1. Unit 2 1D Vectors & Newton’s Laws of Motion

2. A. Vectors and Scalars

3. B. Addition of Vectors & RESULTANT In one dimension, simple addition and subtraction is all that is needed. RESULTANT VECTOR

4. Aristotle vs Galileo

5. FORCES NET FORCE

6. D. TYPES OF FORCES

7. 1) Force of Gravity (Weight) - Without gravity, how can we distinguish between a 1kg and a 2kg mass?

8. 2) Normal Force (Support Force) If the box weighed less, what would happen to the normal force acting on the box?

9. 3) Tension Force

10. 4) Friction Force

11. E. NEWTON’S LAWS

12. Newton’s 1st Law of Motion Also called the law of inertia.

13. Mass

14. Why do all objects fall at the same rate? (|a|=g=9.8m/s 2 )

15. Newton’s 3rd Law of Motion

16. Explain the movement of a rocket using the 3 rd Law.

17. Question: A loaded school bus hits a bug and kills it. Which body receives the greater force of impact, bug or bus?

18. Fan for boat with no wind?

19. Who pulls harder on the rope? Who wins the tug of war?

20. Force Body Diagrams (FBD) using vectors In order to solve problems involving forces, we need to draw an FBD. A box is dragged by a rope towards the right on a smooth floor. Draw the force vectors on the box.

21. Newton’s 2 nd Law of Motion Constant velocity equates to what in regards to F net ?

23. A crane lowers a 1306kg car by a cable with an acceleration of 0.73 m/s 2. The car starts 20.0m above the ground with an initial speed of zero. Example 1 a) What is the tension in the cable? Draw FBD b) How much time will it take the car to reach the ground?

24. Example 2 A person stands on a bathroom scale in an elevator at rest on the ground floor of a building. The scale reads 836N. As the elevator begins to move upward, the scale reading briefly increases to 935N but then returns to 836N after reaching a constant speed. b) If the elevator was moving at 3.0m/s upwards and then uniformly decelerated to rest in 4.7s, determine the scale reading. a) Determine the acceleration of the elevator.

25. Example 3: A force of 75N pushes on 2 boxes as shown. The mass of b 1 is 20kg and the mass of b 2 is 35kg. Surface is smooth. a) Determine the acceleration of the two boxes. b) Determine the net force on b 2. c) Determine the net force on b 1. Why is it different?

26. Example 4: A box (6.2kg) is pulled along a rough, horizontal surface by a rope that is parallel to the surface. The tension in the rope is 23N. The box accelerates from 2.4m/s to 3.6m/s over a distance of 7.5m. Determine the size of the friction force.

27. Force of Friction (F f ) On a microscopic scale, most surfaces are rough. Force of friction tends to oppose the motion of objects Two Types of Friction: 1) Static Friction (F fs ) 2) Kinetic Friction (F fk )

28. Friction depends on two things:

29. In the case of static friction, there is a maximum value at which the static friction force will resist motion between surfaces. This means that if you push a table with 50N of force where maximum static friction is 75N, the table won’t break free. You need to push with just a smidge over 75N where we say you just have to equal maximum static to break free.

30. The static frictional force increases as the applied force increases, until it reaches its maximum.

31. What minimum amount of force is needed to start to make a 250N crate move across a floor if the coefficient of static friction is 0.65? Example1

32. Example2 A physics book is sent sliding across a lab table with a speed of 4.3m/s. If it takes the book 1.6m to stop, determine the value of the coefficient of kinetic friction.

33. A 5.0kg block is pulled by a tension force of 50.0N along a rough horizontal surface at a constant acceleration. If the coefficient of kinetic friction is 0.40, determine the speed of the block after 3.0s if it starts from rest. Example3

34. Terminal Velocity Consider a skydiver who steps off a hovering helicopter at high altitude. NOW consider the effect of air resistance (friction) during the fall. d) As the skydiver continues to fall, describe what happens to their speed and acceleration? Why? b) Initially at t=0, what is the acceleration and velocity of the skydiver? a) Initially at t=0, what forces act on the skydiver? c) As the skydiver begins to fall, what happens to the force of air resistance on skydiver? e) Eventually what happens to the speed of the skydiver?

35. 2D Vectors/Forces

36. A 35.0 kg lawn mower is pushed across a level lawn in a direction of 0.0 . The force exerted on the handle is 100 N @ 310.0 . Assume friction is negligible. Example 4 (a)Determine the acceleration of the mower. (b)Determine the normal force acting on the lawn mower.

37. A 67.5-kg sprinter exerts a force of 775N on a starting block which makes a 20 o angle to the ground as shown (relative to west). Assume sprinter takes off perpendicular to block. Example 5 Determine the resultant acceleration of the sprinter. 20 o θ=?

38. Equilibrium Object is in equilibrium or is balanced when ΣF=0 in a particular direction. Determine the weight of the hanging picture.

39. A traveler pulls a suitcase of mass 8.00kg across a level surface by pulling on the handle with 20.0N at an angle of 50.0° relative to horizontal. Coefficient of kinetic friction against the suitcase is μ k = 0.100. Determine the acceleration of the suitcase. Example2

40. Inclines y x Consider a block that slides down a frictionless incline. θ Since the surface of the incline does not lie along x or y, we can rotate our x-y axis to meet our needs. Draw the force vector, F g, on the box

41. y x Resolve the force of gravity into components θ FgFg θ

42. θ FgFg What is the normal force on the block equal to?

43. A skier moves down a ski slope angled at 30 o. If the length of the slope is 50m, determine the time it takes to reach the bottom if the skier starts from rest. Ignore friction. Example

44. A block of mass 2kg is projected up a rough incline (u k = 0.40) at 6.2m/s where the angle of the incline is 25 o. Example 2 a) Determine the distance along the incline it slides before coming to rest. b) Determine the acceleration of the block on the way down the incline.

45. System of Bodies: Multiple bodies connected together is called a system where all bodies MUST accelerate at the same value.

46. Assume m A = 1kg, m B = 3kg, m C = 4kg and the surface on which they sit to be smooth. If block C is pulled with a force F equal to 15N, determine: a) The acceleration of the system. b) The tension in each string between A & B and between B & C.

47. Example2 Block m 2 (5.0kg) sits on rough surface where u s = 0.65. Determine the minimum value of m 1 to accelerate the system. Assume a frictionless & negligible mass pulley. If m 1 = 6.0kg, determine the tension in the string if u k = 0.30.

48. Example3 Assume a frictionless & negligible mass pulley. If the system is released from rest, determine the speed of the 5kg mass after it has fallen for 1.3s. b) Determine the tension in the string.

49. Example 3 If m 1 is 4kg and m 2 is 3kg, determine the tension in the string if u k = 0.35. Assume m 1 falls. Angle is 30 o