Motion

1. Chapter 2 Motion

2. Describing Motion Motion is the change in position relative to a frame of reference. Frame of Reference: The object or point from which movement is determined. Example: When we say that a space shuttle moves 8 km/sec, we mean that its movement relative to Earth below. When we say a racing car in the Indy 500 reaches a speed of 300 km/hr, of course we mean relative to the track. Unless stated otherwise, when we discuss the speeds of things in our environment, we mean speed with respect to the surface of the Earth.

3. Describing Motion Motion is measured by distance and time. Distance (d): How far an object moves. Time (t): Continuous period measured by clocks, watches, and calendars. Displacement (?x) is the distance and direction of an object�s change in position from the starting point. Displacement = Final Position � Initial Position ?x = xf - xi Displacement and distance are not the same thing. Example: Suppose a runner jogs to the 50-m mark and then runs back to the 20-m mark. The runner travels a distance of 80-m (50-m + 30-m). The runner only displaces himself 20-m (20-m � 0-m). The only time distance and displacement are the same is if the motion was in a single direction.

4. Describing Motion Speed: The distance traveled by a moving object per unit of time. Speed = Distance/Time Units of Speed: meters/second (m/s), kilometers/hour (km/hr), miles/hour (mph), feet/second (ft/s). Example: A car traveling at a constant speed covers a distance of 750-m in 25-s. What is the car�s speed? Speed = Distance/Time Speed = 750-m/25-s Speed = 30-m/s

5. Describing Motion Examples: A car travels 300-km in 6-hrs. What is the speed of the car? Speed = 300-km/6-hrs Speed = 50-km/hr What is the speed of a jet plane that flies 7200-km in 9-hrs? Speed = 7200-km/9-hrs Speed = 800-km/hr The speed of a cruise ship is 50-km/hr. How far will the ship travel in 14-hrs? Speed = Distance/Time 50-km/hr = Distance/14-hrs Distance = (50-km/hr) � (14-hrs) Distance = 700-km

6. Describing Motion Constant Speed: Speed that does not change. The graph to the right shows the constant speed of a runner. Notice that a distance-time graph for constant speed is a straight line. Example: What is the speed of the runner? Speed = 50-m/5-s Speed = 10-m/s

7. Describing Motion The slope of the distance-time graph is directly related to the speed. The steeper the slope, the faster the speed. Example: What is the speeds of the swimmers in the graph to the right? Speed 1 = 100-m/50-s Speed 1 = 2-m/s Speed 2 = 50-m/50-s Speed = 1-m/s

8. Describing Motion Usually speed is not constant. Average speed describes speed of motion when speed is changing. Average Speed: The total distance traveled by the total time of travel. Average Speed = Total Distance/Total Time The graph to the right is a graph of a cyclist that keeps changing speeds during the trip. Example: If the rider in this graph covers a distance of 5-km in 0.25 hours, what is the average speed? Average Speed = 5-km/0.25-hrs Average Speed = 20-km/hr

9. Describing Motion Example: According to this distance-time graph, how far did the object move between the first and second hour? What was the average speed after one hour? What was the average speed after two hours? What was the average speed for the entire trip?

10. Describing Motion Instantaneous Speed is the speed at a given point in time. Example: Your car�s speedometer. A speedometer shows how fast a car is going at one point in time or at one instant. When something is speeding up or slowing down, it instantaneous speed is changing. The speed is different at every point in time. If an object is moving with constant speed, the instantaneous speed doesn�t change. The speed is the same at every point in time.

11. Describing Motion As we have seen, the motion of an object over a time can be shown on a distance-time graph. Time is plotted on the horizontal axis and the distance traveled is plotted on the vertical axis. If the object moves with a constant speed, the increase in distance over equal time intervals is the same. This results in a straight line.

12. Describing Motion Example: Draw a distance-time graph for the following motion. Is this a graph for constant speed or changing speed? How do you know? What is the average speed for this trip?

13. Describing Motion Example: Draw a distance-time graph for the following motion. Is this a graph for constant speed or changing speed? How do you know? What is the average speed for this trip?

14. Describing Motion Velocity is speed in a given direction. Velocity = Displacement/Time Examples: The speed of a hurricane is 20-km/hr. The velocity is 20-km/hr east. Why is a direction necessary? Navigation by land, sea, or air requires precise measurements of velocity (speed and direction). If a pilot wants to reach the Hawaiian Islands, a pilot must determine both the direction and speed of the plane. If either measurement is wrong, the plane will not reach its destination.

15. Describing Motion Because velocity depends on direction as well as speed, the velocity of an object can change even if the speed of the object remains constant. Example: A race car traveling around a track at a constant speed. Even though the speed remains constant, the velocity changes because the direction of the car�s motion is changing constantly.

16. Describing Motion Examples: A person walked a distance of 1.60-km east in 30-minutes. What is the velocity of the person in kilometers per hour? Velocity = 1.60-km/0.50-hrs Velocity = 3.2�km/hr East A car travels straight south for 200-miles in 2.5-hours. What is the velocity of the car in miles per hour? Velocity = 200-miles/2.5-hours Velocity = 80-mi/hr South

17. Acceleration Acceleration is the rate of change in velocity. When the velocity of an object changes, the object is accelerating. To calculate acceleration, divide the change in velocity by the time it takes the velocity to change. Acceleration = (Final Velocity � Initial Velocity)/Time a = (vf � vi)/t Unit of Acceleration: meters per second per second (m/s/s or m/s2), miles per hour per second (mph/s), or kilometers per hour per second (km/hr/s).

18. Acceleration A decrease in velocity is called deceleration. Because the final velocity is less than the initial velocity, deceleration has a negative value. Deceleration is sometimes called negative acceleration. Example: A roller coaster�s velocity at the top of a hill is + 10-m/s. Two seconds later it reaches the bottom of the hill with a velocity of + 26-m/s. What is the acceleration of the roller coaster?

19. Acceleration Examples: A roller coaster has a velocity of 10-m/s at the top of a hill. Two seconds later it reaches the bottom of the hill with a velocity of 20-m/s. What is the acceleration of the roller coaster? A roller coaster is moving at 25-m/s at the bottom of a hill. Three seconds later it reaches the top of the next hill, moving at 10-m/s. What is the acceleration of the roller coaster?

20. Acceleration A change in velocity can be either a change in how fast something is moving or a change in the direction of movement. Any time a moving object changes direction, its velocity changes and it is accelerating. Examples: A horse on a carousel. Although the speed is constant, the horse is accelerating because it is changing direction constantly as it travels in a circular path. The Earth�s orbit. The Earth is accelerating constantly as it orbits the Sun in a nearly circular path.

21. Acceleration The data in the table to the right is of a professional drag-strip race. The driver traveled a distance of 5-m after 1-s. The distance covered in the next second was 15-m. By the end of 4-s, the driver had traveled 80-m. The graph is a curve rather than a straight line. A distance-time graph for acceleration is always a curve.

22. Acceleration Just as it was useful to graph a changing position versus time graph, it is also useful to plot an object�s velocity versus time. Notice that the graph is a straight-line, which means that the object was speeding up at a constant rate. The rate at which the car�s velocity is changing can be found by calculating the slope of the velocity-time graph. Slope = Rise/Run The slope of the line is the acceleration of the object. Example: What is the acceleration (slope) in this graph? a = (20.0-m/s � 10.0-m/s)/2.00-s a = (10.0-m/s)/2.00-s a = 5.00-m/s/s

23. Acceleration A speed-time or velocity-time graph can tell you whether the acceleration is positive or negative. If the acceleration is positive, the line slopes upward to the right. If the acceleration is negative, the line slopes downward to the right.

24. Motion and Forces A force is a push or a pull. A force may give energy to an object and cause it to start moving, stop moving, or change its motion. Ex: Kicking a soccer ball at rest, hitting a tennis ball back to your opponent, playing billiards, etc. A force also may or may not produce a change in motion. Ex: Two students pushing on a box against each other with equal amounts of force.

25. Motion and Forces When two or more forces act on an object at the same time, the forces combine to form the net force. Forces on an object that are equal in size and opposite in direction are balanced forces. Ex: Two students playing tug-of-war pulling with an equal amount of force but in opposite directions. Forces on an object that are not equal in size or opposite in direction are unbalanced forces. Ex: Two students playing tug-of-war pulling with unequal amounts of force in opposite directions.

26. Motion and Forces Adding forces: If two or more forces are acting in the same direction, you can add them together to get the total or net force. Ex: John and Sue are pushing a cart with a force of 5 lb. and 7 lb. respectively, in the same direction. Find the net force acting on the cart.

27. Motion and Forces Subtracting forces: If two or more forces act in opposite directions, you can subtract them to get the total or net force. Ex: John is pushing to the right with 5 lb. of force on a cart. Sue is pushing to the left with 7 lb. of force. Find the net force acting on the cart.

28. Motion and Forces Inertia is the tendency of an object to resist any change in its motion. Example: If an object is moving, it will keep moving with the same speed and in the same direction unless an unbalanced force acts on it. The greater the mass of an object the greater the inertia. Mass is the amount of matter in an object. Example: A bowling ball and a table-tennis ball are both moving at 5-m/s, which one is easier to stop? Why? The table-tennis ball is easier to stop because it has a small mass and therefore requires less force to stop its motion.

29. Motion and Forces Forces change the motion of an object in specific ways. Sir Isaac Newton (1642 � 1727) was able to state rules that describe the effects of forces on the motion of object. These rules are known as Newton�s Laws of Motion. These rules apply to the motion of all objects, no matter how large or how small.

30. Motion and Forces Newton�s First Law of Motion: An object at rest remains at rest and an object moving with some velocity continues to move with the same velocity unless acted upon by an outside force. The tendency of an object to continue in its original state of motion is called inertia. Newton�s first law is sometimes called the Law of Inertia.

31. Motion and Forces The law of inertia can explain what happens in a car crash. Example: When a car traveling at 50-km/hr collides head-on with something solid, the car crumples, slows down, and stops within approximately 0.1-seconds. Any passenger not wearing a safety belt continues to move forward at the same speed the car was traveling. Within about 0.2-seconds, after the car stops, unbelted passengers slam into the dashboard, steering wheel, windshield, or the backs of the front seats. They are traveling at the car�s original speed of 50-km/hr.

32. Motion and Forces Safety belts loosen a little as its restrains the person, increasing the time it takes to slow the person down. This reduces the force exerted on the person. The safety belt also prevents the person from being thrown out of the car. Air bags, soft dashboards, crumple zones, etc., all reduce injuries in car crashes by providing a cushion that reduces the force on the car�s occupant�s.