Sec. 11.1- Distance and Displacement

Imagine, if you will, a day in the life of a butterfly The butterfly flies quickly past you, then slowly, and stops on a nearby flower to grab a snack A butterfly’s day involves a great deal of motion

In order to describe a butterfly’s motion, we must think of: How fast is the butterfly moving? It is flying toward the flower or away from it?

When describing an object in motion, you must always describe the direction the object is moving, how fast it is moving, as well as specifying its location at a certain time.

Frame of Reference As you are sitting in your seats, how fast do you think you are moving?

Well, since we are all located ON Earth, and Earth is moving- both orbiting the Sun and rotating on its axis, we are also moving with the same speed and direction We are all orbiting the Sun at about 18 miles per second We are all spinning around Earth’s axis at about 1037 mi/hr

Why do you think we do not “feel” like we are moving? What about the butterfly we were talking about earlier- how fast is it moving?

In order to accurately describe motion, a frame of reference is required Frame of reference is a system of objects that are not moving in respect to one another The answer to “How fast is the butterfly moving?” depends on which frame of reference we use to measure motion

Consider: People on train Relative Motion Consider: People on train How fast are they moving? Depends on the frame of reference you choose!

Relative motion- motion in relation to a frame of reference Relative to people standing on a platform at train station, the people on a moving train are moving pretty fast Relative to one another on the train- does one person on the train feel like other people are moving in relation to him/her?

Choosing Frame of Reference Choosing a meaningful frame of reference allows you to describe motion in a clear way Ex: If you are on a train and use a tree outside as your frame of reference, you can describe your motion in relation to the ground outside

If you look at the seat or floor of the train as you get up and walk around- what frame of reference is this? What would your motion be relative to? Would this tell you how you are moving in relation to the ground outside?

Distance- length of the entire path between two points Measuring Distance Distance- length of the entire path between two points Distance depends on the path an object takes If object moves in straight line, the distance it moved it equal to the length of that line If object moves in zig zags, distance it moved is equal to the sum of all the zig zag lengths

Distance is measured in base unit meters (m) For large distances, we use kilometers (km) For small distances we use centimeters (cm)

What unit would you use to measure the length of Mississippi River? What unit would you use to measure the distance a marble rolls?

Displacement Distance is good and all, but it does not give us enough information about an object’s position- doesn’t tell us what direction the object moved/is moving Displacement is more useful for describing motion of an object- tells us the direction an object moves and the NET distance it moved

Displacement- direction object moved from starting point, and length of straight line from starting point to end point

Displacements are sometimes used when giving directions Instead of saying “Walk 5 blocks”, saying “Walk 5 blocks North” would ensure someone arrives at the correct location Which set of directions would be using displacement instead of distance?

Roller Coaster tracks Curvy, loopy, crazy Distance= length of entire track added together Displacement= length from starting point to end point on the track- what would be the displacement of a roller coaster car that completed it’s loop? Why?

Combining Displacements Displacement is a “vector” quantity Vector- quantity that has both magnitude and direction Magnitude?

Arrows on a graph are used to represent vectors Length of arrow= magnitude Arrow head= direction Displacements are added together by vector addition

Displacement Along a Straight Line When two displacement vectors are pointing the same direction, you simply add their magnitudes together to get the total displacement When two displacement vectors are pointing in opposite directions, the magnitudes subtract from each other

Sooo… For finding total displacement- same direction add, opposite direction subtract

Ex: Car travels east for 4 km then stops to take a break Ex: Car travels east for 4 km then stops to take a break. Car then travels another 2 km east. What would be the total displacement of the car’s trip? What about total distance traveled?

Ex: Car travels east for 4 km then stops to take a break Ex: Car travels east for 4 km then stops to take a break. Car then travels another 2 km west. What would be the total displacement of the car’s trip? What about total distance traveled?

If just given initial position and final position, displacement is calculated by subtracting the initial position from the final position This may result in a “negative” displacement- this is fine

Displacement= Final Position – Initial position Ex: