Unit 5 Forces I- Newtonʼ s First & Second Law

Transcription

1 Unit 5 orces I- Newtonʼ s irst & 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, riction, Applied orce) Can exist with NO physical contact, called IELD ORCES ( gravitational, electric, etc)

3 INERTIA a quantity of matter, also called MASS. Italian for LAZY. Unit for MASS = kilogram. Weight or orce 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. m/s/s)? W W = mg W = (85.3)(9.8) MARS = (85.3)(3.) = = 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) orce. There are TWO conditions here and one constraint. Condition #1 The object CAN move but must be at a CONSTANT SPEED Condition # 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 = 0

5 Some orces 1. Gravitational orce. Weight (= Gravitation orce) 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. or 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 orce 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. rictional orce 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. N T Weight(mg) Always drawn from the center, straight down orce Normal( N ) A surface force always drawn perpendicular to a surface. f m 1 g T m g Tension(T or T ) force in ropes and always drawn AWAY from object. riction( f )- Always drawn opposing the motion.

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

9 f N mg

10 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 orce of riction b) Calculate the orce Normal = = 50N a f f N a mg = = ( 10)(9.8) = 98N n mg

11 Suppose the same box is now pulled at an angle of 30 degrees above the horizontal. a) Calculate the orce of riction b) Calculate the orce Normal N a ax f = cosθ = 50 cos30 = a ax = 43.3N = 43.3N f 30 mg ax ay N N N N mg! + ay = 73N = mg = mg ay (10)(9.8) 50sin30

12 NORMAL ORCES 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.

13 When does one object lose contact with another? or 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.

14 a. Draw BD of this System Isolate and Conquer you will draw BD of each part in a system i.e. Box1 and Box separately. If Box 1 = 0 N and Box = 10N Calculate the normal force (b) exerted on box by box 1, (c) exerted on box 1 by box, and (d) exerted on box 1 by the floor.

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

16 Tension

17

18 Remember -We apply NL 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 BD of the 1) Object ) hand when at Static Equilibrium ) Draw BD of the Pulley in (c)

19 1) Draw the ree body diagram for m1 and m ) If the system as a whole is moving with constant speed, what is the frictional force associated with m?

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

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

22 The acceleration of an object is directly proportional to the NET ORCE and inversely proportional to the mass. aα a = NET m NET 1 aα m NET = ma NET = Tips: 1. Draw an BD. Resolve vectors into components 3. Write equations of motion by adding and subtracting vectors to find the NET ORC Always write larger force smaller force. 4. Solve for any unknowns

23 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 1 N frictional force acts upon it. f N mg a 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 Net a = ma = ma 50 1 = 10a a = 3.8 m / s f

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

25 A mass, m 1 = 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, m = 11.0 kg as shown below. ind the acceleration of each mass and the tension in the cable. Net = ma N T T m T g T = m a 1 = m a m 1 g m g m m m a = g m a = g g 1 1 mg m + m m a = m a + m a = a( m 1 + m 1 ) (11)(9.8) 14 = 7.7 m / s

26 Where does the calculus fit in?! = ma! = m dv dt = m d x 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. Here is an example. You are standing on a bathroom scale in an elevator in a tall building. Your mass is 7-kg. The elevator starts from rest and travels upward with a speed that varies with time according to: v ( t) = 3t + 0.0t When t = 4.0s, what is the reading on the bathroom scale (a.k.a. orce Normal)? dv d(3t + 0.0t a = = dt dt a(4) = (4) = ) = t 4.6 m/s/s net N N = ma mg = ma = ma + mg = (7)(9.8) + (7)(4.6) = N N