Week 1 Notes - Scientific Method/ Scientific Notation PDF

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Scientific Method/ Scientific Notation...

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Physics 110 John Graham

Scientific Method: 1. Make and Observation 2. Form hypothesis - generalization 3. Perform an experiment a. Model and theory – more specific than hypothesis b. Make measurements c. Form conclusions Model: analogy – representation of a phenomenon in terms of something familiar Theory – more detailed w quantitatively testable prediction Law – general statement that has been tested experimentally and is broadly valid Principle – a more specific law

Measurement – Significant figures – - Multiplication/division -result should have no more sig figs than the number in the calculation having the fewest sig figs - Addition/subtraction - result should have the same number of decimals places as the number in the calculation having the fewest decimal places Scientific Notation - 9,473  9.473 x 10^3 - 0.0095  9.5 x 10^-3 Precision is NOT = accuracy Precision – how repeatable an experiment is using a given instrument Accuracy – how close a measurement is to the true value SI Unit : systeme international - Mars climate orbiter – 1999: software provided output in US customary instead of SI unit – $327M loss - Length – meters (m) o 1,000m = 1 km (kilo = 103) o 0.1 m = 1 dm (deci = 10-1)

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o 0.01 m = 1 cm (cent = 1-2) o 0.001m = 1 mm (milli = 10-3) o 0.000001 = 1 Mm (micro = 10-6) o Nano = 10-9 o Pico = 10-12 o 1A = 10-10 (antrum) Time – seconds (s) Mass – kilogram (kg) o 0.001 kg = 1 gram (g) o 0.000001 kg = 1 milligram (mg) Temperature – Kelvin (K) o Celsius = °C

Unit Conversion - 5,280m = 5.28 km o 5,280m x 1km 1,000m - How many cm are in 1in ? o 2.54 cm/in - How many m are in 1 in? o 0.0254m/in - 357 in = 906.78 cm = 907 cm (sig fig) - 907 cm = 9.07 m Reference Frames - Where you are relative to what you are observing - If you are on the bus, what speed will you measure the person sitting to be traveling at ? 0m/s - Bus is traveling at speed (v) while you are on the sidewalk. What speed do you measure for the person sitting on the bus? The speed is (v) o Same situation, but person on bus walking forward toward the front of the bus w speed V2? V + V2 - Can choose reference frame for convenience - 1D (1 dimensional) motion – use only x-axis o +x  o +Y ^ Distance Traveled v. Displacement - Distance traveled is the total distance covered in an action - Displacement has magnitude and direction – a vector - Distance traveled has only a magnitude – scalar - Delta x = displacement - Delta x does not always have to be >0

- Distance traveled = X1 +(X1-X2) Velocity – has magnitude and a direction (vector) Speed – only has magnitude Average speed – (distance traveled/time elapsed) Bar over a variable indicates it is the average of that variable Arrow over variable to indicate it is vector Delta = the change in ___ Speed will always be > 0 Average velocity = (displacement/ time elapsed) Instantaneous velocity - Units: meters/second - Velocity measure over an infinitesimally small-time interval - V = limit as delta T goes to 0 = (Delta X/Delta T) - Instantaneous speed = |instantaneous velocity| - V= |V|(vector) - When an object moves at a constant velocity for a time (delta T) the velocity is constant o V= Vbar - Average velocity = (V1 +V2)/2 Acceleration – change in velocity in some time interval - Units: meters/second2 - Abar = Delta V/Delta T - Ways that velocity changes o Speed up -positive accel, slow down – negative accel (deceleration) o Change in direction – can be without change in magnitude - Instantaneous acceleration = DeltaV/DeltaT - Deceleration o Relationship between v and a during deceleration  V and a are opposite in direction  V+  A-  Motion at constant acceleration - A=Abar - Vbar = DeltaX/Delat T = x-x0 / t-t0 = x-x0/t - A=abar= DeltaV/DeltaT = V-V0/T-T0 = V-V0/T

Determine the velocity (v) after moving some time (t), at constant acceleration 1. V-V0 = a (t)  V = V0 (a)(t) 2. Position: x = x0 +Vbar(t) 3. Since a is constant, delta V is unifiorm a. So Vbar = VfinalV0 / 2  

Then substitute 3 and 1 into 2 to get X = X0 V0 t +(1/2) a t2 If time is not known combine 2 and ,solve 1 for t anf substitute into the combined equation (2 +3) to get ------- V2 = V02 +2a(X-X0)

1-D kinematic equations – constant acceleration  get X = X0 V0 t +(1/2) a t2  V = V0 + (a)(t)  V2 = V02 +2a(X-X0)  Vbar = VfinalV0 / 2

Drove speed of car to 340mph in 1,000ft from a dead stop. How long did the trip take?  340 mph =  1,000 ft = 0.189 miles  1,000ft = 304.8 meters (340miles/1hr) (580ft/mile) (12in/ft)(0.0254m/1in)(1hr/3600s) = 151.9 m/s V2 = V02 +2a(X-X0) 151.92 = 0 +2a(304.8) A = 37.85 m/s2 V = V0 + (a)(t) 151.9 = 0+(37.85) t T = 4.01 seconds    

deltaX = 1,000 ft V = 340mph T=? V0 = 0 m/s The trip took about 4 seconds Actual speed 339.87 mph Actual time 3.8 sec...