EF 5 Final Exam, Spring, 9 Page of EF 5 Final Exam, Spring, 9 Page of Name: Section: Guideline: Aume 3 ignificant figure for all given number unle otherwie tated Show all of your work no work, no credit Write your final anwer in the box provided Include unit for all anwer Include direction for all vector Geometry/Trig a c Ueful Converion gallon = 3 cubic inche gallon = 4 quart gallon = 8 fluid ounce m 3 = L acre = 43,56 ft mile = 8 furlong mile = 58 ft fathom = 6 ft rod = 6.5 ft chain = yard inch = 5.4 mm watt = N m/ec hp = 745.7 watt (approx.) hp = 55 ft lb / ec lb = 4.45 N (approx.) m = mm g = 3. ft/ec = 9.8 m/ec C Circular Motion arc length v peed an centripetal acceleration at tangential acceleration radiu of curvature φ angle angular peed -- angular acceleration T period f frequency = ρ φ v = ρω = ρα Conervation of Energy mgh + k x + Win = mgh f f + k xf + E b A Area of a circle = πr Volume of a cylinder = πr h Law of Sine ina in inc = = a b c Law of Coine c = a + b ab coc Rocket Propulion m v = uex ln gt m t thrut = uex(dm/dt) m : initial ma mt : final ma = m (dm/dt)t dm/dt : rate of fuel burn uex : exhaut peed of gae relative to the rocket. Contant Acceleration v = v + a t v + v = + t = + v t + a t v v = + a a t a =v ρ = ρω n π T = ω f T ω = πf lo Projectile Motion g y y ( ) ( )( ) = x x tan + tan x x v launch angle v launch velocity x, y launch poition, poitive up Relative Motion v = va + v G G A v = v va A G G v = va A Force and Acceleration F net =ma Friction Fmax = µ N Fkinetic = µ kn Work W = F r = F r co Power P = F v dw P = dt Spring force F = k x Impule / Momentum / Retitution t mv = mv + Fdt t v = mv ( v v ) = (line of impact) m e v v Contant Angular Acceleration ω = ω + α t ω + ω = + t = + ω t + α t ω ω = + α Center of Ma mr + mr + + mr n n R = m + m + + mn Parallel Axi Theorem I = I + cm Mh Torque τ = Fr in τ = r F Torque and Acceleration τ Iα net = Angular Impule / Momentum Iω + I ω = Iω + I ω t Iω = Iω + τdt o L = r p L = angular momentum p = linear momentum
EF 5 Final Exam, Spring, 9 Page 3 of EF 5 Final Exam, Spring, 9 Page 4 of 3 numeric problem - 7 pt each 9 concept quetion - pt each 3. How fat i Zach going if he i moving around a 48 ft radiu curve with a total acceleration of 5 ft/ and he i lowing down at a rate of ft/?. The poition of a car driving in the African afari i decribed by the following equation: 3 S ( t) = [( 4 ˆ) jt + (5ˆ i + ˆ) jt + 3] meter. What i the magnitude of the velocity of the car at t = 3ec? 4. Shane it in a wagon (total weight 85 lb) and roll down a incline. He drag hi feet to prov ide a force of 4 lb in an attempt to low the wagon. What i the acceleration of the wagon? (FD = KD required, ue poitive parallel to and down the hill). An elevator i moving upward at a contant peed of 7.5 m/. At 3 m above the level ground, a tenni ball i hot from the elevator at a peed of 34 m/ and angle of above horizontal, relative to the elevator. How long (time) doe it take for the ball to hit the ground? (Neglect air reitance) 5. How hard mut Nate puh to keep the box moving at a contant peed? (FD required) P kg =.7 k=.6
EF 5 Final Exam, Spring, 9 Page 5 of EF 5 Final Exam, Spring, 9 Page 6 of 6. A 4 hp crane lift a 35 lb load at a contant peed to a height of 6 ft in 5 econd. How efficient i the crane in thi ituation? 8. A grocery tore paid a monthly power bill of $475. Electricity cot 9 cent per kw hr. How many Joule of energy were ued in that month? 7. A varying magnitude force i applied to a 6.5 kg object that ha an initial peed of 5. m/. The force i applied parallel to the direction of motion and i depicted a a half of a circle with a radiu of 8. What i the object' peed after 8 econd? Force (N) 3 9. (A) A very light pring hang vertically in equilibrium with no ma at it end. () A. kg ma hang from the pring in equilibrium. (C) The ma i pulled down a ditance c and releaed. (D) The ma i at the reference height moving with a peed of v=4. m/. How far down (c) wa the ma pulled before it wa releaed? (Hint you can calculate the pring contant with the given information) A C D 5. cm 5 c v 8 Time (ec)
EF 5 Final Exam, Spring, 9 Page 7 of EF 5 Final Exam, Spring, 9 Page 8 of. Two identical car collide and their bumper interlock. Each car wa moving with peed of 5 mph, one coming from the outh and the other from the eat. What i the peed of the car after the colliion?. A horizontal dik (I = 6.5 kg-m ) pin at 6 rad/ec. A. kg glob of clay i dropped vertically onto the dik and tick, reulting in a new angular peed of 3 rad/ec. How far i the clay from the center of the dik?. A baketball hit a wall with the velocity hown. The coefficient of retitution between the ball and the wall i.85. What i the peed of the ball when it leave the wall?.3 ft/ 33 3. A dik (I = 6.5 kg-m ) tart from ret and rotate freely about it center. Two contant force are applied a hown. What i the angular acceleration of the dik? (ue CCW a the poitive direction) Top View =44N r=.5 m 5 A=33N
EF 5 Final Exam, Spring, 9 Page 9 of EF 5 Final Exam, Spring, 9 Page of Concept Quetion point each circle the correct anwer. C. What i the dot product of the following vector: ( 3ˆ i + 4 ˆ) jlb,( ˆ i + ˆj + 5kˆ ) ft? A. ( 6ˆ i + 4 ˆj ) lb ft. (ˆ i + 5 ˆj + 5kˆ ) lb ft C. ( )lb ft D. (7.)lb ft E. None of the above C. If A and are vector, which of the following i NOT poible? A. A + = A +. A + < A + C. A + > A + C3. Two object are dropped from the roof of a foot tall building. oth tart from ret. Object A i lb and object i lb. Neglecting air reitance, which of the following i true? A. Object A will reach the ground firt. Object will reach the ground firt C. They will reach the ground at the ame time D. Not enough information C4. Which of the following i NOT a poible unit for momentum? A.. kg m ec N ec C. N ec D. lug ft ec C5. A particle i initially at ret when it uddenly explode into eparate, equal ma halve. After the exploion one half ha a velocity of ( 5ˆ i 3 ˆ) j m /. What i the velocity of the econd half? A. ( 5ˆ i 3 ˆ) j m /. ( 5ˆ i + 3 ˆ) j m/ C. ( 3ˆ i 5 ˆ) j m / D. ( 3ˆ i + 5 ˆ) j m/ E. Not enough information C6. A projectile ha a peed of 5 ft/ at it highet point. If it wa launched at an angle of 3 abo ve horizontal, what wa it launch peed? A. ft/`..5 ft/ C. 4.3 ft/ D. 5 ft/ E. 5.8 ft/ F. ft/ C7. A block i puhed a hown. The block doe not lide. What i N the magnitude of the friction force between the block and the floor? 6 N =.6 k =.5 A. N. N C. N D. N E. 3 N F. 36 N C8. A mall train ( engine and coal car) i accelerating at.6 ft/ on level ground with a tractive force of, lb. How doe the tractive force (T) of the engine compare to the coupling force (C) between the engine and firt coal car? A. T < C. T = C C. T > C C9. Initially, a -kg ma i whirling at the end of a tring (in a circular path with a radiu of.75 m) on a horizontal frictionle urface with a tangential peed of 5 m/. A the ma rotate the tring wrap around a vertical rod, and a few econd later the length of the tring ha hortened to.5 m. How doe the intantaneou peed at r=.5m compare to the original peed at r=.75? A. New peed < Original peed. New peed = Original peed C. New peed > Original peed