3. Forces There are essentially only three types of forces in the universe: gravitational gravitational electric electric nuclear nuclear vectors. All forces are vectors. directionmagnitude They have an associated direction attributable to them as well as magnitude (size) e.g. weight is a force which acts towards the centre of the Earth scalarsmagnitude (scalars only have magnitude e.g. mass).

4. Adding and subtracting vectors is easy! consider the following forces: 10 N7 N = 17 N OR 10 N-7 N = 3 N Note that these forces act through one point. centre of gravity (mass) That is convenient for the moment and practical as it is often true - the point is often the centre of gravity (mass), as described earlier.

5.  The resultant force calculated acting on a given mass will cause it to accelerate.  When mass is in kilograms and acceleration is in m/s/s, the unit of force is in Newtons (N). Definition - One Newton is equal to the force required to accelerate one kilogram of mass at one meter/second/second.

6.  How much force is needed to accelerate a 1400 kilogram car 2 ms -2  Write the formula  F = m x a  Fill in given numbers and units  F = 1400 kg x 2 ms -2  Solve for the unknown  2800 kgms -2 or 2800 N F = ma

7.  1. What acceleration will result when a 12 N net force applied to a 3 kg object? A 6 kg object?  2. A net force of 16 N causes a mass to accelerate at a rate of 5 ms -2. Determine the mass.  3. How much force is needed to accelerate a 66 kg skier 1 m -2 ?  4. What is the force on a 1000 kg elevator that is falling freely at 9.8 m -2 ?

9. So what is gravity and what does it cause?? These are two questions, the answers to which we normally take for granted! Gravitycentre of the Earth Gravity is the force that pulls us towards the centre of the Earth Weight It causes our Weight So why is it different on different planets? masses They have different masses gravitational pull So do all objects have a gravitational pull? massive Yep! The difference is that the more “massive” an object is the greater the pull of gravity. Therefore terrestrial objects do not exert a big enough force to notice compared to that of the Earth!

10. Might help explain why you are not attractive!! Might help explain why you are not attractive!! So what is the link between the mass of an object and its weight? First the definitions. The mass of an object is a measure of the amount of matter contained in it. Measured in Kg. The weight is the force of gravity pulling a mass towards the centre of the object causing the gravitational field. Measured in N

11. So what is the link between Weight and Mass? accurately as possible Try to measure the masses and weights as accurately as possible and plot a graph of them. straight linegradient If it is a straight line what is the gradient? gravitational field strength of 9.81 NKg -1 It should be the value for the gravitational field strength of 9.81 NKg -1 or acceleration due to gravity  g = 9.81 ms -2 or acceleration due to gravity  g = 9.81 ms -2

12. We therefore get the relationship Weight = mass * gravitational field strength W = mg WeightforceNewtons Weight is a force measured in Newtons MassKilograms Mass is measured in Kilograms gms -2 Nkg -1 “g” is either in ms -2 OR Nkg -1

13.  Tension - the force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends. The tension force is directed along the length of the wire and pulls equally on the objects on the opposite ends of the wire  Normal contact force – is the component, perpendicular to the surface of contact, by an object. for example, the surface of a floor or wall, preventing the object to fall.

14.  Upthrust – the force that a fluid will exert upward on a body if it is partly or wholly submerged within it.  Friction - refers to any force that resists relative tangential motion (or intended motion). Its direction is opposite the relative velocity (or intended velocity).

15.  Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. A free-body diagram is a special example of a vector diagrams.

16.  The size of the arrow in a free-body diagram reflects the magnitude of the force.  The direction of the arrow shows the direction that the force is acting.  Each force arrow in the diagram is labelled to indicate the exact type of force.  http://www.physicsclassroom.com/Physics-Interactives/Newtons-Laws/Free-Body- Diagrams/Free-Body-Diagram-Interactive

17. Newton’s First Law of Motion  Any body will remain in it’s state of rest or uniform motion in a straight line unless caused by some external NET FORCE to act otherwise. It essentially means that a body will do one of two things: · accelerate if you apply a force to it · not accelerate if you don’t

18. Explain the motion of the following, refer to all the forces acting on the object: a car going “flat out” at 120 kmh -1 a parachutist hitting the ground at 200 kmh -1 without a parachute if he jumps from 2000m or 5000m the rate of acceleration of car decreasing as it gets faster. No acceleration as balanced forces of drag and weight reach equilibrium Has reached this equilibrium point - terminal velocity - before he has fallen 2000m Engine produces a constant force - accelerates and so drag increases. This decreases the net accelerating force

19. “add” them, taking into account their direction In order to decide whether forces or velocity vectors do cause a resultant in any given direction we need to “add” them, taking into account their direction. How can we calculate the resultant? Resultant“vector sum” In all cases the Resultant is the “vector sum” of the components…………WHAT!!!!!

20. For example, if you were swimming in a moving river, what direction would you end up moving in and how fast? Again you can get a feel for this from your everyday experience – USE THIS “FEEL” IN THE EXAM TO GAUGE IF YOU ARE RIGHT! There are two methods to solve this Trigonometry and Pythagoras 1) Using Trigonometry and Pythagoras Drawing a scale diagram and measuring the size and direction of the resultant 2) Drawing a scale diagram and measuring the size and direction of the resultant (but we don’t really want to do this!)

21. 1)Trigonometry and Pythagoras If a person can swim at 1.5 ms -1 in still water but the current of the stream flows at 2 ms -1 at 90 o to the swimmer. What is their speed and direction? The current flows at 2 ms -1 A person swims at 1.5 ms -1 in still water The RESULTANT is the vector that joins the start of one vector with the end of the last one after joining them as described! “nose to tail” The vectors should always be drawn “nose to tail” as shown on the left.

22. 1.5ms -1 2 ms -1 Using Pythagoras’ theorem 1.5 2 + 2 2 = 6.25 so R =  6.25 = 2.5ms -1  Tan  = 2 / 1.5  = 53.1 0 RESULTANT So the RESULTANT is the person travelling at 2.5ms -1 in a direction 53 o from the direction that the person was swimming in.

23. Example A body of mass 0.6kg falls vertically. A wind blows horizontally with a force of 8N. What is the magnitude and direction of the resultant force on the mass? (g=10 Nkg -1 ) Which angle on the diagram is measured though?! Tan(  ) = 6/8   = 37 o R 2 = 6 2 + 8 2 R 2 = 36 + 64 R 2 = 100 R = 10N 8N 6N

24. These forces can be investigated using a force board where the forces are in equilibrium and the angles indicated by the string and magnitude by the weights suspended at the 3 points.

25. Resolving Vectors If we want to know what the effect of a force is in a certain direction or if we are to add vectors, we need to know what they are doing in specific directions. The easiest to use are vertical and horizontal directions ie. Resolve them vertically and horizontally Tension in the rope Vertical component Horizontal component

26. Direction of boat Wind direction Force produced by keel As you can see from the example above we can make a triangle of forces from just about any situation. If a force is not acting vertically or horizontally we can consider it being made up of a vertical and horizontal force, just as you can walk somewhere by going forwards, backwards, left and right without moving diagonally!

27. Sideways pull of rope on barge Forward pull of horse Actual Pull of horse So how can we calculate the components of a force at 90 o to each other? If the Horse pulls with a force of 750 N at an angle of 45 o What would be the forwards force? Show your working and annotate the actions you are taking in these questions!!

28. Diagonal force upwards eg dragging a sledge  If the force needed to pull this sled is 100 N and you pull at an angle of 25 o what are the vertical and horizontal components of this force? If a husky pulls a sled at an angle of 10 o to it’s line of travel, what is the vertical component of the force and the horizontal component if the dog pulls with a force of 700N. If the sled and load weighs 100Kg what acceleration will the dog cause the sled to have?

29. Discuss the following situations with the other members of your group. Try to come up with specific and complete answers. ("Gravity", for instance, is not a complete answer.) Each individual in the group should record their own answer. Situation: A book is lying at rest on a table. Why? In other words, what causes the book (or any object) to remain at rest? Situation: The Voyager spacecraft is moving out of the Solar System in a straight line with constant speed. Why is it doing that? What causes an object to move with constant velocity? Situation: A pencil rolls off the desk and falls to the floor. Why does it move the way it does? We know a lot about this motion (free fall) - but what causes it to happen? Why do objects accelerate? Situation: A book sliding across a table gradually comes to a stop. Why? What causes a moving object to gradually come to a stop?

30.  Practical 4.4 – Drag and TV