1. Vocab (5.5, 5.9) April 10 th, 2007: 1. Weight: F w ; the amount of gravitational force that the earth exerts on an object 2. Acceleration due to gravity: a g ; the constant rate of acceleration when an object falls; 9.8 m/s 2

2. Acceleration due to Gravity PS-5.5: Explain how acceleration due to gravity affects the velocity of an object as it falls.

3. Gravity All objects accelerate as they fall because Earth continually exerts a force (gravitational force) on them. All objects accelerate as they fall because Earth continually exerts a force (gravitational force) on them.

4. When we drop something… It accelerates. It accelerates. The direction of the force is always downward. The direction of the force is always downward. The acceleration is in the direction of the force so the direction of acceleration is downward as well. The acceleration is in the direction of the force so the direction of acceleration is downward as well.

5. When we drop something… It has an initial velocity of ZERO. It has an initial velocity of ZERO. It will accelerate at a constant rate of 9.8 m/s 2. It will accelerate at a constant rate of 9.8 m/s 2. –This means the object will speed up at a constant rate of 9.8 m/s every second it is falling (in the absence of air resistance).

6. How velocity is affected… vivivivi vfvfvfvf 1 st sec 0.0m/sec9.8m/sec 2 nd sec 9.8m/sec19.6m/sec 3 rd sec 19.6m/sec29.4m/sec 4 th sec 29.4m/sec39.2m/sec 5 th sec 39.2m/sec49.0m/sec

7. Conclusion 9.8 m/s 2 IS the acceleration of gravity. 9.8 m/s 2 IS the acceleration of gravity. It’s symbol is a g. It’s symbol is a g. Since the object is accelerating because of Earth’s gravity, the velocity of the object continues to increase in speed and continue in a downward direction until it hits the ground. Since the object is accelerating because of Earth’s gravity, the velocity of the object continues to increase in speed and continue in a downward direction until it hits the ground.

8. Motion Diagram for a falling object

9. Practice Problems— Show all your work! 1.Hallie chased the penguin for 5 meters. It took her 15 seconds to catch it. What was her speed? 2.Duncan slammed on brakes while he was driving 50 m/s. It took him 25 seconds to stop. What was his acceleration? 3.Daniela lifted her 10kg bookbag with a force of 20 N. With what acceleration did she move the bookbag? 4.Robert grinds the railing of the steps with his skateboard but missed it by a centimeter. The board goes flying across the pavement, but Robert magically lands on his feet. Which of Newton’s laws does this demonstrate?

10. The Relationship Between Mass and Weight PS-5.9 Explain the relationship between mass and weight by using the formula F w = ma g

11. The gravitational force keeps the planets in orbit around the Sun.

12. The Rules of Gravity on Earth Objects accelerate as they fall Objects accelerate as they fall The only way that an object can accelerate is for a net force to act on it. The only way that an object can accelerate is for a net force to act on it. What about objects in freefall? What about objects in freefall? –the net force acting on falling objects = gravitational force exerted by Earth. (neglecting air resistance) –amount of force by Earth depends on the object’s mass

13. Gravity on Earth: MASS The greater the mass, the greater the gravitational force. The greater the mass, the greater the gravitational force. The amount of gravitational force that the earth exerts on an object is called weight. The amount of gravitational force that the earth exerts on an object is called weight.

14. Newton’s 2 nd Law Rewritten F w = ma g F w = Weight of object F w = Weight of object m = mass of the object (….kg) m = mass of the object (….kg) a g = acceleration of gravity for all objects = 9.8m/s 2 a g = acceleration of gravity for all objects = 9.8m/s 2 This formula is sometimes written as This formula is sometimes written as w = mg

15. Examples Austin measures the mass of an apple to be 0.15 kg. What is it’s weight? Austin measures the mass of an apple to be 0.15 kg. What is it’s weight? What is the mass of Noell’s car if it weighs 9800 N? What is the mass of Noell’s car if it weighs 9800 N? A satellite with a mass of 230 kg experiences a gravitational force of 1380 N. What is the acceleration due to gravity at the altitude where the satellite is orbiting? A satellite with a mass of 230 kg experiences a gravitational force of 1380 N. What is the acceleration due to gravity at the altitude where the satellite is orbiting?

16. Examples A high school student has a mass of 60 kg. What will be the student’s weight on the moon, where the acceleration due to gravity is 1/6 that of the Earth’s gravity? A high school student has a mass of 60 kg. What will be the student’s weight on the moon, where the acceleration due to gravity is 1/6 that of the Earth’s gravity? How much gravitational force is exerted on Joey’s bookbag, which has a mass of 18 kg? How much gravitational force is exerted on Joey’s bookbag, which has a mass of 18 kg?

17. Calculating a g Calculate the acceleration due to gravity from your measurements of F w and mass, using the balance and the spring scale. Calculate the acceleration due to gravity from your measurements of F w and mass, using the balance and the spring scale. You must do this for 10 objects of your choosing that are less than 0.4 kg (400g). You must do this for 10 objects of your choosing that are less than 0.4 kg (400g). Find an average value for a g. Find an average value for a g.

18. Data Table Organize your work in a nice summary that includes: Question, Hypothesis, Data Table, Answers to follow up questions, Conclusion. Organize your work in a nice summary that includes: Question, Hypothesis, Data Table, Answers to follow up questions, Conclusion. You must attach a sheet which shows your calculations in the correct format! You must attach a sheet which shows your calculations in the correct format! Object Description FwFwFwFwm agagagag

19. Follow Up Questions Do objects accelerate as they fall? Do objects accelerate as they fall? What must act on an object for an object to accelerate? What must act on an object for an object to accelerate? What is the relationship between mass and weight? What is the relationship between mass and weight? What is the relationship between mass and gravitational force? What is the relationship between mass and gravitational force? If two objects have the same mass, will they have the same weight? Why? If two objects have the same mass, will they have the same weight? Why? Suppose two identical objects were subjected to different accelerations due to gravity, would they still have the same weight? Why? Suppose two identical objects were subjected to different accelerations due to gravity, would they still have the same weight? Why?

20. Calculating Heights From careful measurements of time and using a g = 9.8 m/s 2, you will calculate the height of the stadium bleachers. We will be going outside, so be on your best behavior, or else you will be written up and receive a ZERO for the lab exercise! You will calculate x - the height of the bleachers. Everyone must do their own work!

21. Instructions: Copy the data table on the next slide. Perform the procedure. Record the results. Knowing v i, calculate d - the height of the bleachers. Everyone must do their own work! Answer the follow up questions.

22. Data Table Organize your work in a nice summary that includes: Question, Hypothesis, Data Table, Answers to follow up questions, Conclusion. a g (m/s 2 ) t (s) v i (m/s) x (m)

23. Follow Up Questions Draw a motion diagram of the ball falling, include scaled arrows to indicate changes in velocity. How does the velocity and displacement of an object vary with time as the object falls? Be specific. Explain what it means when we say that the acceleration due to gravity is constant. Suppose the true height of the bleachers was 1 meter taller than what you calculated, what could account for this error? How could a skydiver calculate the height of the airplane he jumped from?