Physical Science II

1. Physical Science II Motion

2. Motion • Why is being able to describe motion important?

3. Motion • Being able to accurately describe motion has been a vital part of our global culture. • As a race, humans have made significant advantages in being able to describe location and motion. • Examples • Using Landmarks • Magnetic Compass • Detailed Maps • Global Positioning System (GPS) • Odometersand Speedometers

4. Motion • Describing motion can be tricky. • Take for example the following statement: • “Everything is moving.” • Do you agree with that statement? Why or why not?

5. Frame of Reference • In order to accurately describe motions in the universe, there needs to be a Frame of Reference. • A Frame of Reference is simply a group of objects that are not moving with respect to one another. • Examples: The classroom, the floor, the ground, Hershey, Pa.

6. Frame of Reference • Let us go back to the previous quote: • “Everything is moving.” • This statement can be right or wrong depending on your chosen frame of reference. • If your frame of reference is this room, then certainly not all objects are moving. • However, if your frame of reference is the sun, then this room along with everything inside is moving as the Earth rotates and revolves around the sun.

7. Frame of Reference • Let us try another example: • A man and a woman are seated inside a train that is driving from Harrisburg toward Philadelphia at 65mph. • The woman believes they are not moving, while the man believes they are moving. • Who is correct in this situation?

8. Distance vs. Displacement • Assume for a minute that you are lost somewhere in Pennsylvania. • A helpful resident tells you that you are 50 kilometers from Hershey. • With this information can you get back home? • What other information would you need?

9. Distance vs. Displacement • Imagine again you are lost somewhere in Pennsylvania. • The same helpful resident instead tells you that you are 50 kilometers northwest of Hershey. • Can you find your way home?

10. Distance vs. Displacement • What we have just discovered is there are two types of length measurements. • The first scenario describes a measurement of distance. • Distance is simply a measurement of length, it has no direction. • Examples: • You are 50 kilometers from Hershey. • I am 3 meters from the door. • The athlete ran 5 kilometers.

11. Distance vs. Displacement • The second scenario described a measurement of displacement. • Displacement is a length measurement that also has a specific direction. • Examples: • You are 50 kilometers northwest of Hershey. • I am 3 meters to the south of the door. • The athlete ran 5 kilometers to the east.

12. Distance vs. Displacement • We’ve identified the difference between distance and displacement, but what is the importance of having two different types of length measurements?

13. Speed vs. Velocity • In the previous section we looked at the difference between distance and displacement and determined there are two distinct ways of measuring the length you’ve traveled. • In addition to measuring how much length something has travelled, it is often important to know how fast an object is or was moving.

14. Speed vs. Velocity • Imagine you are going to travel to the beach on vacation. • In your preparations before travel, you may want to know things like: • Directions – What roads do I take? • Travel Time – How long will I be driving? • Travel time is of course dependent on many factors: • How much traffic. • How far must you travel. • How many stops you make. • How fast can you drive.

15. Speed vs. Velocity • The final bullet point “How fast can you drive.” is a measurement of speed. • Instantaneous Speed – a measurement of how fast you are moving at one particular moment. • Example: At 8:30 am we were traveling at 15 m/s (meters per second) • This measurement is only a snapshot in time, since at 8:31 you may have been traveling at 40 m/s.

16. Speed vs. Velocity • Average Speed – a measurement of how much distance you’ve traveled in a certain amount of time. • While driving to the beach our average speed was 20 m/s. • To calculate average speed use the following equation:

17. Speed vs. Velocity • Example Problems: • A runner traveled 1000m in a time of 250s. What was the runner’s average speed? • How long did it take a bullet to travel 300m if it had an average speed of 350m/s?

18. Speed vs. Velocity • Sometimes knowing only how fast something travels is not enough information to completely analyze a situation. • It may also be important to know which way an object is or was moving. • Instantaneous Velocity – measures how fast an in what direction and object is moving at one particular moment. • At 8:30 we were traveling 15m/s to the east. • Again this measurement is only a snapshot in time.

19. Speed vs. Velocity • Average Velocity – a measurement of how much displacement occurred in a certain amount of time. • While driving to the beach our average velocity was 10m/s to the southeast.

20. Speed vs. Velocity • Example Problems • A truck traveled 2000m north in 65s. What was the average velocity for this vehicle? • A cheetah ran at an average velocity of 25m/s west for 15s. What was the displacement of the cheetah?

21. Velocity Vectors • Sometimes the motion of an object involves more than one velocity. • When this happens it becomes necessary to find the resultant velocity. • The resultant velocity is the sum of all the individual velocities of an object’s motion. • When finding this sum it is important to consider the direction of the velocity as well as the numerical value.

22. Velocity Vectors • This involves using vectors. • A vector is simply an arrow that is used to represent velocity. • The length of the tail indicates the size of the velocity and the arrow head points out the direction. Head Tail

23. Velocity Vectors • When vectors are in the same direction, they are added together. • If velocity vectors are in opposite directions they are subtracted from each other. • When velocities are at right angles to each other you must add them using the Pythagorean Theorem.

24. Velocity Vectors • Examples: • A river is flowing downstream at a speed of 2-m/s. If a person is floating in a raft on this river, how fast are they moving past the shoreline? • A boat is traveling downstream at a speed of 10-m/s in a river that is flowing at a speed of 2-m/s. What is the resultant velocity of the boat with respect to the shoreline? • A boat is traveling upstream at a speed of 10-m/s in a river that is flowing at a speed of 2-m/s. What is the resultant velocity of the boat with respect to the shoreline? • While in a canoe, two people row with a velocity of 4-m/s north across a river that is flowing with a velocity of 3-m/s east. What is the resultant velocity of these two people?

25. Displacement Vectors • Displacement can also be represented by a vector. • Examples: • A girl rides her bike 200-m east, pauses for a moment and then continues to ride another 50-m east. What was the resultant displacement of the girl? • A person drives their car 20-mi to the north, then turns and drives 5-mi to the south. What is the resultant displacement of the person? • A man drives his car 3-mi to the east, then turns left and drives 4-mi to the north. What is the resultant displacement of the man?

26. Acceleration • In the previous section we discussed how most objects do not travel at a constant velocity. • When the velocity of an object is changing, the object is undergoing an acceleration.

27. Acceleration • Acceleration – the rate at which velocity is changing. • Three ways an object can experience an acceleration: • The object’s speed can increase. • The object’s speed can decrease. • The object can change direction. • Changing any one of these three will cause the velocity of an object to change, but in many cases of acceleration both speed and direction will be altered.

28. Acceleration • Mathematically, acceleration is defined as: Acceleration is measured in meters per seconds squared:

29. Acceleration • Example: • A car experiences a change in velocity from 7-m/s to 12-m/s, which is caused by an acceleration of 2.5-m/s2. How long was the car accelerating? • In a time period of 4 seconds a truck accelerates from rest to a velocity of 10-m/s. What was the acceleration experienced by this truck? • While driving a car at a velocity of 20-m/s, a person spots a deer standing in the roadway. To avoid striking the animal the person applies the brakes and brings the car to rest. If the brakes caused the car to stop in 2 seconds, what was the vehicle’s acceleration?

30. Gravitational Acceleration • The acceleration due to gravity on Earth is approximately 9.8-m/s2. • This acceleration affects all objects that are near the surface of the planet Earth regardless of their size, shape or mass. • Example: • Which object accelerates faster: a penny or a feather? • In the absence of air resistance, both objects fall at the same rate! • This shows that Earth’s gravitational acceleration affects all objects equally.