FORCE

1. FORCE

2. Newton’s Laws Three Laws of Motion

3. Aristotle’s Motion • Natural Motion is up or down • Down for falling objects • Up for smoke • Circular for heavenly bodies since without end • Violent Motion • Due to imposed forces such as wind pushing a ship or someone pulling a cart • Natural state of motion is rest • A force is needed to keep something moving

4. Aristotle’s Basic Error • Friction not understood as a force

5. Galileo’s Motion • Force is a push or a pull • Friction is a force that occurs when objects move past each other • Friction due to tiny irregularities • Only when friction is present is a force required to keep something moving

6. Ball rolling downhill speeds up Ball rolling uphill slows down He asked about ball on smooth level surface Concluded it would roll forever in absence of friction Galileo’s Inclined Planes

7. Inertia • Resistance to change in state of motion • Galileo concluded all objects have inertia • Contradicted Aristotle’s theory of motion • No force required to keep Earth in motion around sun because no friction

8. Newton • Born 1665 • Built on Galileo’s ideas • Proposed three laws of motion at age of 23

9. Newton’s First Law Ourtesy www.lakeheadu.ca/~alumni/ hockey.gif • Every object continues in its state of rest, or of motion in a straight line at constant speed, unless compelled to change that state by forces exerted on it. • Also called Law of Inertia: things move according to their own inertia • Things keep on doing what they are doing • Examples: Hockey puck on ice, rolling ball, ball in space, person sitting on couch

10. Mass • Amount of inertia depends on amount of mass…or amount of material (number and kind of atoms) • Measured in kilograms • Question: Which has more mass, a kilogram of lead or a kilogram of feathers? • Mass vs. Volume: volume is how much space something occupies

11. Experiencing Inertia • Inertia is resistance to shaking • Which is easier to shake, a pen or a person? • Why is it so hard to stop a heavy boat?

12. Inertia in a Car • Discuss three examples of inertia in a car • Car hitting a wall • Car hit from behind by a truck • Car going around a corner

13. Newton’s Second Law • Law of Acceleration • The acceleration produced by a net force on an object is directly proportional to the magnitude of the net force, and is inversely proportional to the mass of the body. • Acceleration = net force ÷mass • F =ma • Acceleration is in direction of net force

14. Units • F = ma • Unit of force is the Newton (N) • 1 N = 1 kg m/s2

15. Net Force • Net Force means sum of all forces acting • Sum is Vector sum F2 F1 Resultant force

16. Understanding the Second Law Force • The cause of acceleration is… • _________ resists acceleration • The greater the force, the ________ the ______________ • The greater the mass, the _________ the acceleration. Mass or inertia greater acceleration less

17. F = ma is Three Equations • F and a are vectors • So F = ma equation is really three SFx = max SFy = may SFz = maz

18. Examples • What force is required to accelerate a 1000 kg car at 2.0 m/s2 ? Answer: F = ma = 1000 kg x 2.0 m/s2 = 2000 N. • What is the acceleration of a 145 g baseball thrown with a force of 20.0 N? a = F/m = 20.0 N/0.145kg = 138 m/s2

19. F = ma Example; m unknown • An astronaut puts a 500.0 N force on an object of unknown mass producing an accelerations of 0.462 m/s2 . What was the mass? • M = F/a = 500.0N/0.462 m/s2 = 1082 Kg = 1.08 x 103 Kg

20. Net force example If four teams are playing tug of war (imagine a rope that looks like a cross, with the flag tied in the middle). Each team is 90⁰ from each other. Team A pulls with an overall force of 350 N to the North, Team B pulls with an overall force of 270 N to the South, Team C pulls with an overall force of 150 N to the East and Team D pulls with an overall force of 250 N to the West. If the flag in the middle has a mass of .25 kg, what is the magnitude and direction of its acceleration?

21. Putting it all together……. Calculate the change in force of a car that has a mass of 2500 kg if it goes from 45 m/s to rest in 7 seconds at a stop sign, then accelerates up to 65 m/s in 5 seconds.

22. a= vf-vi/t or a = F/m a1 = 0-45/7 = -6.42 m/s2 a2 = 65-0/5 = 13 m/s2 The difference between them is 19.42 m/s2. F = m x a = 2500 kg x 19.42 m/s2 = 48550 N difference between the two accelerations

23. Newton’s Third Law • Forces always come in pairs • Two forces on different objects • Every action has an equal and opposite reaction • Whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first • Example: hammer hits nail

24. Example: pushing on wall • What are the forces when you push on a wall? • You exert force on wall • You accelerate in the opposite direction • Wall must have exerted a force on you in the direction you accelerated (by 2nd Law)

25. Example: person walking • Foot exerts force backward on ground • Ground exerts force forward on foot

26. Example: Throwing ball • Pitcher exerts force on ball • Ball exerts equal and opposite force on pitcher • Why doesn’t pitcher move?

27. Example: Rocket • Rocket engine exerts rearward force on gas molecules • Molecules exert forward force on rocket.

28. Book on Table • The mass of the book is one kg. What is the force (magnitude and direction) on the book? • 9.8 N upward

29. Really putting it all together…… Calculate the Force necessary to launch a cannonball with a mass of 15 kg if it is fired at an angle of 43⁰ if it hits a target 210 m away in 6.3 seconds? What can we solve in this problem? What equations do we need to solve this problem?

30. What we need to solve the force Vx = dx/t = 210/6.3 = 33.3 m/s Vf2 = Vi2 + 2 a(d) Vi = 0 for this problem a = Vf2/2d = 33.32 / 2(210) = 2.64 m/s2 Force of the cannon: F = m(a) F = 15 kg (2.64 m/s2) = 39.6 N

31. The Horse and the Cart Problem If there is always an equal an opposite reaction, how does anything move? For example, if you have a horse and a cart, how does the horse pull the cart?

32. The Horse and Cart Problem. A= - B B= - C C= -D A=B=C=D no acc! These appear to be the equalizing forces.

33. The Horse and Cart Problem. Because it is accelerating, the force the horse exerts on the cart has increased. By Newton's third law, the force of the cart on the horse has increased by the same amount. But the horse is also accelerating, so the friction of the ground on its hooves must be larger than the force the cart exerts on the horse. The friction between hooves and ground is static (not sliding or rolling) friction, and can increase as necessary (up to a limit, when slipping might occur, as on a slippery mud surface or loose gravel). So, when accelerating, we still have B = -C, by Newton's third law, but D>C and B>A, so D>A.

34. More Examples • Can you think of some more examples of Newton’s Third Law in Action? • Imagine an astronaut floating in deep space, with only his spacesuit. Is there any way for him to move himself back to earth?

35. Mass vs. Weight • Mass is intrinsic property of any object • Weight measures gravitational force on an object, usually due to a planet • Weight depends on location of object • Question 1: How does mass of a rock compare when on Earth and on moon? • Question 2: How does its weight compare?

36. Review Mass vs. Weight • What is mass? • Answer: quantity of matter in something or a measure of its inertia • What is weight? • Answer: Force on a body due to gravity

37. Weight of 1 Kilogram • 9.8 Newtons • About 2.2 pounds • Compare the weight of 1 kg nails with 1 kg styrofoam • Answer: Same

38. Weight Examples • What does a 70 kg person weigh? Weight = mass x g(acceleration due to gravity) W = mg = 70 kg x 9.80 N/m2 = 686 N • An object weighs 9800 N on Earth. What is its mass? • m = W/g = 9800 / 9.8 m/s2 =1000 kg

39. Atwoods Lab You have 25 washers on your lab setup, if you have a unbalanced force, you will have acceleration. You will be using the stopwatch function of your data collector. Make a chart to record mass, time, acceleration and force. Put all washers on one side, raise that side to the top, then release it timing how long it takes to reach the bottom. Record this time. The mass of one washer is 16 g. It is the difference in mass that causes the acceleration. Calculate the difference in mass and record in table. 1st mass is 25 x 16, 2nd mass is 23 x 16, 3rd mass is 21 x 16 etc. Calculate the Acceleration = 2d/t2 (d = 1 m for the fall) so a = 2/ t2 Calculate the Net force of the fall and record. (F= ma) Move one washer at a time over to the other side and repeat. Continue until the machine no longer turns (12 or 13 trials)

40. FRICTION Sliding (motion) & Static (stationary)

41. Sliding Friction • Often called kinetic friction • A force opposite to direction of motion • Due to bumps in surfaces and electric forces Surface under microscope Ff

42. Kinetic Friction is… • Dependent on nature of the two surfaces • Directly proportional to the normal force between the surfaces • Normal Force is perpendicular to the surface. If it is on a flat surface, it is equal to the weight of the object. • Independent of velocity

43. Reducing Friction • In order to reduce friction we can: • A. Reduce surface area • B. Reduce weight of object • C. Change type of friction • - sliding(the greatest amount) • - rolling (use wheels to ease friction) • - fluid ( Eliminate contact by using liquids or gases)

44. Coefficient of friction mk • Generally between zero and one • Based on comparing Friction Force to Normal Force • Normal Force is always perpendicular to surface • Calculate from Ff / FN = µk • Can be more thanone for special rubber • Very low for ice, Teflon, lubricated surfaces, ball bearings

45. Friction: Good or Bad • Mostly undesirable since reduces useful force and wastes energy • Friction produces heat • Necessary for walking! • Necessary for braking

46. Static Friction • Force to start something moving • Usually larger than kinetic friction for same surfaces • Requires force to be exerted • Before sliding begins, is equal and opposite to applied force

47. Where are all the forces? • Block on an inclined plane

48. Free Body Diagram Example 1 If the box below accelerates to the right at 1 m/s2 Solve all of the following:

49. Solution 1 Fgrav = m x g = 5 x 9.8 = 49 N Using the angle and the F applied, we can calculate the X and Y component of that force. Fx= 15 sin 45 Fy = 15 cos 45 Fx = 10.6 N Fy = 10.6 N If the force of gravity is 49 N down and the applied force is 10.6 N up, then the normal force applied is the difference between the two. F norm= 49-10.6 = 38.4 N

50. Solution 1 cont. If the object has an a of 1 m/s2 and a mass of 5 kg, then it has a net force of 5 N in the X direction. If the applied force in the X is 10.6 and the net is 5, then the force of friction is the difference between the two. Ffric= 10.6-5 = 5.6 N To solve the coefficient of friction we use this equation: Ff = mkFN mk= Ff/FN = 5.6/ 38.4 = .145