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University of Bahrain Physics Department Physics 101 Final Exam Spring 2007 Thursday, 14/6/2007 8:30 – 10:30 Name: ID no.: Section: Instructor Name: MCQ Prob 1 Prob 2 Prob 3 Prob 4 Total 48 12 12 12 12 96 Total 40 Use: g=10m/s2 , sin 37◦ = cos 53◦ = 0.6, sin 53◦ = cos 37◦ = 0.8 PART 1: Choose the correct answer for the following questions: GRADING: 4 points each question, total: 48 points out of 96 1. The coordinate of a particle moving along the x axis as a function of time is given by x = 2t2 − 4t + 5 where x in m and t in s. The particle has zero velocity at t in s equals to: (a) 0 (b) 1 (c) 2 (d) 3 (e) 4 2. A boy throws a ball vertically upward and catches it after 4 s. maximum height in m reached by the ball is: (a) 1 (b) 5 (c) 20 (d) 45 The (e) 80 3. A stone is dropped from a height h and strikes the ground after time t. Considering upward as the positive direction, which of the following v − t graphs represents the stone motion? v v 0 v v t/ 2 -v t t 0 v v t/ 2 t t -v (a) 0 v v t/ 2 -v (b) 0 t t v v t/ 2 -v (c) 0 t t -v (d) (e) 4. If the coefficient of kinetic friction between the road and the tires of a car µk =0.1 and that of static friction µs =0.5, then the maximum acceleration in m/s2 the car can have is: (a) 1 (b) 2 (c) 3 (d) 4 (b) 14.1 (c) 24.6 (d) 41.2 a (e) 5 5. A roller coaster has a speed of v=20 m/s at mid-point of a vertical circular loop, point A in the figure. If the radius of the loop r=10 m, then the magnitude of the total acceleration in m/s2 at point A is: (a) 10.0 t t t/ 2 (e) 63.3 r v A 6. A force F =10 N can compress a spring a distance x=0.05 m, then the work in J needed to stretch this spring a distance x=0.4 m is: (a) 1 (b) 4 (c) 9 (d) 16 (e) 25 7. A block of mass m=2 kg slides on the rough track shown in the figure. If at point A the block is at a height hA =5 m moving with a velocity vA =10 m/s and at point B at a height hB =2 m moving with a velocity vB =11 m/s, then the work in J done by the frictional force on the block as it moves from point A to point B is: A vA (a) 0 (b) -16 (c) -39 (d) -60 (e) -79 B vB hA 8. A 1 kg block slides down a rough 37◦ incline a distance d=1 m. If µk =0.1, then the work done in J by the normal force is: hB d µk (a) -8.0 (b) -6.0 (c) -0.8 (d) -0.6 (e) 0.0 θ 9. A 0.1 kg ball is dropped from a height hi =1 m, strikes the ground and bounces back a maximum height hf =0.8 m. If the ball is in contact with the ground for t=0.01 s, then the magnitude of the average force in N applied by the ground on the ball is: (a) 79.4 (b) 82.1 (c) 84.7 (d) 87.1 hi hf (e) 81.3 10. A wheel initially at rest starts to rotate with a constant angular acceleration α=4 rad/s2 , the number of revolution made in t=2 s is: (a) 1.27 (b) 2.86 (c) 5.09 (d) 7.96 (e) 11.46 11. A disc with radius r=0.1 m starts to rotate from rest at a constant rate of 1 rad/s2 . The magnitude of the radial (centripetal or central) acceleration in m/s2 after t=3 s for a point P on the rim is: (a) 0.1 (b) 0.4 (c) 0.9 (d) 1.6 (b) 20 (c) 30 (d) 40 r (e) 2.5 12. Five forces are applied on a square of side length of 2 m. If F =20 N, then the magnitude of the net torque in N·m about the center C is: (a) 10 P (e) 50 2F F F C 2F F PART 2: Answer the following questions in the space provided: GRADING: 12 points out of 96 1. A physics 101 student decides to work in a circus as a the canon-ball-man! He is projected by a canon with a speed of v0 =30 m/s at an angle of θ0 =37◦ above the horizontal, as in the figure. The student is ejected from a height h1 =2 m above the ground and the safety net that he should lands in is h2 =5 m above the ground. (a) (4 points) Calculate the time he is in the air. (b) (4 points) How far from the nozzle, x, the net should be placed? (c) (4 points) How fast will the student be traveling just before hitting the net? vο θο h2 h1 x =? GRADING: 12 points out of 96 2. A block of mass m1 =4 kg is held compressing a spring with force constant k=1000 N/m a distance x=0.2 m, on the smooth track shown. The block is then released. (a) (4 points) Find the speed of the block after leaving the spring. (b) (4 points) m1 then collides with a stationary mass m2 =6 kg and stick together. Find their common speed V . (c) (4 points) The two blocks then move up the ramp. Find the maximum height reached by the two blocks. x k m1 v2 = 0 m2 V h GRADING: 12 points out of 96 3. A block of mass m1 =4 kg is placed on a rough horizontal surface with µk =0.2, and connected via a massless string to a hanging mass m2 =3 kg. The connecting string passes over a pulley in the shape of a uniform cylinder of mass M =6 kg and moment of inertia I = M R2 /2. The system is released from rest. Find: (a) (8 points) the acceleration of the mass m1 , (b) (2 points) the tension on each side of the string, (c) (2 points) the time it takes m1 to move a distance d=1 m to the right. d m1 M, R, I µk m2 GRADING: 12 points out of 96 4. A rod, of mass M =3 kg and length L=4 m and moment of inertia I = M L2 /12, has two point masses each of mass m=2 kg located at its two ends. The rod is rotating about its center at an angular speed ωi =2 rad/s as in figure A. (a) (2 points) Calculate the moment of inertia of the system as in figure A (b) (2 points) Calculate the angular momentum. (c) (4 points) The two masses are then moved half way to a distance of 1 m from the rotation axis, figure B. Calculate the new angular speed ωf . (d) (4 points) Calculate the change in energy. m M 2m ωi 2m Figure A ωf 1m 1m Figure B m