Calculus Based Physics I
Calculus Based Physics I PHYS 2110
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This 13 page Class Notes was uploaded by Mrs. Charity Bradtke on Wednesday October 28, 2015. The Class Notes belongs to PHYS 2110 at Volunteer State Community College taught by Timothy Farris in Fall. Since its upload, it has received 14 views. For similar materials see /class/230704/phys-2110-volunteer-state-community-college in Physics 2 at Volunteer State Community College.
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Date Created: 10/28/15
Ch 15 Oscillatory Motion 151 Motion of an Object Attached to a Spring Consider a mass m on a springHooke39s Law F kx l This IS called a linear re rmg force N34 LTgt Fr 3 ca I 1390 lm kx ltX I axr 77quot a U axubx thx Anytime we have a linear restoring force the acceleration amp F is directly proportional to the negative of the displacement In this case the movement will besimple harmonic motion shm 152 Simple Harmonic Motion 2 a x Propose x e A on EH Agt Lh fkh La OMGJs dnaalquot 4r 1u n 7 Le 13 2 P k LMJJbvf JL Hal a mu MormonBlunts Cola A m mk f39Q T3 7 ya 39 r us4 mg e a55 Am Cut4 gt2 L3quotX Q J M For the spring L kM 05 Period T time for complete oscillation l 1 p T zyg 71quot39 D7 2 a 1 93quot T 2 1 Ul ll The frequency f is the of cycles oscillations per second measured in hertz Hz or s39 t 77 t wlv 5 w 14 ikviw rs NOTE Arguments of sines amp cosines must be in radians Check your calculators We said that quotAquot was the amplitude of the position or the maximum displacement from equilibrium x LH A m ml HQ What are the corresponding maximum velocity and acceleraton u69 w5c ampAu4 4L4 g an u Ptg M 6x Uquot Vm x w A sz H MAY 4 I ahak Example A 300kg mass oscillates on a spring with a period of 200 s lt39s released from its maximum extension of 500 cm a Find the amplitude and angular frequency of its motion a I gt 339 a l L Aoo LL 4 A 1n w 9 9 1 carnu b Find the phase angle lt uwmmwwerMWQ 5259 m 2 1 3 te0 c Write down the function that represents the position as a function of time He 4 w Lu 2 Ww9mua d Write down functions for the velocity amp acceleration fa s 1 m4 4 147 15 E 500 Wth z lt41 6quot l CXI U Q 1463 xLat 3 L M Vang l fJ l a 04m l 51 u Feb 7 Sat Olympiad Apr 2 Thursday Science amp Math Expo HW due Wed Jan 21 Ch 15 pp 476477 P3 7 9 11 15 16 74 Work Done by a Varying Force continued Particular case Force exertedgl a stretched or compressei spring and the work done to stretchcompress it lt r Frrww I W Huhquot 39 quot 3quot x3 9 PF 39l 3 quotquot7 a II r P sjfAJ Ltuquot quotkquot is called the quotspring constant It39s a measure of a particular spring39s stiffness To stretchcompress the spring the applied force must 5 g F 4 L17 A m So the work done in stretchingcompressing the spring is w 51 FA l39quot h 3 395 0 In L 3 2 Mirquot 2 Example A door spring with k 380 Nm is stretched 60 cm Calculate the work done on the spring in doing so 75 Kinetic Energy amp the WorkKinetic Energy Theorem Go back to a constant force w pig A TEz st o39 393 t I U3 byquot 439 Zn 6 lt 7 u 1u 45 L quot7 Uquot Define the kinetic energy 5 of an obejct with mass m moving at a speed ofv as Ki 3er This is the workkinetic energy theorem Example A 140g baseball moving at 500 ms receives 150 J of work done on it by an outside force to change its speed How fast will it be going afterwards AJ k439k 1 t 4 KL iM l 4 34H 7 Kit EMU J1 amp1 mul 397 quot339 s 7rT K42 Wake lJioT Instr 39 IL 1rquot LEW 1 q imp ZIL Z i n L 2 4M 01901 n m 54i 76 NonIsolated Systems amp Conservation of Energy Reread this carefully 77 Situations with Friction The kinetic energy can be reduced by frictional forces AK guilty Example A 60N force is applied to a 30kg block to slide it 50 m across the floor If it starts from rest how fast will it be going after the 50 m The coefficient of kinetic friction between the block amp floor is 035 g w w Ll W s o quot 5 W w MV r sue r my 917 IntIL I 504 417 bank a r p A 97 quot h 3 74 v3 I 1 03 3aLvgt xru 11171 Azu raw m 2s1 am 4 K 292 Jzmr litanyr 22 uquot 39 We Hull 3 78 Power Power is the rate at which work is done A quotW quot 4 wA t39 be K 1 1Y f hue ow 444 4 1 napL x hm AWquot 57 oval 1 w 10 a H Note that for a constant force 5 r as Liraw F A 0 Units the watt W 1v1Tl I Lnrgpu r VY W Example How much work is done in mowing the front yard Using a 12hp mower it takes you 20 minutes 1200 s f a Wf 39t 7 llWlt1y 21er W I 795 5 7n72o k 101 u quot7 w HMquot
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