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Chapter 4

Chapter 4. Force and Motion. Section 4.1: Force and Net Force. Section 4.2: Inertia and Newton’s First Law of Motion.

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Chapter 4

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  1. Chapter 4 Force and Motion

  2. Section 4.1: Force and Net Force

  3. Section 4.2: Inertia and Newton’s First Law of Motion • In the absence of an unbalanced force (Fnet=0), a body at rest remains at rest, and a body in motion remains in motion with constant velocity (constant speed and direction) • This law is sometimes called the Law of Inertia.

  4. Section 4.3: Newton’s Second Law of Motion • The acceleration of an object is proportional to the force acting on it and inversely proportional to its mass.

  5. Section 4.4: Newton’s Third Law of Motion • For every force there is an opposite and equal reaction.

  6. Free Body Diagrams • Blocks Examples

  7. Sledding down a hill (skip for Phys 100) • A child and sled with a combined mass of 56.0 kg slide down a frictionless hill that is 8.52 m high at an angle of 37 degrees from horizontal. If the sled starts from rest, what is its speed at the bottom of the hill?

  8. Elevator Physics 1 "You are standing on a bathroom scale in an elevator. You are holding an apple. (Yes, people are staring at you...) You weigh 500 Newtons, so your mass is about 50 kg."

  9. Elevator Physics 2 • Part A: Elevator Is At Rest. You have just boarded the elevator, so it (with you inside) is at rest... • Question #1: What does the scale read? • Answer: There are 2 forces acting on you. (See the diagram at right.) The Earth pulls down on you with the force we call your weight (= mg) of 500 Newtons. The other force is the normal force from the scale. Since the elevator is at rest, your acceleration is 0 m/s2. Since your acceleration is 0 m/s2, Newton's First Law says the net force on you must be 0 Newtons. Since the net force on you is 0 Newtons, the upward forces and downward forces on you must balance exactly. Therefore the scale must push on you with a force of 500 Newtons, and the scale must read 500 Newtons. • Question #2: If you let go of the apple, what does it do? • Answer: The apple would be in free fall, so its acceleration relative to the earth is 10 m/s2 downward. Since you are at rest relative to the earth, the apple's acceleration relative to you would be 10 m/s2 also, so the apple would appear to fall just as it does anywhere else on the earth.

  10. Elevator Physics 3 • Part B: The Elevator Accelerates Upward. The elevator, (with you inside) begins to accelerate upward from rest at 2 m/s2. • Question #3: What will the scale read now? • Answer: There are 2 forces acting on you. Your weight pulls down with a force of 500 Newtons. The other force is the normal force from the scale. Your acceleration is 2 m/s2 upward, Newton's Second Law says that there must be a net force pushing you upward, and the net force has a magnitude Fnet = ma. So the net force on you,Fnet = (50 kg)(2 m/s2) = 100 Newtons (upward). Since the net force on you is 100 Newtons, the upward forces and downward forces on you must cancel to leave a 100 Newton upward force. Therefore the scale must push on you with a force of 600 Newtons, and the scale must read 600 Newtons as the elevator accelerates upward. • Question #4: If you let go of the apple now, what does it do? • Answer: The apple would be in free fall, so its acceleration relative to the earth is 10 m/s2 downward. Since you are accelerating at 2 m/s2 upward relative to the earth, the apple's acceleration relative to you would be 10 m/s2 + 2 m/s2 = 12 m/s2, so the apple would appear to fall faster inside the elevator than it does in "normal" free fall on the earth. To the occupants of the upwardly accelerating elevator, it appears that gravity is stronger, since they seem to weigh more and objects fall faster than "normal."

  11. Elevator Physics 4 • Part C: The Elevator Moves Up With Constant Velocity. The elevator (and you) accelerated for 5 seconds, so it is moving upward with a velocity of 10 m/s. It now moves with this constant upward velocity of 10 m/s. • Question #5: What does the scale read now? • Answer: There are 2 forces acting on you. Your weight pulls down with a force of 500 Newtons. The other force is the normal force from the scale. Since the elevator is moving with constant velocity, your acceleration is 0 m/s2. Since your acceleration is 0 m/s2, Newton's First Law says the net force on you is 0 Newtons. Since the net force on you is 0 Newtons, the scale must push on you with a force of 500 Newtons, and the scale must read 500 Newtons. • Question #6: If you let go of the apple, what does it do? • Answer: The apple has no acceleration relative to you. So its acceleration relative to the earth is 10 m/s2 downward. Since you are moving at a constant velocity relative to the earth, the apple's acceleration relative to you would be10 m/s2 also, so the apple would appear to fall just as if you were at rest.

  12. Elevator Physics 5 • Part D: The Elevator Slows Down (While Going Up) The elevator, (with you inside) begins to slow down as it approaches its destination. Its acceleration (or deceleration) is 2 m/s2 downward. • Question #7: What does the scale read now? • Answer: There are 2 forces acting on you. The Earth (your weight) pulls down with a force of 500 Newtons. The other force is the normal force from the scale. Since your acceleration is 2 m/s2 downward, Newton's Second Law says that there must be a net force pulling you downward, and the net force has a magnitude Fnet = ma. So the net force on you,Fnet = (50 kg)(2 m/s2) = 100 Newtons (downward). Since the net force on you is 100 Newtons downward, the upward forces and downward forces on you must cancel out to leave a 100 Newton downward force. Therefore the scale must push on you with a force of 400 Newtons, and the scale must read 400 Newtons as the elevator accelerates downward. • Question #8: If you let go of the apple now, what does it do? • Answer: The apple would be in free fall, so its acceleration relative to the earth is 10 m/s2 downward. Since you are accelerating at 2 m/s2 downward relative to the earth, the apple's acceleration relative to you would be 10 m/s2- -2 m/s2 = 8 m/s2, so the apple would appear to fall slower inside the elevator than it does in "normal" free fall on the earth. To the occupants of the downwardly accelerating elevator, it appears that gravity is weaker, since they seem to weigh less and objects fall more slowly than "normal."

  13. Elevator Physics 6 • Part E: The Elevator Speeds Up (While Going Down) The elevator, (with you inside) reaches its floor, stops for a while, and then begins to accelerate downward. Its acceleration is 2 m/s2 downward. • Question #9: What does the scale read now? • Answer: There are 2 forces acting on you. The Earth (your weight) pulls down with a force of 500 Newtons. The other force is the normal force from the scale. Since your acceleration is 2 m/s2 downward, Newton's Second Law says that there must be a net force pulling you downward, and the net force has a magnitude Fnet = ma. So the net force on you,Fnet = (50 kg)(2 m/s2) = 100 Newtons .(downward) Since the net force on you is 100 Newtons downward, the upward forces and downward forces on you must cancel out to leave a 100 Newton downward force. Therefore the scale must push on you with a force of 400 Newtons, and the scale must read 400 Newtons as the elevator accelerates downward. • Question #10: If you let go of the apple now, what does it do? • Answer: The apple would be in free fall, so its acceleration relative to the earth is 10 m/s2 downward. Since you are accelerating at 2 m/s2 downward relative to the earth, the apple's acceleration relative to you would be 10 m/s2- -2 m/s2 = 8 m/s2, so the apple would appear to fall slower inside the elevator than it does in "normal" free fall on the earth. To the occupants of the downwardly accelerating elevator, it appears that gravity is weaker, since they seem to weigh less and objects fall more slowly than "normal."

  14. Elevator Physics 7 • Part F: The Elevator Moves Down With Constant Velocity. The elevator (and you) accelerated for 5 seconds, so it is moving downward with a velocity of 10 m/s. It now moves with this constant downward velocity of 10 m/s. • Question #11: What does the scale read now? • Answer: There are 2 forces acting on you. (Complete the diagram.) Your weight pulls down with a force of 500 Newtons. The other force is the normal force from the scale. Since the elevator is moving with constant velocity, your acceleration is 0 m/s2. Since your acceleration is 0 m/s2, Newton's First Law says the net force on you is 0 Newtons. Since the net force on you is 0 Newtons, the scale must push on you with a force of 500 Newtons, and the scale must read 500 Newtons. • Question #12: If you let go of the apple, what does it do? • Answer: The apple has no acceleration relative to you. So its acceleration relative to the earth is 10 m/s2 downward. Since you are moving at a constant velocity relative to the earth, the apple's acceleration relative to you would be10 m/s2 also, so the apple would appear to fall just as if you were at rest.

  15. Elevator Physics 8 • Part G: Oh, No! The elevator cable snaps, and the elevator (with you inside!) begins to fall! Perhaps you have time for one last Physics observation! • Question #13:What does the scale read as the elevator falls? • Answer: There are 2 forces acting on you. The Earth (your weight) pulls down with a force of 500 Newtons. The other force is the normal force from the scale. Since the elevator and you are in free fall, your acceleration is 10 m/s2 downward. Newton's Second Law says that there must be a net force pulling you downward, and the net force has a magnitude Fnet = ma. So the net force on you,Fnet = ma = (50 kg)(10 m/s2) = 500 Newtons. Since the net force on you = 500 Newtons downward, the upward forces and downward forces on you must cancel out to leave a 0 Newton downward force . Therefore the scale must push on you with a force of 0Newtons, and the scale must read 0 Newtons as the elevator accelerates downward. • Question #14: If you let go of the apple now, what does it do? • Answer: The apple would be in free fall, so its acceleration relative to the earth is 10 m/s2 downward. Since you are accelerating at 10 m/s2 downward relative to the earth, the apple's acceleration relative to you would be 10 m/s2- -10 m/s2 = 0 m/s2, so the apple would appear to float inside the elevator!!

  16. Elevator Problem Imagine a boy with a mass of 25 kg is in an elevator. Sketch a free-body diagrams for the boy and calculate the normal force for these situations: • The elevator has no acceleration (standing still or moving with constant velocity) • The elevator has an upward acceleration (accelerating upward, or decelerating while on the way down) of 3 m/sec2 • While the elevator is accelerating upwards, the boy jumps up with an acceleration of 2 m/sec2. What is his normal force as he jumps? • The elevator has a downward acceleration (accelerating down, or decelerating while on the way up) of 3 m/sec2. • While the elevator is accelerating downwards, the boy jumps up with an acceleration of 2 m/sec2. What is his normal force as he jumps?

  17. Static and Kinetic Friction • Understand the Difference Between Static & Kinetic Friction • Solve Problems Involving Friction Effects

  18. What is Friction? • Force that acts oppose the relative motion of two surfaces • High for dry and rough surfaces • Low for smooth and wet surfaces

  19. Free Body Diagram Normal Force FN Applied Force F Friction Force ff Gravity Force Fg Fg = mg FN = Fg ff = F

  20. Static Friction The Force of Static Friction keeps a stationary object at rest! FN F fs Fg

  21. Kinetic Friction Once the Force of Static Friction is overcome, the Force of Kinetic Friction is what slows down a moving object! Motion FN F fk Fg

  22. Types of Friction To initiate motion of the box the man must overcome the Force of Static Friction Upon sliding, the baseball player will come to a complete stop due to the Force of Kinetic Friction I better be safe Ump!!

  23. Static & Kinetic Friction Coefficients

  24. Static VS. Kinetic Friction

  25. Application Analysis An empty cart is being rolled across a warehouse floor. If the cart was filled, the coefficient of kinetic friction between the cart and the floor would • Decrease • Increase • Remain the same

  26. Application Analysis An empty cart is being rolled across a warehouse floor. If the cart was filled, the force of kinetic friction between the cart and the floor would • Decrease • Increase • Remain the same

  27. Application Analysis • Sand is often placed on an icy road because the sand: • Decreases the coefficient of friction between the tires of a car and the road • Increases the coefficient of friction between the tires of a car and the road • Decrease the gravitational force on a car • Increases the normal force of a car on the road

  28. Example #1 1) A desk has a mass of 27.5 kilograms. If the coefficient of static friction between the desk and the floor is 0.44, what force must be used to move the desk from rest? b) Once the desk above is in motion, what force must be used to keep it moving at a constant velocity if the coefficient of kinetic friction is 0.29?

  29. Example #2 A 3.2 x 103 kg sailboat is sailing at 6.2 knots (1 kt = 1.852 km/h) when the wind dies. The boat drifts for 65 m before coming to a stop. a) What is the coefficient of friction between the hull and the water? b) How long does it take to stop?

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