Physics and Honors Physics Kinematics

Physics – Forces We will complete this chapter in two parts: first WITHOUT friction and then WITH friction. If you understand without friction, adding friction in is very easy. If you do not understand the chapter without friction, the concepts with friction only become harder!!! I. Force Force  any influence that COULD cause an object to accelerate. IN OTHER WORDS: ACCELERATIONS ARE CAUSED BY FORCES  Vector Quantity 2 SAY WHAT???? Just because an object  Units: Newton = 1 kgm/s doesn’t accelerate does NOT mean there Dyne = 1 g-cm/ s2 2 are no forces….it may mean the forces are Pounds = 1 slug-ft/ s balanced!!

FYI – Pressure vs Strain  is the ratio of the force to cross sectional area (Generally think of it as how the force is spread out) P = σ = F/A *this concept is very important to your bridge project that will be assigned next week. Types of Forces 1) Contact Forces  forces that require direct physical contact 2) Field Forces  forces that act at a distance (requiring NO physical contact) II Free Body Diagrams Free Body Diagrams: is a simplified representation of all the forces acting on an object Your diagrams will get complicated/cluttered quickly so it is best to keep it simple

EX 1) consider the forces on the cart. Ground Weight Force of man friction Free Body Rules 1. Draw the object as a box – Don’t care if it’s a banana, car ball or whatever. Draw as a box  2. Use a vector to represent each separate force – make sure it points in the appropriate direction!! a.All vectors need to “touch” the center of the free body to be considered an official free body b. DO NOT use numbers in the free body diagrams c.You can draw another working free body diagram to put additional information on it

Free Body Views: On the Ground/Surface Overhead

Can view Fweight Cannot view Fweight Can view FNormal Cannot view FNormal Can view FFriction (f) Will not have to worry about FFriction (f) Movement = left/right or up/down Movement = vector analysis (x & y (hint – if Fw or FN is given/shown then chart) ground view)

III. Specific Forces #1 Net Force (Fnet)  vector* sum of all the forces (or components of the forces) PARALLEL to the acceleration/motion *yes force is a vector so magnitude and displacement rules apply  Unit: Newton (N) AKA: kgm/s2 pounds (the english unit)

EX 1) a force of 20N is applied to the east on a box. A second force of 30N is applied to the west on the same box. What is the net Force? Fnet = F1 + F2 F F 1 2

*the negative indicates West *in this case the forces are not balanced meaning they do not cancel out……. this would result in an acceleration.

An Unbalanced Net Force (Fnet = 0) will result in an acceleration

A Balanced Net Force is when the vector sum of all of the forces is zero (the forces cancel each other out). When this occurs the object will NOT accelerate, we say it is in equilibrium

Static equilibrium is when the object is at rest (static) and not accelerating (equilibrium)

EX 2) What if we now have a 20N Force North and another 30N force West? What is the Fnet? F 2

F 1 It might help if you look at the diagram another way.

F 1 F F F1 2 1 F F2 2

All three diagrams show the same thing but some are easier to for vector addition and other show the proper free body diagram ϴ

Answer:  Do not confuse the unit N (Newton) for the direction N (north)

#2 Weight (Fw = mg)  the force on an object due to the gravitational pull of the Earth*. Unit : Newton This force is always directed downward (toward the center of the Earth*) Calculated by multiplying mass (in kilograms) by the acceleration due to gravity “g” (on Earth = “g” = “a” = 9.8m/s2. Other planets have different accelerations due to gravity) Weight is NOT the same as mass! Mass is a physical property of the object and is constant, regardless of the force of gravity (which varies with location). Weight CAN vary (with gravitational acceleration, “g”) BUT mass is constant It is good to know your own weight in Newtons: What weight (in Newtons) is a 150lb person? 1Kg = 2.2 lbs

It’s a big value…….do not be confused by this! 1 Newton is a very small amount of force. So you will typically deal with larger values. *show newton scale

#3 Tension (T or FT)  the force in a string, chain, wire, etc.  tensile forces always act to pull objects. Unit: Newton! Nothing too special about tension. It’s just the force in a rope. Typically we use it when we can’t directly pull something.

Ex. You pull on the rope with 120N of force. The tension in the rope is 120N and imparts your force to the box.

#4 Normal Force (FN)  AKA: perpendicular force  The support force that a surface exerts on the object  If the object pushes on the surface the surface must be pushing back otherwise the object would move the surface  It always acts PERPENDICULAR to the SURFACE!!!  What does this look like?

**do not confuse FN (normal force) with Fnet (net force). They are VERY different! Fnet: consider all forces (or components of forces) parallel to the motion FN: consider all the forces (or components of the forces) perpendicular to the surface

FYI when you stand on a bathroom scale it actually indicates FN…….most of the time FN = weight but not always. We will revisit this idea soon 

Solving for FN: Method: Use forces up = forces down

EX 1) Let F= 150N and m = 15kg Solve for FN Solve for Fnet

Ex 2) Let F= 150N and m = 15kg Solve for FN Solve for Fnet

#5 Force Friction (Ff or f)  the force acting on a surface as two materials move past one another. Friction always acts to impede the relative motion (or attempt at motion) between two surfaces. always acts OPPOSITE of the direction of acceleration/motion for now you can think of friction as the resistive force acting between the surface and an object.  We will come back to friction later – for now we will continue to ignore it IV. Newton’s Laws of Motion Galileo (1564-1642) noticed that larger (more massive) objects resisted changes in their motion. For example a cannon ball rolling across the ground was harder to stop than an apple rolling across the ground. He coined the term inertia to describe this. Inertia is the natural tendency of an object to resist changes in its current state of motion. Inertia is measured in terms of an object’s mass. In other words inertia and mass are proportionally related. More mass = more inertia Inertia is NOT a force. Forces are needed to overcome inertia

Newton (1643-1727) expanded on this concept of inertia and developed his 3 laws of motion. These three laws are the foundation for classical mechanics (that is the branch of physics we are studying) NEWTON’S LAWS OF MOTION 1st Law = Law of Inertia Neglecting an outside net unbalanced force, an object at rest will remain at rest and an object in motion will maintain its current state of uniform motion* (in other words NO acceleration) *uniform motion = constant velocity = no acceleration = no change in speed or direction

Science of football

Demos: 1) cart + PEZ (why wear a seat belt?) 2) Dollar and Bottles

3) table Cloth 4) eggs and glasses 2nd Law (this law quantifies how forces change motion) The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object’s mass.

a  Fnet (a is proportional to Fnet)

AND a  1/m (a is inversely proportional to mass) SO THIS is the second law! Proportions can only take us so a  Fnet / m far, we can use a constant of proportionality to find an equation.

Newton defined the unit of force (the Newton) as 1 kgm/s2, so the constant of proportionality is 1 and we have: F = ma

Question…so why is weight = mg? Science of football Ex. #1 Mrs McGrath applies a eastward horizontal force of 270N to a 20kg crate. Ms. Boron applies a second westward horizontal force of 380N to the same crate. Determine the acceleration of the crate.

#2 Now Mrs. McGrath’s force is east and Ms Boron’s force is south.

#3 Mrs McGrath pulls on a wagon via a rope. She pulls with a force of 350N so that it makes an angle of 48° with the ground. What is the acceleration of the wagon? 3rd Law = the law of action-reaction pairs For every action (force) there is an equal* and opposite** reaction (force) These action/reaction pairs happen simultaneoulsy * equal in magnitude FAB = -FBA ** opposite in direction This is NOT cause and effect! It does not mean if a bat hits a ball then the ball will move It does mean: if a bat hits a ball than a ball hits a bat

Science of foot ball

Example  if you slam on your breaks in your car, the seatbelt exerts a force on you and you exert the same force in the opposite direction on the seatbelt.

Example: The picture to the right show a child hanging from a tree branch. Identify the action-reaction pair.

The boy lets go of the branch and falls towards the ground. Identify the action-reaction pair now. Demo: scooters CAUTION: Again this is NOT a cause and effect!!! Although these forces ARE equal and opposite, the results can be significantly different due to the different objects involved. Question If I push on an object and it pushes on me with the same force, then why don’t they cancel out (giving no net force and thus no acceleration)? Answer – the forces act on different objects so they can’t cancel! SAY WHAT???? For example……think about this If the earth is pulling on me with a force and I am pulling on the Earth with an equal but opposite force, then why doesn’t the earth have the same acceleration as I do? Answer – the masses are very different! The forces are the same, but the results are VERY different! FEme = -FmeE mEaE = mmeame

ma = ma

(big mass gives small acceleration)

(little mass gives big acceleration) V. SYSTEMS V. Systems  Multiple objects moving together (via ropes, chains). METHOD 1) Assign positive direction for the motion (figure out a direction of motion or guess if you have no idea how it will move) 2) Draw free-body diagram for EACH object 3) Apply F = ma (to EACH object) 4.) Add the equations together 4) Solve Ex.1 “horizontal system” a. What is the acceleration of the system below? b. what is the tension in the rope connecting the blocks?

200N 25kg 15kg Ex 2 “vertical system” = Atwood) Atwood machines are devices that consist of pulleys, strings and masses. For the purpose of this class the pulley and string will be considered mass-less and for now we will not deal with friction. *Since the objects are tied together they will move with the same acceleration. *use the system methodology you learned above to solve! * make sure to assign each mass and tension a number!

50kg Ex 3 Elevators

Elevator problems are problems in which an object is accelerated vertically. Usually the problem involves an elevator with a person standing on a scale or an object attached to a rope. Therefore ...use the system methodology you learned above to solve! (if no direction of motion is given you must assign a positive direction)

a. Elevator is standing still When a person is standing on a scale, the scale shows the NORMAL FORCE on the surface of the scale! At rest OR not accelerating on a level surface the scale will read the weight of the person. Lets prove this mathematically 

b. Now the elevator is traveling at a constant speed of 2m/s When the person is accelerating either up or down, the scale will show a different value. c. Now the elevator is traveling at a constant acceleration of 2m/s2 upwards.

d. (last scenario) Now the elevator is traveling at a constant acceleration of 2/m2 downward

Now you try some with some actual numbers!

Ex2. While conducting an experiment Ms. Boron stands on a bathroom scale in an elevator (weird huh?) If Ms Boron has a mass of 58.0kg determine the reading on the scale in the elevator. *remember the scale indicated the force normal!!

a. The elevator is moving downward with a constant acceleration of 4.6m/s2

b. The elevator is moving upward with a constant velocity of 4.6m/s. VI. Equilibrium Equilibrium – state of constant non-accelerating motion Static equilibrium – state of constant non-accelerating motion AND unchanging rest (v=0)

Vertical Motion Horizontal Motion Object is not accelerating Object is not accelerating

∑Fup = ∑Fdown ∑Fleft = ∑Fright

Conditions for Equilibrium

Remember

Constant velocity = No acceleration = Fnet is 0

Stopped = No acceleration = Fnet is 0 Ex. A 70 kg sign is held from the ceiling (as shown below). What is the tension in each of the ropes?

40° 30°

70kg VII. Inclined Planes 1) Assign positive direction for the motion (figure out a direction of motion or guess if you have no idea how it will move) 2) Draw free-body diagram for EACH object 3) Apply F = ma (to EACH object) 4.) Add the equations together 4) Solve mgcosΘ Normal force the component of the Fw (mg) always acts weight that is Θ straight down perpendicular to the motion/incline mg Θ mgsinΘ the component of the weight that is parallel to the motion/incline

According to Fnet = ma. ONLY the forces that are PARALLEL to the motion affect the acceleration! Therefore PART of the gravitational forces affects the acceleration (the parts parallel to the motion) Ex. A 10kg box is placed on a 30° incline. Neglecting friction, what is the acceleration of the block when it is released from rest?

Ex2. The same block on the same incline, is subjected to a 200N force up the incline and parallel to the motion. What is the block’s acceleration now? Want something a little more challenging???

100N 20kg 50kg 20°

98N 20° VIII. Friction (f)

Friction is the force between two surfaces moving past one another. Friction always acts to impede the relative motion (or attempt at motion) between two surfaces.

Types of Friction

1) Static Friction (fs)  the friction that must be overcome in order to initiate motion. * Can vary from zero to some maximum value (depending on how hard you push/pull)

F = 50N F = 100N F = 101N app app app

If it doesn’t move then: To get it to move you When F is JUST app f = 50N can push harder. greater than friction the v = 0 and a = 0 If it doesn’t move then: object will “break away” f = 100N v = 0 and a = 0 2) Kinetic Friction (fk)  the friction that opposes the motion of an object as it slides across a surface. Kinetic friction < Static Friction (for a given pair of materials)

Source of Friction

Friction depends on two factors: 1) Materials in contact  indicated by the coefficient of friction (μ)  this is a (unitless) value that varies for every combination of materials

2) Normal Force  the force with which the two surfaces are pressed together

f = μFN

But WHY does it exist?

Two schools of though: 1) Friction occurs due to asperities in the surfaces. These asperities cause the ridges (in one material) to get hung up in the valleys (of the other material). According to this theory, rough materials (which have more/deeper asperities) will have higher values for friction. 2) Friction occurs at contact points due to “cold Welding.” The molecules of each object exert (electromagnetic) forces on each other. This bonding is the source of friction. This explains why highly polished (very smooth) objects can have enormous amounts of friction.