Physics 110 Spring 010 Exm #1 April 16, 010 Nme Prt Multiple Choice / 10 Problem #1 / 7 Problem # / 7 Problem #3 / 36 Totl / 100 In keeping with the Union College policy on cdemic honesty, it is ssumed tht you will neither ccept nor provide unuthorized ssistnce in the completion of this work.
Prt I: Free Response Problems Plese show ll work in order to receive prtil credit. If your solutions re illegible no credit will be given. Plese use the bck of the pge if necessry, but number the problem you re working on. Ech subprt of problem is worth 9 points. 1. A Boeing F/A-18 Super Hornet with mss of 30,000kg lnds on the deck of n ircrft crrier t speed of 140 mi/hr (~63 m/s) nd is brought to rest by n rresting cble (shown t the very bck of the ircrft) tht is stretched cross the deck of the crrier s shown in the figure below.. If the jet needs to be brought to rest in 1.5s, wht re the minimum force nd ccelertion exerted by the rresting cble? v fx = v ix + x t 0 = 63 m s x( 1.5s) x = 4 m s = m x = 30,000kg 4 m =1.6 10 6 N s ircrft., both opposite the lnding zxfzdfsdfsdf Arresting cble b. From the time the jet hits the crrier deck, how fr does it trvel before coming to rest? Δx = v ix t 1 t x = ( 63 m 1.5s s ) 1 ( 4 m ) ( 1.5s) = 47.3m s c. Of course in order to lnd the jet, it must hve tken off from the crrier. A stem ctpult locted on the front of the flight deck lunches the plnes. Suppose tht the plne needs to be lunched from rest to 63 m/s. If the flight deck is 100m long, wht is the time it tkes to lunch this plne nd wht re the mgnitudes of the ccelertion nd force needed to lunch this plne? v fx = v ix + x Δx x = v fx Δx = = m x = 30000kg 19.9 m s Δx = 1 x t t = ( 63 m s ) 100m =19.9 m s = 5.95 10 5 N Δx x = 100m 19.9 m s = 3.s in the direction of lunch.
. In locl br, customer slides n empty beer mug down the counter for refill. The brtender is momentrily distrcted nd does not see the mug, which slides off the counter nd strikes the floor 1.40m from the bse of the counter. Suppose tht the height of the counter is 0.86m bove the floor.. Wht ws the speed of the mug when it leves the counter? b. Wht is the impct velocity of the mug just before the floor? c. How long does it tke the mug to rech the floor?
3. Suppose tht you re given the rrngement of msses shown below where the left mss m L = 1kg, center mss m C = ½ kg nd the right mss m R = 4kg. The msses re on frictionless surfces nd re relesed from rest. You my ssume tht the center mss moves to the right.. Drw crefully lbeled force digrm showing ll of the forces tht ct on ech mss. You cn drw these on the digrm below, but be sure to specify coordinte system for ech mss. The tringulr mss on the left is on n incline tht is oriented t 51 o with respect to the horizontl. F TL F TL F NC F NL F WC F WL F WR b. Wht is the mgnitude of the ccelertion of the system? m C : m R : m L : : F TL = m c : m R g = m R = m R g m R : F TL m L gsinθ = m L F TL = m L gsinθ + m L F TL = m R g m R m L gsinθ m L = m c = m R g m L gsinθ m L + m C + m R = ( ) ( 1kg 9.8 m sin51 s ) 4kg 9.8 m s 5.5kg = 5.74 m s c. Wht re the mgnitudes of the tension forces tht ct on the left (F TL ) nd right ( ) sides of the center mss? = m R ( g ) = 4kg 9.8 m 5.74 m s s ( ) =16.N ( ) =13.4N F TL = m L ( gsinθ + ) =1kg 9.8 m sin51+ 5.74 m s s d. How long does it tke the center mss to move 0.5m nd how fst is the rightmost block moving fter it hs trveled 1.m? Δx = v ix t + 1 xt t = Δx x = 0.5m 5.74 m s = 0.4s v fx = v ix + Δx v fx = Δx = 5.74 m 1.m = 3.7 m s s
Prt II: Multiple-Choice Circle the best nswer to ech question. Any other mrks will not be given credit. Ech multiple-choice question is worth points for totl of 10 points. 1. In the digrm below, the block of mss m is pulled to the right by n pplied force F A oriented t n ngle θ bove the horizontl nd the block experiences n ccelertion. The mgnitude of the frictionl force is given by. F A sinθ m b. F A cosθ m c. F A cosθ + m d. F N F A m. Suppose tht you stnd up quickly nd ccidentlly bump your hed on hevy object locted bove your hed. The greter force of impct will be. on the your hed. b. on the hevy object. c. the sme for both. d. unble to be determined with the informtion given. 3. Suppose tht n object trvels in three steps. In the first step the object covers 100m in 10 seconds in the negtive x-direction then the second step hs the object decelertes to rest from velocity of 10 m/s in 10 seconds nd third step hs the object trveling 150m in the positive x-direction for 5s. For the entire trip, the verge velocity of the object is. -4.8 m/s b. 0 m/s c. 9.8 m/s d. 1.7 m/s 4. Suppose tht 10,000kg block is sitting on horizontl frictionless surfce. A 0.01kg wsher is connected to the block by string pssing over pulley tht is ttched to the block. If the wsher is relesed from rest, the ccelertion of the block is. equl to 0 m/s b. 0 m/s < < 9.8 m/s c. greter thn 9.8 m/s d. unble to be determined. 5. Two mrbles sitting on tbletop. One is dropped from rest verticlly (mrble A) nd the other shot horizontlly off the tble (mrble B). Compred to mrble B, the ccelertion of mrble A s is. the sme. b. greter. c. less. d. unble to be determined.
Useful formuls: Motion in the r = x, y or z-directions Uniform Circulr Motion Geometry /Algebr r f = r 0 + v 0r t + 1 rt r = v r Circles Tringles Spheres v fr = v 0r + r t F r = m r = m v v fr = v 0r + r Δr v = πr T F G = G m 1m r r C = πr A = 1 bh A = 4πr A = πr V = 4 3 πr3 Qudrtic eqution : x + bx + c = 0, whose solutions re given by : x = b ± b 4c Vectors Useful Constnts g = 9.8 m s G = 6.67 10 11 Nm kg N A = 6.0 10 3 toms mole σ = 5.67 10 8 W m K 4 k B = 1.38 10 3 J K v sound = 343 m s Liner Momentum/Forces Work/Energy Het p = m v K t = 1 mv p f = p + i F Δt K r = 1 Iω F = m F s = k x U g = mgh U S = 1 kx F f = µf N W T = FdCosθ = ΔE T W R = τθ = ΔE R W net = W R + W T = ΔE R + ΔE T ΔE R + ΔE T + ΔU g + ΔU S = 0 ΔE R + ΔE T + ΔU g + ΔU S = ΔE diss Rottionl Motion Fluids Simple Hrmonic Motion/Wves ω = πf = π T T S = π m k T P = π l g Sound v = ± k m A 1 x A ( ) = Asin( πt ) x t v( t) = A k m T 1 πt cos( T ) ( t) = A k πt sin( T ) m v = fλ = F T µ f n = nf 1 = n v L I = π f ρva