to describe motion in a clear and relevant manner.


What is “moving”?

• An object is moving if its position relative to a fixed point is changing.

• Ex. Space shuttle is moving at 30 kilometers per second relative to the sun

or

8 km/s relative to the earth.


Frame of Reference

• Summary• Always choose a

reference point.• The object’s

position is its location with respect to a chosen reference point

• Class will divide and half will be doing the lab and the other half on computers.– Frame of

Reference– Observing and

Describing Motion

Scalar quantities:

• Have magnitude (size) but no direction.

• Examples: distance (10m) time (6 s) speed (12.3 km/h)

Vector quantities:

• Have both magnitude (size) and direction.

• Examples: * position (12 km due south)

* displacement ( 3m upward)

* velocity ( 13.5 m/s downward)

Distance is the length of a path between two points. When an object moves in a straight line, the distance is the length of the line connecting the object’s starting point and its ending point.

• The SI unit for measuring distance is the meter (m).

• For very large distances, it is more common to make measurements in kilometers (km).

• Distances that are smaller than a meter are measured in centimeters (cm).

Measuring Distance

Distance and Displacement

•Distance and displacement are two quantities which may seem to mean the same thing, yet they have distinctly different meanings and definitions.

•Distance (d) is a scalar quantity which refers to "how far an object has moved" during its motion.

•Displacement (d) is a vector quantity which refers to the object's change in position.

Position

• Location of the object at a specific time

displacement = Positionfinal - Positioninital

Where?

• Position—reference point needed

• Distance versus Displacement

Position, Distance, Displacement

• Position—reference point needed

• Distance—no reference point needed

• Displacement—change in position

Displacement Vs distance

displac

emen

t

distance

Stopped here

Example A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

• Even though the physics teacher has walked a total distance of 12 meters, her displacement is 0 meters.

• During the course of her motion, she has "covered 12 meters of ground" (distance = 12 m).

• Yet, when she is finished walking, she is not "out of place" – i.e., there is no displacement for her motion (displacement = 0 m). Displacement, being a vector quantity, must give attention to direction.

• The 4 meters east is canceled by the 4 meters west; and the 2 meters south is canceled by the 2 meters north.

Example:

• Tommy walks from home (0m) to school which is 4.55 m North of his house. What is his displacement?

• ∆d = df – di

= 4.55m – 0m

= 4.55 m N or +4.55m

Example:

• A dog escapes from his owner’s house and finds a garden to dig up 21 m east of his house. He is scared off by a cat and ends up under a tree 6.5 m east of his house. What is his displacement?

• ∆d = df – di = 6.5 m – 21m

= -14.5 m (or 14.5 m west)

Elaboration

• Summary

• Introduction to Position, Distance, and Displacement Activity

• Measuring Distance and Displacement Lab (Introduces Vectors)

Introduction to Vectors

• Vectors and Football

• Pythagorean Theorem

A. Add the magnitudes of two displacement vectors that have the same direction.

B. Two displacement vectors with opposite directions are subtracted from each other.

Combining Displacements

• Vector addition is the combining of vector magnitudes and directions

• EX:5km 10km

5 + 10= 15km

10km 3km

10 – 3= 7 km

Examples Combining displacements


Distance is the length of a path between two points. When an object moves in a straight line, the distance is the length of the line connecting the object’s starting point and its ending point.

• The SI unit for measuring distance is the meter (m).

• For very large distances, it is more common to make measurements in kilometers (km).

• Distances that are smaller than a meter are measured in centimeters (cm).

Measuring Distance


To describe an object’s position relative to a given point, you need to know how far away and in what direction the object is from that point. Displacement provides this information.

Measuring Displacements


Think about the motion of a roller coaster car.• The length of the path along which the car has

traveled is distance. • Displacement is the direction from the starting

point to the car and the length of the straight line between them.

• After completing a trip around the track, the car’s displacement is zero.

Measuring Displacements


How do you add displacements?

A vector is a quantity that has magnitude and direction.

Add displacements using vector addition.



Displacement is an example of a vector. • The magnitude can be size, length, or amount. • Arrows on a graph or map are used to represent

vectors. The length of the arrow shows the magnitude of the vector.

• Vector addition is the combining of vector magnitudes and directions.



Displacement Along a Straight Line

When two displacements, represented by two vectors, have the same direction, you can add their magnitudes.

If two displacements are in opposite directions, the magnitudes subtract from each other.



A. Add the magnitudes of two displacement vectors that have the same direction.

B. Two displacement vectors with opposite directions are subtracted from each other.



Displacement That Isn’t Along a Straight Path

When two or more displacement vectors have different directions, they may be combined by graphing.



Measuring the resultant vector (the diagonal red line) shows that the displacement from the boy’s home to his school is two blocks less than the distance he actually traveled.















The boy walked a total distance of 7 blocks. This is the sum of the magnitudes of each vector along the path.

The vector in red is called the resultant vector, which is the vector sum of two or more vectors.

The resultant vector points directly from the starting point to the ending point.


The head of the vector must point in the direction of the quantity

Vectors can be combined (added)

Resultant Vector

• The resultant is the vector sum of two or more vectors.

• It is the result of adding two or more vectors together.

+ =

5 5 15

+

5






What is the resultant vector?

Steps for Graphical Addition

1. Choose an appropriate scale (e.g.. 1cm = _____ m/s)

2. Draw all vectors with tail starting at origin

3. Redraw vector from “head to tail” while maintaining original direction of vector.

4. From tail of first vector to head of last connect lines (this is resultant) direction is towards head of last original vector

5. Measure length and convert back using scale.

6. Measure resultant from 0 degrees.

What happens now?

Graphical:Scale: 1 box = 50 km/h

Head to Tail Method Tail to Tail Method

Finding the Resultant Vector

• Pythagorean Theorem

c2 = a2 + b2

Head to Tail Method

1. 3.0 m/s, 45 deg + 5.0 m/s, 135 deg

5.83 m/s, 104 deg

5.0 m/s, 45 deg + 2.0 m/s, 180 deg

3.85m/s, 66.5 deg

Vector Practice

• Vector Activity

• Vectors Vectors Everywhere!

• Practice with vectors

• Mathematical Vector Addition.

• Vectors and Scalars

Closure

• What is the difference between distance and displacement? Give an example of each one.

• Kahoot 11-1

Documents

Objectives: The students will be able to: Identify frames of reference and describe how they are used to measure motion. Identify appropriate SI units