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# Forces

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1. Forces

2. What is a force? • Forces are a vector quantity, meaning they need both magnitude and direction • It is defined as either a push or pull on object • The symbol for force is F

3. Measuring force • Force is measured in Newtons. (The unit is called a Newton and represented with an N) • 1 N is roughly equal to the pull the earth exerts on a medium sized apple (think of Sir Isaac Newton's famous discovery)

4. The units • 1 N = 1 (kg)(m)/(s2) • One Newton is equal toone kilogram meter per second squared

5. Types of Forces • Some of the commonly occurring forces are • Force of gravity (weight) • Force of friction • Normal force • Force of tension • Elastic or spring forces • The Force

6. Defining forces • Normal force • Always acts perpendicular to the surface on which a given object is sitting (has to do with Newton's Laws, we'll get to those) • Force of gravity • Always acts directly towards the centre of the earth • Force of friction • Always acts to resist motion. (This force is always opposite in direction to motion or tendency toward motion)

7. Drawing forces • Forces are most commonly drawn using a "free-body diagram" • Free-body diagrams are used to isolate the object from its surroundings to help examine it

8. Drawing a free-body diagram • Draw the object by itself • Locate, with a single point, the approximate centre of mass of the object • From the point, draw a force vector to represent EVERY force that is acting ON the object • **Do NOT include forces that the object is exerting on its surroundings**

9. Free-body diagram for a mass on a string

10. Draw object without surroundings

11. Identify approximate centre of mass

12. Draw forces acting ON the object Be sure to indicate the direction that force is acting on the object. (Which direction it wants to move the object) Be sure to indicate the approximate magnitude of the forces if possible Draw forces in the location that they are acting on the object as well

13. Label all forces string gravity

14. Include any numbers that are known or given string gravity

15. Finding the sum of forces • You will often need to find the sum of many forces acting on a single object • The sum of all forces acting on an object is known as the net force and is indicated asFnet • We can determine net force by finding the vector sum of the forces acting on the object. (Welcome back to vector addition)

16. Net Force • Objects which do not move always have a net force of zero • If net force is zero, then the sum of all the forces acting on the object must also be zero. • A net force indicates that motion is occurring in the same direction as the net force

17. Collinear (1 dimensional) forces • Collinear forces are solved the same way as collinear vectors (we already did that) • Simply find their sum in a direction chosen as positive. • Multiple vectors can be added in this way as long as the vectors added are collinear with each other • (If you get lost, just use the "tail to tip" method)

18. Try it • You are pushing a large box across a level floor. You push with a force of 700N, the force of friction is 300N and gravity acts on the box with a 1200N force. • Draw a free-body diagram for this situation • Calculate the net force on the box

19. FBD

20. FBD Fn = 1200 N [up] Fp = 700 N [forward] Ff = 300 N [back] Fg = 1200 N [down]

21. FBD Up (+) Left (-) Right (+) Fn = 1200 N [up] Down (-) Fp = 700 N [forward] Ff = 300 N [back] Fg = 1200 N [down]

22. Net Force • Since I have indicated positive directions I can add my forces • Vertical Fnet = Fn + Fg • Vertical Fnet = 1200N [up] + (-1200N [up]) • Vertical Fnet = 0N • Horizontal Fnet = Fp + Ff • Horizontal Fnet = 700N [forward] + (-300N [forward]) • Horizontal Fnet = 400N [forward]

23. 2-D Forces (non-collinear) • This is the same as when we added 2-dimensional vectors earlier • Use the tail to tip method • You can draw a scale diagram and actual measurements OR • You can use trigonometry to calculate the values

24. Try it • You are still pushing your large box across a level floor. You push with a net force of 400N [E]. Your friend decides to push the box north with a net force of 300 N. • Draw a free-body diagram for this situation • Calculate the net force on the box

25. FBD

26. FBD Ffr = 300 N [N] Fy = 400 N [E]

27. T2T Ffr = 300 N [N] Fy = 400 N [E] Ffr = 300 N [N] Fy = 400 N [E]

28. T2T Fnet = 500 N [N 53° E] Ffr = 300 N [N] Fy = 400 N [E] (Fnet)2 = (Fy)2 + (Ffr)2 tanθ = 400N [N] / 300N [E] (Fnet)2 = (400N)2 + (300N)2θ = tan-1 (400N [N] / 300N [E]) Fnet = 500N θ = 53° east of north

29. Mass • Mass is defined as the amount of material in an object • The mass of an object NEVER changes unless matter is added or removed from the object. • Mass is measured using grams, although the kilogram is a more practical unit for most things.

30. Weight • Force of gravity is defined as the force of attraction between any two masses in the universe. • Weight is the term used to describe the force of gravity that a celestial body (usually planets) exert on a mass

31. Example • When we say a person weighs 800N on the earth, we mean that the force of gravity of the earth ON the person is 800N. • On the surface of a planet the terms "force of gravity" and "weight" are often used interchangeably

32. Mass vs. Weight • Although the mass of an object is never variable at an instant in time, the weight of an object will be affected by both its mass and its distance from the centre of the planet. • The force of gravity on a 2 kg mass is twice as great as the force of gravity on a 1kg mass. • The force of gravity is greater at sea level then at the top of Mt. Everest • The force of gravity is also greater at the poles compared to the equator.

33. Law of Universal Gravitation • The force of gravity between two masses in the universe is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centres.

34. Law of Universal Gravitation • Fg = Gm1m2 / (Δd)2 • Where • Fg is the force of gravitational attraction between the two masses in Newtons • m1 is the mass of the first object in kg • m2 is the mass of the second object in kg • Δd is the distance between the centres of the objects in metres • G is the universal gravitational constantG = 6.67 x 10-11 (N)(m)2 / (kg)2

35. Universal gravitation Magnitude of force First mass Second mass Distance F m Δd m 2F 2m Δd m 6F 2m Δd 3m ½ Δd 4F m m m 2Δd m ¼ F 6/4 F 2m 2Δd 3m

36. Is it significant? • It takes the force of gravity of the entire planet to attract a 1kg mass with a force of 9.8N Try this • Terry, a fullback on the football team is sitting 0.60m from Jamie, a forward on the basketball team. If Terry has a mass of 80kg and Jamie has a mass of 55kg, what is the force of gravitational attraction between them?

37. Gravitational Field Intensity • The earth exerts a force of gravity on every mass • The result is that everything on or near the earth is pulled towards its centre • The greater the mass, the stronger the pull • If you create a force vs. mass graph, the slope of the line will be gravitational filed intensity

38. Gravitational Field Intensity • g = Fg / m • Where g = the gravitational filed intensity in N/kg Fg = the force of gravity on an object in N m = the mass of the object in kg

39. Gravitational Field Intensity • Although g varies slightly from place to place on the earth you should always use g = 9.8 N/kg [Down](Hmm…what do the units indicate?) unless otherwise stated. • Note: "down" in the case of gravity, always means "towards the centre of the earth"

40. Try it • What is the force of gravity on an elephant with a mass of 1365kg?

41. Changes in field intensity • Over time it has been found that g varies slightly. We still have no explanation for this • By location, if you think back to our equation for gravitational field intensity you should be able to come up with the two locational changes that can effect gravitation

42. Field intensity above the earth's surface • Think back to the field intensity equation and answer the following questions • If an object at some distance d is attracted with a force of 1N, how much force will an object at 2d experience? • What about an object at 5d?

43. The trick • Combine equations • g = Fg / m • Fg = Gm1m2 / (Δd)2 • g = (Gm1m2 / (Δd)2) / m • g is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them.

44. What does it mean? • g = 1; m1 = 1; m2 = 1; Δd = 1 • g = 2; m1 = 2; m2 = 1; Δd = 1 • g = 6; m1 = 2; m2 = 3; Δd = 1 • g = 3; m1 = 2; m2 = 3; Δd = 4

45. Try it • The average radius of the earth is about 6.4 x 103 km. An astronaut has a mass of 80 kg. What is the force of gravity acting on the astronaut directly above Calgary at a distance of 3.2 x 104 km from the centre of the earth?

46. Gravitational Field Intensity in the Universe • The gravitational field intensity varies directly with mass and distance from the centre of any planet. • However, since these two factors do not affect field intensity equally • Remember distance from centre is squared while mass is taken at value

47. A Review • Equations for solving any motion problems aav = Δv / Δt vav = Δd / Δt vr = vobject1 – vobject2 (gives vr of 1 relative to 2) Δv = vf – vi Δd = df – di Δt = tf – ti ***THESE EQUATIONS CAN BE CAREFULLY REARRANGED TO GET ANY MOTION INFORMATION YOU MAY NEED!!!***

48. Constant Acceleration Equations

49. Steps to solve a physics problem • Read the question CAREFULLY • Write down ALL variables you are given and label them properly • Choose a method to solve the problem (graphing, pictures, equations) which you are familiar with and comfortable doing • Try to set up your solution so that you have only one unknown value in your work • If you cannot set up a method with only one unknown, you must determine a way to either solve for or eliminate one of the unknowns.(Or choose a different way to solve)

50. Steps to solve a physics problem • Carry out drawing/measuring/calculating carefully and as accurately as possible. Avoid rounding often, always keep units with numbers, keep an eye on sig. digs. and be careful of typos • Check that your final answer is what you were trying to solve for. • Check that your final answer makes sense in the question, if not, find out why. Ensure that final answer has appropriate sig. digs. and correct units. • If time permits, recalculate the question to be sure you get the same answer twice. (That means start at the beginning again and recalculate, not just the last one or two) • Circle your final answer including units and write a concluding statement to finish the problem.