CH5 Forces and Newton’s Laws of Motion Physics Fall, 2015 Mrs. Kummer 1

CH4 topics Vector Characteristics Vectors are described by their components Vector components depend on length and direction Vector components can be combined into one vector, the resultant You need trig Vectors can be added by placing them head to tail Vectors are unchanged if moved to other locations Vectors can be added graphically Vectors can be added with components 2

What is a Force? Force: Push or Pull on a body Units (Metric): Newtons (N), kg∙m/s 2 (English): Pounds (lb f ) Vector Quantity: Has Magnitude & Direction – Ex. F = 8 N upward – Ex. F = 60 N westward Symbol: F (capital) To get familiar with units: It takes 3N to lift a can of pop 3

4 Types of “Strong” Forces Gravitational Force, Weight, Fw or F g Tension/Compression Force, F t /F c Normal Force, Support Force, F N Frictional Force, F f 4

Gravitational Force, Fw Fw = The attractive force of the Earth on any mass on or near Earth We say, “Force due to gravity” or “Weight” We measure MASS, we calculate WEIGHT Fw = m ∙ g (Eq.13) g = 9.81 (m/s 2 ) m=mass (kg) MUST BE IN kg!!!! Fw = Weight (N) 5

Tension/Compression Forces, Ft and Fc Tension = Pull on an Object – Ex. Tie a boat down to the docks – Ex. Big Cables on the Mackinac Bridge Compression = Push on an Object – Ex. Pushing your grocery cart – Ex. Pushing your car out of deep snow! These Forces always work OPPOSITE of EACH OTHER, so be careful with your signs F t = - F c 6

Normal Force, F N Normal Force: A support force that holds two objects together – “Normal” in Math/Science = Perpendicular – Ex. Book resting on table: Downward force of book, weight = Fw Upward force of book = F N F N = - Fw Normal Force opposite of Weight Force F N =-Fw 7

Frictional Force, F f F f : The force opposing sliding motion of two surfaces in contact Depends on the materials in contact with each other: surface finish, actual material, etc. Two Types of Frictional Force: – Static Friction, (object to slide is initially at rest) – Sliding Friction, (object is already sliding on surface) F f OPPOSITE of moving Force (Ft, Fc, etc.) 8

Net Force We say: Net Force is the sum of all forces acting on a body We write: ∑Fnet = Fw + -F N + …. (Eq.14) When ∑Fnet = 0, (Eq.15) or when all forces on a body cancel each other, the body is in EQUILIBRIUM 2 Types of Equilibrium: 1.Static Equilibrium (object is not moving) 2.Dynamic Equilibrium (object is moving at constant velocity) 9

How Do We Find Fnet? Draw a Free Body Diagram (FBD) with all forces acting on object Using sign convention, add up forces! Free Standing ObjectSupported Object 10

Practice Problem #1 A painter stands on scaffolding that is suspended at the ends by two vertical ropes. The painter and the board are in static equilibrium. The tension in each rope is 350(N), and the painter weighs 550 (N). What is the weight of the scaffolding? 11

Practice Problem-Static Equilibrium 1.Draw FBD: 2.Identify Knowns: Ft = 350 (N) ea rope Fwgirl = 550 (N) Static Equilibrium = No motion, & ∑Fnet = 0 3. Identify Unknown(s): Fwboard = ? 4. Add Forces to FBD 5. Write Equation: ∑Fnet = 0 Fnet = 2∙Ft – Fwgirl –Fwboard 6. Plug In Values & Solve: 0 = 2∙350 (N) – 550 (N) –Fwboard Fwboard = 150 (N) downward 12

Practice Problem #2 You hit a hockey puck with an applied force of 50 (N). The puck travels down the ice rink at a constant speed of 2.60 m/s. If the puck is in dynamic equilibrium, what is the frictional force applied by the ice/puck contact? 13

Practice Problem-Dynamic Equilibrium 1.G: Draw FBD: 2.List Givens: Fapplied = 50 (N) v = 2.6 m/s (constant) Dynamic Equilibrium = In Motion, v=constant & ∑Fnet = 0 3. U: Ff = ? 4. Add Forces to FBD 5. F: ∑Fnet = 0 Fnet = Fapplied - Ff 6. P & S: 0 = 50 (N) - Ff Ff = 50 (N) to the left 14 Fapplied Ff

Vocabulary: Scalar Qty: number only, no direction (e.g. time, temperature, speed). Vector Qty: number and direction (e.g. velocity, 75 mph southbound on I-275) Compass directions: N, E, S, W (remember, NEVER EVER SMOKE WEED) Resultant Magnitude: H (hypotenuse) Resultant Direction: ∠ ° made by vector and x-axis and compass direction Vectors 15 N E S W

How Do You Find Resultant Vectors? 16 Pythagorean Theorem c c 2 =a 2 +b 2 c=hypotenuse a a&b = legs b MUST BE A RIGHT TRIANGLE!!!! Recipe to Find Resultant Vector or NET FORCE: Step 1: Solve for hypotenuse using Pythagorean Theorem. Step 2: Solve for angle z° using TAN Trig. Function. Step 3: Add direction (e.g. NE, SE, SW, etc.) Step 4: Put all three together as answer. Step 5: Circle your answer.

How Do You Find Components of a Vector? 17 Recipe to Find Components of Vectors: Step 1: Make triangle with vector and x-axis. Step 2: Circle ∠ vector makes with x-axis. Step 3: Label O,A,H. Step 4: Add y to O side. Add x to A side. Step 5: Use SIN function to find y Use COS function to find x. Step 6: Write your answer as ordered pair (x,y)…change signs if needed, depending what quadrant you are in…

Trig. FunctionsTrig. Equations SinSin (z)° = O Opp H Hyp CosCos (z)° = A Adj H Hyp TanTan (z)° = O Opp A Adj SOH-CAH-TOA 18