95.141 Exam 2 Spring 2014 Section number Section instructor Last/First name Last 3 Digits of Student ID Number: Answer all questions, beginning each new question in the space provided. Show all work. Show all formulas used for each problem prior to substitution of numbers. Label diagrams and include appropriate units for your answers. Write your name and section number at the top of each page in the space provided and write the name of your section instructor in the place provided in the cover sheet.you may use an alphanumeric calculator (one which exhibits physical formulas) during the exam as long as you do not program any formulas into memory. By using an alphanumeric calculator you agree to allow us to check its memory during the exam. Simple scientific calculators are always OK! A Formula Sheet Is Attached To The Back Of This Examination For your convenience you may carefully remove it from the Exam. Please take it with you at the end of the exam or throw it in a waste basket. Be Prepared to Show your Student ID Card Score on each problem: 1. (25) 2. (25) 3. (30) 4. (20) Total Score (out of 100 pts)
2 1. (25 point) Put a circle around the letter that you think is the best answer. 1.1. (5pts) As a car drives with its tires rolling freely without any slippage, the type of friction acting between the tires and the road is A) static friction B) kinetic friction C) a combination of static and kinetic friction D) neither static nor kinetic friction, but some other type of friction E) it is impossible to tell what type of friction acts in this situation 1.2. (5pts) How much work must be done to stop a 1000-kg car travelling at 30 m/s? A) 450,000 J B) 30,000 J. C) -15,000 J D) -450 kj. E) None of the above. 1.3. (5pts) The work done by the centripetal force on an object with a mass of 1 kg moving with a constant velocity of 4 m/s into a circular path of radius 2.0 m for one full cycle is A) 100.7 J. B) 8.0 J. C) 0 J. D) 40 J. E) None of the above.
3 1.4. (5pts) How do the escape velocities for two rockets, the first weighing 20 N and the second weighing 20,000 N compare A) The escape velocity for the lighter rocket is smaller than that for the heavier rocket. B) The escape velocity for the lighter rocket is the same as that for the heavier rocket. C) The escape velocity for the lighter rocket is greater than that for the heavier rocket. D) It is impossible to compare the two escape velocities.. 1.5. (5pts) An object is under the influence of a force as represented by the force vs. position graph in the figure. What is the work done as the object moves from 4 m to 12 m? A) 20 J B) 30 J. C) 0 J D) 50 J E) None of the above
4 2. (25 pts) A bucket of mass m=2.00 kg is whirled in a vertical circle of radius R=1.10 m. 1) At the lowest point of its motion the tension in the rope supporting the bucket is 25.0 N. a) (5 pts) Draw a free body diagram b) (7 pts) Find the speed of the bucket. 2) Consider the top of the circle a) (5 pts) Draw a free body diagram b) (8 pts) How fast must the bucket move at the top of the circle so that the rope does not go slack?.
3. (30 pts) A block of m=4.00 kg is on an incline plane of θ=30.0 degree as shown in the figure. The coefficient of kinetic friction between the block and the incline is μ=0.30. An external horizontal force F=50.0 N is applied on the box and it moves up. a) (5 pts) Draw a free-body diagram of all the forces on the box. b) (7 pts) Determine the normal force acting on the block. c) (8 pts) Determine acceleration of the box. d) (10 pts) How much work is done by this horizontal force F on the block when the block moves 5.0 m up the incline plane? 5
4. (20 pts) Consider the track shown in the figure. The section AB is one quadrant of a circle of radius 2.0 m and is frictionless. The section B to D is a horizontal and also frictionless. A block of mass 1.0 kg is released from rest at A. After sliding on the track, it compresses the spring by 0.20 m. Determine: a) (10 pts) the velocity of the block at point C b) (10 pts) the stiffness constant k for the spring. 6
7 Trig: sin = a/ /c cos = b/ /c tan = a/ /b c 2 = a 2 + b 2 Quadratic Formula: Ax 2 + Bx + C = 0 has solutions: B B 2 4AC x 2A Misc Formulas: Circumference of a circle = 2R Area of a circle = R 2 Surface Area of a Sphere = 4R 2 Volume of sphere = (4/3)R 3 Volume of cylinder = R 2 L Differentiation: dx n /dx = nx n-1 (n 0) dcos(x)/dxx = sin(x) (x in radians) dsin(x)/dxx = cos(x) (x in radians) d(f(x) + g(x))/dx = df(x)/dx + dg(x)/ /dx Integration: x x n 1 n dx C n 1 1-D Motion: displacement = x v average : x/t = (x 2 x1)/(t 2 t 1 ) a average : v/t = (v 2 v 1 )/(t 2 t 1 ) Given x(t) v(t) = dx/dt (instantaneous) a(t) = dv/ dt = d 2 x/dt 2 (i instantaneous) 1-D Motion with Const. Acc.: x(t) = x 0 + v 0x t + (1/2) at 2 v(t) = v 0 + at v 2 = v 2 0 + 2a(x x 0 ) Projectilee Motion: x(t) = x 0 + v 0x t v x (t) = v 0x a x (t) = 0 y(t) = y 0 + v 0y t + (1/2) a y t 2 v y (t) = v 0y y+ a y t a y (t) = a y For motion over level ground Range = [v 2 0 sin(2 )]/g Acceleration due to gravity: g = 9.8 m/s 2 downwardd Newton's Second Law: ma F net Circular Motion: a c = v 2 /R T = 1/f v = 2R/T Frictional Forces: fs µ µsf N fk = µ k F N µs > µk Work and Kinetic Energy W = Fx r W F. dr 2 r1 F ext K = (1/2)mv 2 Wnet = K K = K f K i Potential Energy U U x) U ( x ) ( 0 0 F(x) = du(x)/dxx x For gravity on earth's surface: F g = mg U(y) ) = U 0 + mgy For gravity in general: F g = GmM E /R 2 U(r) = GmM E /R For springs: F = kx U(x) ) = (1/2)kx 2 Withh conservative forces only: E tot = K + U (a constant) E tot t = K + U = 0 Withh non-conservative forces: E tot t = K + U = W NC x0 Fdx Gravity Kepler's third law: T 2 /R 3 = 4 /GM su G = 6.67 x 10-11 un N.m 2 /kg 2 Power P avg = W/t P = dw/dt P F v