According to Newton’s 2 nd Law

1. According to Newton’s 2nd Law the relationship between mass and acceleration is direct/inverse. If the force is held constant the relationship between force and acceleration is direct/inverse. If the mass is held constant In this situation . . . the relationship between mass and force is direct/inverse. If the acceleration is held constant

3. Mass Weight Force which a given mass feels due to the gravity at its place Depends on gravity at the place Is measured in Newtons Is measured using a scale Depends on: Mass of the object Mass of the object that is attracting it • Amount of matter in an object • Is always constant at any place and time • Is measured in kilograms • Is measured using a balance • Is an intrinsic property of an object and is independent of any external factor

4. To calculate weight: • When you know the mass use ΣF = ma • If standing on the Earth (no friction force), acceleration due to gravity is 9.8 m/sec/sec Mass = 65.0 kg Weight on earth? Weight on the moon? Weight on Jupiter?

5. Free Fall • Falling without air resistance • Gravity is the only force acting upon the object causing the object to change it’s velocity • Acceleration (change in velocity) due to gravity on earth is 9.8 m/sec/sec for all objects • That means . . . When an object is in free fall it will be increasing its velocity 9.8 m/sec every second ∑F=ma

6. Free Fall on the Moon

7. In Free Fall

8. a = 9.8 m/sec/sec In Free Fall

9. Free Fall neglecting friction – which object – the elephant or the feather-will hit the ground first • The elephant and the feather each have the same force of gravity • The elephant has the greatest acceleration (change in velocity) • On earth, all objects (whether an elephant or a feather) have the same force of gravity • The elephant and the feather have the same acceleration (change in velocity) due to gravity True or false:

10. Free fall cont. • In the absence of air resistance, the elephant and the feather land at the same time. • The force of gravity experienced by an object is dependent upon the mass of that object. RULE: all objects (regardless of their mass) experience the same acceleration (change in velocity) when in a state of free fall

11. Free Fall Draw a velocity vs. time graph Draw an acceleration vs. time graph v a t t -9.8 m/s/s Slope = -9.8 m/s/s

12. Acceleration of fall is less when air resistance (drag) acts • Air resistance is the result of collisions of the object's leading surface with air molecules. • Fluid friction (air drag) depends on two things: surface area & speed • The greater the surface area, the greater the friction • As an object falls, the friction increases as the speed increases ∑F=ma

13. Falling with Air Resistance

14. Falling with air resistance Same size, different mass ΣF = ma ΣF & m are directly related Because a is not zero the balls are speeding up, friction increases bigger mass = bigger weight a(change in velocity) = 9.8 m/sec/sec ΣF on each ball decreases ΣF and a are directly related smaller ΣF = smaller a Because a is not zero the balls are still speeding up, friction gets bigger Balls are still speeding up but not as much as they were before ΣF = 0 ΣF is smaller than before so a is smaller a = 0 Because a = 0 ball no longer speeds up; ball will travel at that speed the rest of the way down (terminal velocity) Ball will continue to speed up but not as much as it was before

16. Terminal Velocity Draw a velocity vs. time graph Draw an acceleration vs. time graph v a t t

17. Lab 4 Air Resistance • Purpose: Does changing the mass of a falling object affect the velocities observed on the motion graphs? • Method: • Materials: motion detector on ceiling; laptop; coffee filters • Hypothesis: • Procedure: • Data: 5 different velocity vs. time graphs • Analysis: analyze motion on graphs and label with descriptions of motion (ie where is the terminal velocity) • Conclusion:

18. Which object - the elephant or the feather - will hit the ground first? True or false: • The elephant encounters a smaller force of air resistance than the feather and therefore falls faster. • The elephant has a greater acceleration (change in velocity) due to gravity than the feather and therefore falls faster. • Both elephant and feather have the same force of gravity, yet the feather experiences a greater air resistance. • The feather has a smaller force of gravity so friction equals the force of gravity sooner causing a net force of zero (no acceleration); whereas the elephant has a net force that is not zero and will continue to speed up.

20. What is the acceleration for A? • What is the acceleration for B? • What is the acceleration for C? • What is the acceleration for D?

23. Which encounters the greater force of air resistance—a falling elephant or a falling feather?

24. Two smooth balls exactly the same size, one made of wood and the other made of iron, are dropped from a high building to the ground below. The ball to encounter the greatest force of air resistance on the way down is the:a) wooden ballb) iron ballc) ... both the same

25. As she falls faster and faster through the air, her acceleration (change in velocity)a) increasesb) decreasesc) remains the same

26. What will be the acceleration (change in velocity) of a rock thrown straight upward at the moment it reaches the tippity-top of its trajectory (no air)?

27. Chapter 3 Review • On a long alley a bowling ball slows down as it rolls. Is any horizontal force acting on the ball? How do you know? • What is the net force on a 1-N apple when you hold it at rest above your head? What is the net force on it after you release it? • A bear that weighs 4000 N grasps a vertical tree and slides down at constant velocity. What is the friction force that acts on the bear? • Two basketballs are dropped from a high building through the air. One ball is hollow and the other filled with rocks. Explain in detail the fall of the two balls.

28. Review 6. Upon which will air resistance be greater; a sheet of falling paper or the same paper wadded into a ball if they have both reached terminal velocity? (Careful!) 7. Aristotle claimed the speed of a falling object depends on its weight. We now know that objects in free fall, whatever their weights, undergo the same gain in speed. Why does weight not affect acceleration? 8. Why is it that a cat that accidentally falls from the top of a 50-story building hits the ground no faster than if it falls from the 20th story?

29. End of Chapter Exercises • What is the net force on a bright red Mercedes convertible traveling along a straight road at a steady speed of 100 km/h? • Your empty hand is not hurt when it bangs lightly against a wall. Why is it hurt if it does so while carrying a heavy load? Which of Newton's laws is most applicable here? • When a junked car is crushed into a compact cube, does its mass change? Its weight? Its volume? Explain. • If it takes 1 N to push horizontally on your book to make it slide at constant velocity, how much force of friction acts on the book? • A parachutist, after opening the chute, finds herself gently floating downward, no longer gaining speed. She feels the upward pull of the harness, while gravity pulls her down. Which of these two forces is greater? Or are they equal in magnitude?

30. Why will a sheet of paper fall slower than one that is wadded into a ball? • How does the force of gravity on a raindrop compare with the air drag it encounters when it falls at constant velocity? • How does the gravitational force on a falling body compare with the air resistance it encounters before it reaches terminal velocity? After?