Q x = cos 1 30 = 53.1 South

Transcription

1 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q1. A particle mves in ne dimensin such that its psitin x(t) as a functin f time t is given by x(t) = t t, where t is in secnds and x(t) is in meters. At what psitin des the particle change its directin f mtin? A) 56 m B) 54 m C) 7 m D) 81 m E) 100 m dx = 0 = 7t t dt t =.0 s x(t) = t t x() = ( + 7 7)m x() = ( )m = 56.0 m Q. What is yur ttal displacement when yu fllw directins that tell yu t walk 40.0 m nrth then 0.0 m east? A) 50.0 m, 5.1 Nrth f East B) 50.0 m, 5.1 East f Nrth C) 50.0 m, 45.0 East f Nrth D) 45.0 m, 45.0 East f Nrth E) 45.0 m, 0.1 Nrth f East West 40 cm Nrth 0 m D θ x East D = 0 i + 40 j m D = 50.0 m Q x = cs 1 0 = Suth

2 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page Q. A prjectile is fired frm the grund with an initial velcity v (0.00 ˆ 19.6 ˆ = i + j) m/s. Find the hrizntal distance the prjectile travels befre hitting the grund. A) 10.0 m B) m C) m D) m E) 400. m v 0x = 0.0 m/s ; v 0y = 19.6 m/s Time t reach grund: 0 y = 19.6 t 1 gt t = 19.6 = 4.0 s 9.8 x = v 0x xt = ( ) = 10.0 m Q4. There are tw frces n the.00 kg bx in the verhead view f Figure 1, but nly ne is shwn. Fr F 1 = 0.0 N, a = 1.0 m/s, and θ = 0.0, find the secnd frce in unit vectr ntatin. A) ( 8.0 N) iˆ+ ( 1. N) ˆj B) ( 51. N) iˆ ( N) ˆj C) ( 8.0 N) iˆ+ ( + 1. N) ˆj D) ( N) iˆ+ ( + 1. N) ˆj E) ( 1. N) iˆ+ ( 8.0 N) ˆj F 1 + F = ma 0.0 i + F = Sinθ i 1.0 cs θ j = i j N = 18.0 i 1. j N F = 0.0 i 18.0 i 1. j N F = ( 8.0 N) i + ( 1. N) j Fig# 1

3 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page Q5. A blck slides with a cnstant acceleratin dwn a rugh plane inclined at an angle f 40.0 with the hrizntal. If the blck starts frm rest and slides a distance f 9. m dwn the plane in 4.00 s, calculate the cefficient f kinetic frictin between the blck and the plane. A) B) 0.15 C) 0.15 D) E) θ f k mgsinθ µ k mgcsθ = ma a = gsin40 0 µ k gcs40 = µ k a = µ k x = v 0 t + 1 at 9. = ( µ 8 k) = µ k µ k = Q6. A 100-kg parachute falls at a cnstant speed f 1.00 m/s. At what rate is energy being lst? A) 980 W B) 19.8 W C) 89.0 W D) 49.0 W E) 490 W P = mgv = = 980 W

4 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 4 Q7. The wrk dne by a cnservative frce acting n a bdy A) des nt change the ttal energy. B) des nt change the ptential energy. C) des nt change the kinetic energy. D) is always equal t zer. E) is always equal t the sum f the changes in ptential and kinetic energies. A Q8. The velcity f a given bdy is increased t such an extent that the kinetic energy f the bdy is increased by a factr f 16. The mmentum f the bdy is increased by a factr f: A) 4.0 B) 16 C) 8.0 D).0 E) 1.0 k i = 1 mv 1 = P 1 m k f = 1 mv = P k f = P k i P 1 4 = P P 1 P = 4.0 P 1 m

5 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 5 Q9. A.0-kg thin lp has a radius f.00 m and is rtating at 80 rev/min abut its central axis. What is the average pwer required t bring it t a stp in 0.0 s? A) W B) W C) W D) W 1 E) W ω i = 80 rev rad min π = 9. rad/s min rev 60 s I = MR =.0 (.0) = 18 kg. m P = W t = k t = 1 I (ω f ω i ) = 0.5 P = W 1 18 (9.) 0 J / S Q10. A unifrm slid sphere rlls dwn an incline. What must be the incline angle if the linear acceleratin f the center f the sphere is t have a magnitude f 1.96 m/s? A) 16. B) 45.0 C) 0.0 D) 60.0 E) 5.4 a = g sin θ I + I = MR g sin θ 1 + MR = 5 MR gsinθ 7 5 a = 5 7 gsinθ 1.96 = sinθ 7 sinθ = 0.80 θ = 16.6 = 16.

6 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 6 Q11. A unifrm beam is held in a vertical psitin by a pin at its lwer end and a cable at its upper end (see Figure ). The tensin in the cable is 7.0 N. Find the hrizntal frce F acting n this beam. Fig# A) 99.8 N B) 10 N C) 65.0 N D) 15 N E) 50. N τ 0 = 0 5 F = 7 cs cs 0 8 F = = N = 99.8 N 5 Q1. A meter stick balances hrizntally n a knife-edge at the 50.0 cm mark. With tw 5.00 g cins stacked ver the 10.0 cm mark, the stick is fund t balance at the 45.5 cm mark. What is the mass f the meter stick? A) cm kg B) 78.9 kg C) kg D) kg E) kg 0 cm mg 45.5 Mg 100 cm τ 0 = 0 mg ( ) = Mg ( ) (5.5) = M (4.5) M = (5.5) 4.5 = kg

7 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 7 Q1. A 1-gram bullet is fired int a gram wden blck initially at rest n a hrizntal surface. After impact, the bullet is imbedded inside the wden blck which slides 7.5 m befre cming t rest. If the cefficient f frictin between the blck and the surface is 0.65, what was the speed f the bullet immediately befre impact? A) 91. m/s B) 49.0 m/s C) 5.0 m/s D) 100 m/s E) 190 m/s v b m b V B = g M B d = 7.5 m µ k = 0.65 m b v b = (m b + M B )v (1) k + u g = W nc () 0 1 (m b + M B )v = µ k (m b + M B )gd v = µ k gd = 9.77 m/s Frm equatin (1): 1 10 v b = v b = 91. m/s Q14. A certain wire stretches 1.00 cm when a frce F is applied t it. The same frce is applied t a secnd wire f the same material with equal length but with twice the diameter. The secnd wire stretches: A) 0.5 cm B) 4.0 cm C).5 cm D) 0.50 cm E).0 cm F 1 A 1 = E L 1 L 1 F A = E L L F A 1 = L L 1 F 1 A L 1 L L = A 1 A L 1 = 1 4 L 1 = 0.5 cm

8 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 8 Q15. A cube f vlume 1.0 m is made f material with a bulk mdulus f N/m. When it is subjected t a pressure f Pa, the magnitude f the change in its vlume is: A) m 4 B) m 4 C) m D).5 10 m E).4 10 m P = B V V V = P V B = = m V = m Q16. Let the acceleratin due t gravity n the surface f Earth be g E. The acceleratin due t gravity (g p ) n the surface f a planet whse mass is equal t that f Earth but whse radius is nly R E is given by (R E is Earth s radius) A) g p = 100 g B) gp = 10.0 g C) gp = 50.0 g D) gp = 5.0 g E) gp = 1.00 g E E E E E g e = GM e R g p = GM p R p g p = 100 g e g p g e = R e = R e R p 0.1R e

9 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 9 Q17. A slid unifrm sphere has a mass f kg and a radius f 1.00 m. What is the magnitude f the gravitatinal frce due t the sphere n a particle f mass m = 1.00 kg lcated at a distance f m frm the center f the sphere A) N 5 B) N C) N 5 D) N 8 E) N r m R M M F = GmM r M M = 4 πr 4 πr = Mr R F = GmMr R = (1.0) = N Q18. Figure gives the ptential energy functin U(r) f a prjectile, pltted utward frm the surface f a planet f radius R s. What kinetic energy is required f a prjectile launched at the surface if the prjectile is t escape the planet? Fig # 9 A) J 9 B) J 9 C) J 9 D) J 8 E) J K + U = 0 K = U k f k i = (U f U i ) k i = (0 U i ) k i = U i k = J

10 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 10 Q19. A satellite travels in a circular rbit arund a certain planet. The rbit has a radius f m and a perid f 8.0 hurs. What is the mass f the planet? T = 4π GM r A) kg 0 B) kg 17 C) kg 6 D) kg 9 E) kg M = 4π GT r = (4) (8 600) = kg Q0. A 50-kg spaceship is in a circular rbit f radius.00 R E abut the earth. Hw much energy is required t transfer the spaceship t a circular rbit f radius 4.00 R E? (R E is the radius f the earth)? 8 A) J 11 B).5 10 J 14 C) J 5 D) J 1 E) J E i = G mm E (.00R E ) ; E f = G mm E (4.00R E ) E = G mm E R E = + G mm E R E 1 1 E = G mm E = R E E = J J

11 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 11 Q1. Find the pressure increase in the fluid in a syringe when a nurse applies a frce f 1.4 N t the syringe s circular pistn, which has a radius f 1.00 cm. P = F A = A) Pa 4 B) Pa C) Pa 6 D) Pa E) Pa 1.4 N π(10 ) = N/m Q. In Figure 4, a spring f spring cnstant N/m is between a rigid beam and the utput pistn f a hydraulic lever. An empty cntainer with negligible mass sits n the input pistn. The input pistn has area A, and the utput pistn has area 0 A. Initially the spring is at its rest length. Hw many kilgrams f sand must be (slwly) pured int the cntainer t cmpress the spring by 4.00 cm? A) 10. kg B) 100 kg C) 9.80 kg D) 980 kg E) 50 kg F 1 A 1 = F A = kx A F 1 = kx A 1 A F 1 = A 0 A m = F 1 = = 10 g kg = 10. kg Fig # 4

12 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q. A hllw spherical irn shell flats almst cmpletely submerged in water. The uter diameter is 50.0 cm, and the density f irn is 7.87 g/cm. Find the inner diameter. A) 47.8 cm B) 1.5 cm C) 15.5 cm D) 7.87 cm E) 5.0 cm ρ f V submerged g = ρ 0 V 0 g π(50) = π(50 r in ) r ut r in (50) = 7.87(50 r in ) r in = (50) (50) 7.87 r in = 47.8 cm Q4. Tw streams merge t frm a river. One stream has a width f 8.0 m, depth f 4.0 m, and current speed f.0 m/s. The ther stream is 7.0 m wide and.0 m deep, and flws at 4.0 m/s. If the river has a width f 10.0 m and a speed f 4.0 m/s, what is its depth? A).7 m B) 4.0 m C).0 m D) 8.0 m E) 7.0 m A 1 v 1 + A v = A v = 10 d = 40 d d =.7 m

13 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q5. A liquid f density kg/m flws thrugh a hrizntal pipe that has a crsssectinal area f m in regin A and a crss-sectinal area f m in regin B. The pressure difference between the tw regins is Pa. What is the mass flw rate between regins A and B? A 1 v 1 = A v A) 91. kg/s B) 87. kg/s C) 857 kg/s D) 576 kg/s E) 100 kg/s 10 v 1 = v v 1 = 5v P ρv ρgy 1 = P + 1 ρv 0 + ρgy P P 1 = 1 ρ(v 1 v ) = v v = v v = 10 1 v = 10 = 0.91 m/s 1 Mass lw rate: = A v ρ = 91. kg/s

14 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 14 Q6. What is the phase cnstant fr the harmnic scillatr with the velcity functin v(t) given in Figure 5 if the psitin functin x(t) has the frm x(t) = x m cs(ωt + φ)? The vertical axis scale is set by vrs= 4.00 cm/s. Fig# 5 A) 5.1 B) +5.1 C) 5.4 D) +5.4 E) 40.0 Frm Fig. v s = 4, v = 5 4 v s v = = 5 cm/s x = x m cs(ωt + ϕ) dx dt = x mωsin(ωt + ϕ) v s = vsin(ωt + ϕ) 4 = 5sin(ϕ); t = 0 sin(ϕ) = 4 5 ϕ = sin 1 ( 4/5) = 5.1

15 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 15 Q7. If the phase angle fr a blck-spring system in SHM is π/6 rad and the blck s psitin is given by x(t) = x m sin(ωt + φ), what is the rati f the kinetic energy t the ptential energy at time t = 0? A) B) 1/ C) 9 D) 1/9 E) 5 x (t) = x m sin(ωt + ϕ) ; v = ωx m cs(ωt + ϕ) U = 1 kx = 1 kx m sin (ϕ) k = 1 mv = 1 mω x m cs(ϕ) = 1 k x m cs (ϕ) k U = csϕ sinϕ k U = π = cs 6 sin π 6 Q8. Find the mechanical energy f a blck-spring system having a spring cnstant f.0 N/cm and an scillatin amplitude f.0 cm. A) J 1 B) J C) 1 10 J + D) 1 10 J E) J E = 1 kx m = 1.0 N cm 10 cm 1 m ( 10 m) = = 9 10 J E = 9 10 J

16 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 16 Q9. In Figure 6, a stick f length L = 1.7 m scillates as a physical pendulum. What value f x between the stick s center f mass and its pivt pint O gives the least perid? Fig# 6 A) 0.50 m B) 0.87 m C) 1.7 m D) 0.58 m E) 0.4 m T = π I mgd ; d = x I = 1 1 ml + mx 1 T = π 1 ml + mx mgx 1 1 T = 4π 1 ml + mx mgx T = 4π g 1 1 L x 1 + x T dt dx = 4π g 1 1 L x = 0 L 1x = 1 x = L 1 = (1.7) 1 r x = 0.49 x = m

17 Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 17 Q0. Figure 7 shws the kinetic energy K f a simple pendulum versus its angle θ frm the vertical. The vertical axis scale is set by K s = 0.0 mj. The pendulum bb has mass 0.0 kg. What is the length f the pendulum? Fig# 7 A).04 m B) 1.5 m C).5 m D) m E).05 m θ = rad = 5.7 k max = U max = mgl(1 csθ) 0 10 = (0.0)(9.8)(L)(1 Cs 57 ) 0 10 = (0.0)(9.8)(L)( ) L = 0 10 (0.0)(9.8)( ) L = m =.04 m