NYA final exam - May 1999 (with answers) - 1 PHYSICS 203 =1...

Unformatted text preview: 1 PHYSICS 203 =1 01-73 FINAL mm. MAY 17, 1999. ANSWER ANY E“ OF THE TWELVE BUES'HOHS. 1-] Giventheiwovectors: __3 A' A . 4 A=2i-4i+4k a c_:t«3+5& =-i+3j+k .J_,‘- _ 0 Find a} Thevectorc=A+B , ibis-Q" 35? A b) Theanglebetweennandc f, —a —.~_H «fl 4 c] Thecross-pfoductoanndB LJfiXBm lél «417er The diagram on the left is the velocity-time ' graph of a particle. moving along the x-axis. The particle ts at the origin at t = 0. a) During which time-intervals is the speed of the particle increasng 9' i b] During which time-intervals is the velocity of the particle increasing ? c] What is the acceleration of the particle at t = 55? d) At what time is the particle at its maximum _ distance from the origin? 0‘) C's-"’43 A’VD 53“”63 e) Whatisthlsmaximumdlstance? b) 05 —e L}- 5 (4404751 0025,”. e) 254" 3.] A car and a truck are 120 m apart on a straight road. as shown in the drawing below. The car ls ‘ traveling to the right at 20 mls and is slowing down at the rate of 2.0 mlsz. The truck is traveling to the left at to mis and Is speeding up at the rate of 3.0 mls’. a] When and where do the two vehicles pass each other? [Give the distance from point A In the figure) ' - b) What are the velocities of the car and the truck the instant they pass each other ‘? A rim ——-—~> 4.... m a) 3'3 S J 58%“ b) 71;: iZ-Lrhé 743':—2r-lr”7s h 54 'lli An airplane. diving at an angle of 37“ below the horizontal drops a bag of food from an altitude of 800 m. The bag strikes the ground 5.05 after it had been released from the plane. a} What was the speed of the plane as thebag was released? ' b] How far does the bag travel horizontally during its fall '? c) Find-the velocity of the bag [ its horizontal and vertical components) 10st before it strikes the ground. a) £135 ‘75 m')74::‘li'é”"/5 I (Roz-0" A 3.0 kg mass and horizontal surface and a 1 .0 kg ‘ mass on a 37° incline are attached to each other. as shbwn. The horizontal surface and the pulley are frictionless and the coefficient of kinetic friction between the 1 .0.kg mass and the incline is 1!. =0.2 The i .0 kg mass is pulled by a force F parallel to the incline. a] If F = 20 N. what is the tension in the connecting cord '2 . b] What is the acceleration of the system ? 6.) Acar is driven over a hill: the top of the hill can be - approximated by a circle of radius 250 m. as shown on the left. ' a] Draw a free body diagram for the car as it passes the top of the hill. b] lithe car and rider weigh 500 kg. and the speed of the car is 30 mls find the force. exerted on the car by the road at the top of the hill. c] What is the greatest speed the car can have without -leavlng the road at the top of the hill? a) ‘1"l-5 "~75 7.) The weight W = 20 kg ls supported by Three ropes as shown. Rope #1 makes an angle of 60° with The ceiling and rope #2 makes an ‘ angle of 60 0 with the well, All three ropes are attached too small ring. as shown. 0) Draw a free body diagram for The ring. b) Find the tension in all Three ropes. Illli ii- 8.) A vertical spring of negligible mass and spring ‘ constant k = 1000 N/m has a small object of mass 1 V M = 5.0 kg placed on its Top. The spring ls held Ir ' compressed by a distance D = 25 cm from its equilibrium position, as shown in figure (a). if the _ system is released from rest find The speed of The mass as it passes through The equilibrium position In figure (is). (Use g =.9.6 m/sz) ' 2- re a» (a) (in) /S 9) A 25 kg box is pulled up a 20 m long and 3.0m F high ramp by a constant force F = 120 N parallel To The ramp. if the box starts from rest at the bottom /1 of the ramp and reaches The top with a speed of in m 3m 2.0 m/s, find The coefficient of kinetic friction / t between the box and the ramp. ' to) A bullet of mass = 20.09 ls fired with a mute velocity of 600 m/s from a hunting rifle. The mass of The rifle is 5.0 kg. 0) Find the recoil velocity of The rifle. b) if The rifle is stopped in a distance of 4.0 cm by The shoulder of The hunter. find the . average force exerted on The shoulder by the rifle. _ c) Find the impulse delivered 7 cuanfflh/S b} 3,60.” ' c) TZN—S .1 i.) A 4.0 kg hard rubber ball. moving To The fight at 4.0 m/s collides with a stationary 6.0 kg hard rubber ball. as shown below. it This is an elastic collision, calculate The final velocities of both balls. using first principles. Shaw all your work! v1=4mls v2='0 v"='? v2,=? I before The collision after The collision (b‘: 3-2 0'75 '2—0-800'4'1/5 6 4* 12.) A solid wheel (made of Two disks mounted on the same axis) has a moment of inertia I = 0.4 kgm2 and is free To rotate without friction about its axis Through point 0. A rope wrapped around its outer radius, R1 = 0.25 m exerts 12.0 N a downward force of 9.0 N on The right side of The wheel. A second rope. wrapped around the smaller disk of radius 93 N 2 = 0.10 m exerts a force of 12.0 N. directed perpendicular to R2 . as shown a) Find The Torque due to each of The two forces and find the net Torque on the wheel. b) Find The angular acceleration or of the wheel. c) How many revolutions will the wheel make in i 2.0 s -°\)CEI:—2-7—5Mm T=l-2.Mm Twig-1.05 MW 1. 13) «2—2-43 flaw/k?- (h men/rim MW) C) 30.7, fisv (91 ...
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