FORCES

1. FORCES

2. What is a force? Intuitively, a force is like apush or a pull which produces or tends to produce motion

3. Weight Normal reaction Friction Viscous force Tension Upthrust Lift Electrical force Magnetic force Forces experienced in Daily Life

4. Weight W • weight is not the same as mass; it is a force • it is the gravitational force exerted by the Earth • it passes through the centre of gravity of the body

5. Normal reaction N • two bodies in contact with each other • perpendicular to the surface of contact

6. Friction • friction is exerted two surfaces slide across one another • direction is along the surface of contact

7. Cause of friction movement F • hollows and humps all over the surface • actual contact area only a fraction 1/10000 of total area • extreme high pressure at contact points causes welding of surfaces • forces are needed to overcome these adhesive forces when trying to slide over the surface

8. Static and kinetic friction • It is harder to move a stationary object than to move the object while it is moving • Static friction is the friction exerted by the ground in order to prevent the object from moving • Kinetic friction is the friction exerted by the ground to oppose the motion of the object while it is moving

9. 2 N 2 N 1 N 1 N Limiting friction • Static friction is not constant; it varies in magnitude • Suppose a force P is applied trying to move the object P F • If P is 1 N, F will also be 1 N to prevent object moving • If P increased to 2 N, F also increased to 2 N • But there is limit to how much F can increase to • Maximum possible static friction is called limiting friction • P must exceed limiting friction in order to move object

10. Example 1 InFig 1.1, an object was moving to the right on a rough surface. InFig 1.2, an object rests in equilibrium on a rough slope. In both cases, draw the friction force acting on each object. Fig 1.2 Fig 1.1 friction friction

11. Viscous force • When body moves in fluid, it experiences resistance • such resistance is known as viscous force • examples: air resistance and water resistance • viscous force depends on the speed of the body • the greater the speed, the greater the viscous force

12. F W gathering speed v F W gathering more speed V F W finally reaches constant terminal velocity VT W Terminal velocity release

13. Tension • Tension is exerted by a stretched rope, string or spring. • When a body is attached to a string, the tension in the taut string would tend to pull the body.

14. Hooke’s Law F  (l - lo) => F  e => F = ke where k is force constant (elastic constant, spring constant or stiffness F constant) F

15. F x e Strain energy in a Deformed wire Assume that Hooke’s Law is obeyed. =>For a force-extension graph, it will be a straight line. In general, work done by a force F in extending a wire from x1 to x2is the area under the force-extension graph. =>Work done in extension or strain energy stored in wire, W = ½ Fe = ½ ke2

16. Example 2 A vertical wire suspended from one end is stretched by attaching weight of 20 N to the lower end. If the extension is 1 x 10-3 m, what is (a) the force constant; (b) the energy stored in the wire; (c) the gravitational potential energy loss by the weight in dropping a distance of 1 x 10-3 m?

17. Assuming Hooke’s law is obeyed, (a) F = ke k = F/e = 20/(1x10-3)Nm-1 = 2 x 104 Nm-1 (b) energy stored in wire, W = ½ Fe = ½ (20)(1x10 -3) = 1 x10-2 J

18. Gravitational potential energy lost by weight • = mgh = 2 x 10-2 J • By conservation of energy, • P.E. lost = Energy stored in wire • + • heat dissipated when weight at end of wire comes to rest after • vibrating.

19. Upthrust upthrust • Upthrust is an upward push on a body when it is immersed in a fluid (gas or liquid) • Upthrust is exerted by the fluid • Upthrust is due to pressure difference of fluid at the top and bottom of immersed portion of the body

20. Example 3 Consider an object partially immersed in a fluid of density . The area of the top surface of the object is A and the immersed depth is h. h

21. h (a)What is the pressure difference across the immersed portion of the object? h  g (b)Hence write down the expression for the upthrust acting on the object. h  g A (c)What is the volume of fluid displaced by the object? h A (d)Hence write down the expression for the weight of fluid displaced. h A  g (e)Comment on your answers to (b) and (d). They are the same.

22. Example 3shows that Upthrust = weight of fluid displaced This is actually the Achimedes’ Principle Archimedes’ Principle states that the upthrust on a body in a fluid is equal and opposite to the weight of the fluid displacedby the body.

23. Lift What helps birds and aeroplanes maintain its flight? The answer is the upwardliftforce exerted on their wings when in motion

24. - + + + Electric force Electric force is exerted between two electric charges like charges repel unlike charges attract

25. N N N S Magnetic force Magnetic force is exerted between two magnetic materials or between electric currents like poles repel unlike poles attract

26. Weight Normal reaction Friction Viscous force Tension Upthrust Lift Electrical force Magnetic force Forces experienced in Daily Life

27. normal reaction normal reaction upthrust weight weight weight Different forces

28. lift tension weight weight Different forces

29. How did this ‘forward force’ come about? normal reaction normal reaction air resistance forwardforce friction weight Different forces speed

30. How did this ‘thrust’ come about? Different forces lift air resistance thrust weight

31. What makes a car move? What makes a rocket fly? Who exerts on who A force is always exerted by some body on some other body. Friction exerted by ground on tires Gases expelled by rocket

32. normal reaction weight weight weight FGM Test Yourself. Identify the forces

33. Fundamental types of force When scientists examined all the forces, they found that many of them are similar in nature. Scientists have identified 4 fundamental types of force: • gravitational force • electromagnetic force • nuclear force • weak force

34. All forces in our daily life can be classified into one of the fundamental types. In the following table, identify the nature of each force: gravitational electromagnetic electromagnetic electromagnetic electromagnetic electromagnetic electromagnetic

35. A R B 2 Addition of VectorsParallelogram Rule A B

36. A B B A R Triangle Rule

37. Finding resultant force The magnitude of resultant force can be found by • drawing vector diagram to scale • calculation (pythagoras theorem, cosine rule, etc) • resolution

38. Example 4 Two forces are given below: 70º 5 N 4 N 30º Find the magnitude of the resultant force.

39. Method 1 Drawing vector diagram to scale Scale used is 1 cm : 1 N 5 N (5 cm) 4 N (4 cm) R (5.8 cm) From the vector diagram, magnitude of resultant R is 5.8 N What is missing in the answer?

40. 70 5 N 80 4 N 30 x Method 2: By calculation • Using Cosine rule: x2 = 52 + 42-2 (4) (5) cos800 =>x =5.84 N • Using Sine rule:

41. Method 3 By resolving vectors 4 cos 70° 70º 5 N 5 sin 30° 4 sin 70° 30º 5 cos 30° 4 N Rx = 5 cos 30° + 4 cos 70° = 5.70 N Ry = 5 sin 30° - 4 sin 70° = -1.26 N Rx 5.70 N Ry 1.26 N R Magnitude of resultant R is given by R2 = (5.70)2 + (1.26)2 R = 5.8 N

42. N E Magnitude of second force F =  302 + 402 = 50 N Example 5 Two horizontal forces act at a point to produce a resultant force of magnitude 40 N in the eastward direction. Given that one of the forces is in the northward direction and has a magnitude of 30 N, find the magnitude and direction of the second force. F  30 N 40 N Angle  = tan-1 (40/30) = 53°, direction of F is 53° east of south (or bearing 127°)

43. Centre of gravity and Free body diagram Centre of Gravity • The centre of gravity of a body is the single point at which the entire weight of the body can be considered to act.

44. Free body diagram (Important) • is a diagram showing all the forces acting on a particular object • is an important tool for solving problems

45. Example 6 An object A of weight w rests on top of another object B of weight W placed on the ground, as shown. Draw separate free body diagrams showing forces acting on (a)A only (b)B only, and (c)A and B together.

46. Answer N1 N2 w N3 N3 W W+w N1 = normal reaction exerted by B on A N2 = normal reaction exerted by A on B N3 = normal reaction exerted by ground on B N1 is numerically equal to N2 (action / reaction pair)

47. Common forces in free body diagrams

48. N R F Force exerted by surface (only) Total force R exerted by surface on moving object consists of two components - normal reaction N - frictional force F R is also known as the contact force Motion

49. A Non lecture Note Example An object of weight W, resting on a rough surface, is connected to a suspended object of weight w by a string over a smooth pulley. Draw and label the forces acting on each object. Normalreaction tension tension friction w W

50. Turning effect of a force Consider a water wheel which is free to rotate about its centre. Water flowing to the right exerts force on lower blades. This force causes the wheel to rotate about its centre. We say that the force has a turning effect. Turning effect of a force is also known as its moment. Amount of moment depends on force and distance away.