PHYSICS WALKER 5E CH 01 INTRODUCTION TO PHYSICS www clutchprep com PHYSICS WALKER 5E CH 01 INTRODUCTION TO PHYSICS Physics is the study of natural phenomena including LOTS of measurements and equations Physics math rules UNITS IN PHYSICS We measure in nature Measurements must have For equations to work units have to be with one another For example F m a Force Mass Acceleration A group of units that work together is called a of units QUANTITY In Physics we use the Syst me International Many other conventions standards are used in Physics S I UNIT Non S I measurements must be converted into S I before we plug them into equations VIDEO Unit Conversions Equations must be dimensionally consistent units are the same on both sides VIDEO Unit Analysis PRECISION SIGNIFICANT FIGURES AND SCIENTIFIC NOTATION Measurements must be precise Precision has to do with how many a measurement has When adding multiplying etc measurements we must use Sig Fig Rules VIDEO Significant Figures To compress numbers a use powers of TEN b round to TWO decimal points digits 5 or greater round up We can use to represent numbers EXAMPLE 1 For each number below a How many sig figs does it have b Re write it in scientific notation 2 decimals a 010 000 d 00 010 b 010 000 0 e 382 400 c 010 010 f 23 560 0 Page 2 PHYSICS WALKER 5E CH 01 INTRODUCTION TO PHYSICS CONVERTING UNITS If given units on different systems convert all units to the same system Usually this means converting to S I units EXAMPLE 1 Convert 44 lb into kg 1 kg 2 2 lb PATTERN EXAMPLE 2 Convert 100 m2 into ft2 1 ft 0 305 m EXAMPLE 3 Convert 30 m s into miles per hour 1 mi 1600 m 1 hour 3600 s PRACTICE 4 Convert 10 ft into km 1 ft 0 305 m a 0 00305 km b 327 87 km c 0 0305 km d 30 5 km PRACTICE 5 Convert 2 000 mL into m3 1 L 1 000 cm3 a 0 002 m3 b 0 2 m3 c 20 m3 d 2 000 m3 PRACTICE 6 Convert 80 km h into m s 1 km 1000 m 1 hour 3600 s a 288 m s b 28 8 m s c 4 8 m s d 22 22 m s Page 3 PHYSICS WALKER 5E CH 01 INTRODUCTION TO PHYSICS UNIT ANALYSIS aka Dimensional Analysis Equations must be dimensionally consistent Units on both sides of the equation must be the same For example from speed we can get that distance speed time Because distance is measured in meters and time in seconds speed The second equation is also dimensionally consistent distance speed time EXAMPLE 1 Suppose Wikipedia says that the distance Y in meters that an object free falls from rest in t seconds is given by Y g t2 where g is the acceleration due to gravity in m s2 Is this equation dimensionally consistent EXAMPLE 2 Hooke s law states that the restoring force F on a spring is related to its displacement from equilibrium x by F k x If F is measured in Newtons N and x in meters m what unit s must the force constant k have PRACTICE 3 If distance x is measured in m time t in s speed v in m s acceleration a in m s2 mass m in kg and force F in N kg m s2 show which of the following equations is are dimensionally consistent PRACTICE 4 Newton s Law of Gravitation states that the attraction between two objects is given by F G m1 m2 r2 where F is in kg m s2 m1 and m2 are the objects masses in kg and r is the distance between them in m What unit s must the Universal Constant G have a v2 2 a x b v2 2 a t a kg s2 m3 b m3 kg s2 c m s2 d m3 s2 c F m v2 v1 t Page 4 PHYSICS WALKER 5E CH 01 INTRODUCTION TO PHYSICS SCALARS AND VECTORS There are two types of physical quantities 1 SCALAR 2 VECTOR POSITION DISPLACEMENT DISTANCE POSITION represented by it is the displacement from the Whenever you can ask IN WHAT DIRECTION the quantity is a vector Time Length Mass Temperature Force DISPLACEMENT DISTANCE EXAMPLE 1 Find the distance and displacement for each of the following situations Case 1 1D Motion Case 2 2D Motion Case 3 Circular Motion Page 5 PHYSICS WALKER 5E CH 01 INTRODUCTION TO PHYSICS INTRO TO VECTOR MATH VECTOR COMPOSITION Because Vectors have direction doing math is not as straight forward as with scalars Adding Scalars 10 kg 20 kg Adding Vectors You move 3 m to the right 4 m up your total displacement is Since displacement is a vector we ll work on some displacement problems to illustrate how to manipulate vectors Vectors are added either graphically or algebraically Graphically is more visual duh but algebraically is faster We ll begin playing with vectors graphically Vectors are represented as arrows added using EXAMPLE 1 For each of the following draw your displacement vectors and calculate your total displacement a You walk 3 m to the right then 4 m to the right b You walk 3 m up then 4 m down Vectors in the SAME axis both X or both Y are added just like you would any numbers Just be careful with But when vectors lie on DIFFERENT axes one X one Y we must use to add them EXAMPLE 2 You walk 3 m to the right then 4 m up Draw your displacement and calculate its magnitude and direction We call this Vector because the X Y components are merged to form a 2D vector Forces are also vectors If multiple forces act on an object we can use the similar process to find the force EXAMPLE 3 A box sits on an X Y plane You pull on it with force 6 N towards the X axis while your friend pulls on it with force 8 N directed towards the Y axis Find the magnitude and direction of the NET force acting on the box Page 6 PHYSICS WALKER 5E CH 01 INTRODUCTION TO PHYSICS VECTOR DECOMPOSITION Two vectors can only be combined if 1 They lie on the SAME axis both X or Y 2 One lies on the X one lies on the Y A vector at an angle not on the X or Y must first be into its X Y components EXAMPLE 1 Each square on the grid below represents 1 meter Find the X and Y components of the vectors shown use positive negative to indicate direction Then calculate the magnitude and direction of each Unfortunately vectors typically do NOT fall on pretty grids We use to calculate vector components EXAMPLE 2 You walk 6 m to the right then 5 m directed at 37o above the positive x axis Draw your displacement and calculate its magnitude and direction If angle is 1 against the axis or …