Unit 5 Forces I- Newton s First & Second Law

Transcription

1 Unit 5 Forces I- Newton s First & Second Law

2 Unit is the NEWTON(N) Is by definition a push or a pull Does force need a Physical contact? Can exist during physical contact(tension, Friction, Applied Force) Can exist with NO physical contact, called FIELD FORCES ( gravitational, electric, etc)

3 INERTIA a quantity of matter, also called MASS. Italian for LAZY. Unit for MASS = kilogram. Weight or Force due to Gravity is how your MASS is effected by gravity. W = mg What is the weight of an 85.3-kg person on earth? On Mars=3.2 m/s/s)? W W = mg W = (85.3)(9.8) MARS = (85.3)(3.2) = = N N

4 An object in motion remains in motion in a straight line and at a constant speed OR an object at rest remains at rest, UNLESS acted upon by an EXTERNAL (unbalanced) Force. There are TWO conditions here and one constraint. Condition #1 The object CAN move but must be at a CONSTANT SPEED Condition #2 The object is at REST Constraint As long as the forces are BALANCED!!!!! And if all the forces are balanced the SUM of all the forces is ZERO. The bottom line: There is NO ACCELERATION in this case AND the object must be at EQILIBRIUM ( All the forces cancel out). acc = 0 å F = 0

5 Some Forces 1. Gravitational Force 1. Weight (= Gravitation Force) A gravitational force on a body is a certain type of pull that is directed toward a second body. Like earth pulling us all towards it s center. Do we pull the earth too towards us? The weight W of a body is the magnitude of the net force required to prevent the body from falling freely, as measured by someone on the ground. For example, to keep a ball at rest in your hand while you stand on the ground, you must provide an upward force to balance the gravitational force on the ball from Earth.

6 3. Normal Force When a body presses against a surface, the surface (even a seemingly rigid one) deforms and pushes on the body with a normal force that is perpendicular to the surface. 4. Frictional Force If we either slide or attempt to slide a body over a surface, the motion is resisted by a bonding between the body and the surface. 5. Tension When a cord (or a rope, cable, or other such object) is attached to a body and pulled taut, the cord pulls on the body with a force directed away from the body and along the cord.

7 A pictorial representation of forces complete with labels. Ff m1g FN T T Weight(mg) Always drawn from the center, straight down Force Normal(FN) A surface force always drawn perpendicular to a surface. Tension(T or FT) force in ropes and always drawn AWAY from object. m2g Friction(Ff)- Always drawn opposing the motion.

8 1. Isolate the Object for which you are drawing the FBD 2. Represent it as a circle or square 3.. You will only show Forces acting on it Contact forces Any force that is because of objects touching it Non-contact force there in only one Mg 4. Only full Forces NO components 5. Length of the Forces should indicate relative magnitude

9 Since the Fnet = 0, a system moving at a constant speed or at rest MUST be at EQUILIBRIUM. TIPS for solving problems Draw a FBD Resolve anything into COMPONENTS Write equations of equilibrium Solve for unknowns

10 Ff FN mg

11 A 10-kg box is being pulled across the table to the right at a constant speed with a force of 50N. a) Calculate the Force of Friction b) Calculate the Force Normal F = F = 50N a f Ff FN Fa mg = F = ( 10)(9.8) = 98N n mg

12 Suppose the same box is now pulled at an angle of 30 degrees above the horizontal. a)calculate the Force of Friction b)calculate the Force Normal FN Fa F F ax f = F cosq = 50 cos30 = F a ax = 43.3N = 43.3N Ff 30 mg Fax Fay F F F F N N N N ¹ mg! + F ay = 73N = mg = mg - F ay (10)(9.8) - 50sin30

13 NORMAL FORCES Sketch free-body diagrams for the following situations: (a) a book rests on a table; (b) you exert a downward force on the book as it sits on the table; (c) you tie a helium-filled balloon to the book, which remains on the table.

14 When does one object lose contact with another? For instance, how many helium balloons would we have to tie to the book to make it lift off the table? Objects lose contact when the normal force between them goes to zero. The minimum number of balloons is the numbe needed to reduce the normal force the table exerts on the book (and the normal force the book exerts on the table) to zero.

15 a. Draw FBD of this System Isolate and Conquer you will draw FBD of each part in a system i.e. Box1 and Box 2 separately. If Box 1 = 20 N and Box 2= 10N Calculate the normal force (b) exerted on box 2 by box 1, (c) exerted on box 1 by box 2, and (d) exerted on box 1 by the floor.

16 Checkpoint q In figure shown below, is the magnitude of the normal force FN greater than, less than, or equal to mg if the block and table are in an elevator moving upward (a) at constant speed (a) For constant speed Fnet=0= FN mg=0 FN = mg

17 Tension

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19 Remember -We apply NFL when the object OR every part of a system is at rest or constant motion. If this system is either in rest or in constant velocity means Acceleration ( of the weight and of the hand) = 0 1) Draw the FBD of the 1) Object 2) hand when at Static Equilibrium 1) Draw FBD of the Pulley in (c)

20 1) Draw the Free body diagram for m1 and m2 2) If the system as a whole is moving with constant speed, what is the frictional force associated with m2? Assume Frictional force is directly proportional to the Mass.

21 Considering Systems as a whole or Subsystems will lead to the same result 60 N

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24 Which of the Pulley systems will make your life easier?

25 Mechanical Advantage = Load / Effort

26 What is the value of the missing mass if the system is in static equilibrium a.k.a at rest and m = 10Kg?

27 If an object is NOT at rest or moving at a constant speed, that means the FORCES are UNBALANCED. One force(s) in a certain direction over power the others. THE OBJECT WILL THEN ACCELERATE.

28 The acceleration of an object is directly proportional to the NET FORCE and inversely proportional to the mass. aa F a = NET F m NET 1 aa m F NET = ma F NET Tips: = åf 1. Draw an FBD 2. Resolve vectors into components 3. Write equations of motion by adding and subtracting vectors to find the NET FORCE. Always write larger force smaller force. 4. Solve for any unknowns

29 A 10-kg box is being pulled across the table to the right by a rope with an applied force of 50N. Calculate the acceleration of the box if a 12 N frictional force acts upon it. Ff FN mg Fa In which direction, is this object accelerating? The X direction! So N.S.L. is worked out using the forces in the x direction only F F Net a - = ma F = ma = 10a a = 3.8 m / s f 2

30 Checkpoint q In figure shown below, is the magnitude of the normal force FN greater than, less than, or equal to mg if the block and table are in an elevator moving upward (b) at increasing speed (b) For increasing speed Fnet=ma= FN mg FN = ma + mg FN > mg

31 A mass, m1 = 3.00kg, is resting on a frictionless horizontal table is connected to a cable that passes over a pulley and then is fastened to a hanging mass, m2 = 11.0 kg as shown below. Find the acceleration of each mass and the tension in the cable. F Net = ma FN T T m T g -T 2 = m a 1 = m a 2 m1g m2g m m m a = g - m a = g g m2g m + m 2 2 m a 2 = m a + m a = a( m 1 + m 1 ) (11)(9.8) 14 = 7.7 m / s 2

32 Free Body Diagram Remember to include Isolate the body in consideration Draw the body External Forces Do not include Other bodies Forces exerted by the body Internal Forces

33 Where does the calculus fit in?! F = ma! = m dv dt 2 d x = m dt There could be situations where you are given a displacement function or velocity function. The derivative will need to be taken once or twice in order to get the acceleration.

34 Example: You are standing on a bathroom scale in an elevator in a tall building. Your mass is 72-kg. The elevator starts from rest and travels upward with a speed that varies with time according to: v ( t) = 3t t When t = 4.0s, what is the reading on the bathroom scale (a.k.a. Force Normal)? 2 Apparent weight dv d(3t t a = = dt dt a(4) = (4) = 2 ) = t 4.6 m/s/s F F F net N N = ma - mg = ma F = ma + mg = (72)(9.8) + (72)(4.6) = N N

35 Rem: Treat the x-direction and y direction quantities separately Be careful with sign conventions. If you considered a positive for a certain body, any other body pulled by it will have the same acceleration and sign

36 Parts A, B, and C of Fig. show three situations in which one or two forces act on a puck that moves over frictionless ice along an x axis, in onedimensional motion. The puck's mass is m = 0.20 kg. Forces F1 and F2 are directed along the axis and have magnitudes F1 = 4.0 N and F2 = 2.0 N. Force F3 is directed at angle θ = 30 and has magnitude F3 = 1.0 N. In each situation, what is the acceleration of the puck?

37 N.T. L Newton's Third Law: When two bodies interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction. FBT = - FTB Equal in Mag ; Opposite in direction FBT = FTB

38 On Earth In Space F on man by wall Ffriction on man by ground F on man by wall F on wall by man

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40 Suppose that the cantaloupe and table are in an elevator cab that begins to accelerate upward. (a) Do the magnitudes of FTC and FCT increase, decrease, or stay the same? (b) Are those two forces still equal in magnitude and opposite in direction? (c) Do the magnitudes of FCE and FEC increase, decrease, or stay the same? (d) Are those two forces still equal in magnitude and opposite in direction?

41 2 Masses are stacked inside an elevator as shown. The elevator starts to speed downwards with an acceleration of 2 m/s 2. Find Magnitude and direction of all the contact forces on 20 Kg and 30 Kg a = 2.00 m/s 2 20 Kg 30 Kg ELEVATOR