1 Course Notes in Introductory Physics Jeffrey Seguritan

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1 Intrductin & Kinematics I Intrductin Quickie Cncepts Units SI is standard system f units used t measure physical quantities. Base units that we use: meter (m) is standard unit f length kilgram (kg) is standard unit f mass secnd (s) is standard unit f time ng μc mm kj MPa Prefix Unit What Unit Measures Exercise #1: Which f the fllwing frmulas culd give the speed v (m/s) with which sund travels thrugh a medium whse bulk mdulus is B (kg-m -1 s - ) and whse mass density is ρ (kg/m 3 )? A. v = Bρ B. v = B / ρ C. D. v = v = Bρ B / ρ Vectrs & Scalars Scalars nly have magnitude. Vectrs have bth magnitude and directin. Physical Quantity Time Mass Weight Temperature Vectr r Scalar? [page 1]

2 Physical Quantity Velcity Speed Distance Displacement Acceleratin Vectr r Scalar? Hw d we add vectrs? We can use diagnal r head-t-tail methd. Head-t-tail methd V 1 + V Diagnal methd V 1 + V V V 1 Hw d we subtract vectrs? Flip (180º) the vectr being subtracted and add the tw vectrs. This is like adding the negative f a vectr. V 1 -V V 1 V [page ]

3 We ften prefer t break dwn vectrs int cmpnents. Usually, these cmpnents cnveniently lie alng the hrizntal directin (x-axis) and vertical directin (y-axis). A x A y r = A r = A csθ sinθ It is advisable t memrize the sines and csines f cmmn angles. θ sin θ cs θ = 0.50 = = 0.71 = = 0.87 = [page 3]

4 Kinematics Kinematics is the study f mtin. Imprtantly, we DON T care abut MASS. Displacement Displacement is a vectr. Psitin is merely a lcatin in space. Displacement = Psitin = psitin final psitin initial Displacement is nt the same as distance traveled. Velcity Velcity is a vectr. Velcity says hw fast an bject s psitin changes. Displacement x Average Velcity = = Time t Velcity is different frm speed. Speed is nt a vectr but a scalar. Distance Speed = Time Acceleratin Acceleratin is a vectr. Acceleratin says hw fast an bject s velcity changes. Velcity v Average Acceleratin = = Time t Can an bject accelerate if its speed des nt change? Think f the mn rbiting the Earth. D bjects always accelerate in the directin f its velcity? Think f what happens when we step n the breaks f a car. If an bject s velcity is zer, is its acceleratin zer? Think f a baseball thrwn straight upward int the air. When we try t slve kinematics prblems, we must always knw the state f acceleratin in the system. Zer Acceleratin Case x v = t Is it pssible t ever encunter zer acceleratin in a wrld always influenced by gravitatinal acceleratin? Cnstant Acceleratin Case (als called Unifrm Acceleratin) We ften encunter cnstant acceleratin because f gravity s cnstant pull. There are 3 big equatins t memrize: Equatin 1. v = v at x f +. 1 at 3. v = v + a x (mst imprtant why?) x x x v t f = f = + f v t Missing? [page 4]

5 Exercise #: If an bject released frm rest takes 3 secnds t fall t the Earth, frm what height was it drpped? A. 15 m B. 45 m C. 90 m D. 180 m Exercise #3: A particle with an initial velcity f 4 m/s mves alng the x-axis under cnstant acceleratin. Three secnds later, its velcity is 14 m/s. Hw far did it travel during thse three secnds? A. 1 m B. 4 m C. 7 m D. 30 m Exercise #4: An bject decelerated unifrmly frm an initial velcity f v m/s t a final velcity f (1/)v m/s. If the distance traveled was 1/8 m, what was its acceleratin? A. -6v B. -4v C. -3v D. -v Prjectile mtin is really just the parablic mtin f a prjectile under the influence f gravity. It can be separated int hrizntal mtin (zer acceleratin case) and free-fall mtin (cnstant acceleratin case). In rder t prperly describe prjectile, we need t remind urselves f a few things: The velcity vectr can be brken int a hrizntal and vertical cmpnent. v = v csθ, x v = v sinθ, y Hrizntal mtin is described by the zer acceleratin case, where: x = v t, x Free fall mtin is described by the cnstant acceleratin case, where we must resrt t the big 3 equatins (where a = -g = -9.8 m/s ): 1. v v gt Equatin f, y =, y + y Missing?. 1 gt v y = y f y = v, y t f y, t f, y, y 3. v = v g y [page 5]

6 What can we cnclude abut prjectile mtin? Des velcity change in the hrizntal directin? Des velcity change in the vertical directin? In what way is prjectile mtin symmetric? With respect t time? With respect t vertical velcity? What is the velcity f the prjectile at its highest pint? What is the velcity f the prjectile when it falls back dwn t the grund? Example: A cannnball is fired with an initial velcity f 1 m/s at angle f 30º with respect t the grund. Hw lng des the cannnball stay airbrne? (Ans. 1. s) Hw far des the cannnball travel? (Ans. 13 m) What is the maximum height that the cannnball reaches? (Ans. 1.8 m) [page 6]

7 We ve been assuming that there is n such thing as air resistance. What wuld prjectile mtin lk like if air resistance was cnsidered? Als realize that prjectile mtin appears in different frms: 30º V = 10 m/s Exercise #5: An bject is prjected upward at a 30º angle with the hrizntal with an initial speed f 0 m/s. Hw lng will it take t reach the tp f its trajectry? A. 0.5 s B. 1.0 s C. 1.5 s D..0 s Exercise #6: An bject is prjected upward at a 60º angle with the hrizntal with an initial speed f 30 m/s. Hw far will it travel hrizntally in its first three secnds f flight? A m B m C m D m [page 7]

8 It is imprtant t understand the mechanics and relatinships between kinematic graphs in rder t extract essential infrmatin such as displacement, velcity and acceleratin. Graph Slpe Area Under Curve Displacement vs. Time Velcity vs. Time Acceleratin vs. Time [page 8]