TIME OF COMPLETION_______________           NAME________SOLUTION_____________________

 

 

                                           DEPARTMENT OF NATURAL SCIENCES

 

PHYS 2211, Exam 1                                                                                                             Section 1

Version 1                                                                                                              September 23, 2002

Total Weight: 100 points

 

1.         Check your examination for completeness prior to starting.  There are a total of nine (9) problems on ten (10) pages.

 

2.         Authorized references include your calculator with calculator handbook, and the Reference Data Pamphlet  (provided by your instructor).

 

3.         You will have 50 minutes to complete the examination.

 

4.         The total weight of the examination is 100 points.

 

5.         There are five (5) multiple choice and four (4) calculation problems. Work all multiple  choice problems.  Show all work; partial credit will be given for correct work shown. Solve three (3) out of four calculation problems.

 

6.         If you have any questions during the examination, see your instructor who will

be located in the classroom.

 

7.         Start:                10:30 a.m.

Stop:                11:20 a.m

 

 

 

               PROBLEM

 

                 POINTS

 

                 CREDIT

 

                     1-5

 

                      40

 

 

 

                       6

 

                      20

 

 

 

7

 

                      20

 

 

 

                       8

 

                      20

 

 

 

                       9

 

                      30

 

 

 

                 TOTAL

 

                     100

 

 

 

 

 

           PERCENTAGE

 

 

 

 

CIRCLE THE SINGLE BEST ANSWER FOR ALL MULTIPLE CHOICE QUESTIONS. IN MULTIPLE CHOICE QUESTIONS WHICH REQUIRE A CALCULATION SHOW WORK FOR PARTIAL CREDIT.

 

  1. A furlong is a distance of 220 yards. A fortnight is a time period of 2 weeks. A race horse is running at a speed of 5.00 yards per second. What is his speed in furlongs per fortnight?

 

a.       27,491 furlongs/fortnight.  (5.00 yards/second)(1.00 furlong/220 yards)(14 x 24 x 3600 seconds/1.00 fortnight) =                       

                                                                                                                                               27,491furlong/fortnight

(8)

b.      13,674 furlongs/fortnight.

 

c.       6,221 furlongs/fortnight.

 

d.      2,749 furlongs/fortnight.

 

 

2. Suppose that two quantities, A and B, have   different dimensions. Determine which of the            

   following arithmetic operations could be physically meaningful.

 

 

a.      A +  B

 

b.      A – B

(8)

c.       B – A

 

d.      B/A

 

 

3. A rock is dropped at the same instant that a ball, at the same initial elevation, is thrown     horizontally. Neglect air resistance.

 

a.       The time of flight is the same for both of them.

 

b.      Ball has greater acceleration.

(8)

c.       Range of the ball’s trajectory is less then the rock’s range.

 

d.      We need to know the mass of the rock and the mass of the stone to describe the motion.

 

 

 

 

4.  The normal force on an object in contact with a surface is

 

a.       Parallel to the surface and in the direction of motion.

 

b.      Perpendicular to the surface pointing towards the surface.

(8)

c.       Perpendicular to the surface pointing away from the surface.

 

d.      Towards the center of the Earth.

 

 

 

5.  As a car moves forward on a level road at a constant velocity, the total force acting on the tires is:

 

a.        Greater than the normal force times the coefficient of static friction.

 

b.      Equal to the normal force times the coefficient of static friction.

(8 )

c.       Equal to the normal force times the coefficient of kinetic friction.

 

d.      Zero.

 

 

6. Deep inside an ancient physics text you discover two vectors:

             

 A:  45.0 m @150.0 o

 B:  30.0 m @ -15.0 o

 

Not content with these hoary relics, you are asked to find a new vector R = A - B.

  1. Find the magnitude and direction of vector R

 

 

  A: 45.0 m @ 150o

  B: 30.0 m @ -15.0o

 

            Ax = A cos(qA) = 45.0m cos(150o) = -39.0 m

            Ay = A sin(qA) = 45.0m sin(150o) = 22.5 m

         

            Bx = B cos(qB) = 30.0m cos(-15.0o) =  29.0 m

            By = B sin(qB) = 30.0m sin(-15.0o) = -7.76 m

 

           Rx = Ax - Bx  = -39.0 – 29.0 m = -68.0 m

           Ry = Ay - By = 22.5 m + 7.76 m = 30.3 m

 

           R = (Rx2 + Ry2)1/2 = ( (-68.0 m)2 + (30.3 m)2)1/2 = 74.4 m

qR  = tan-1 (Ry /Rx) = tan-1 (30.3 m /-68.0 m) = -24.0o  + 180o = 156o  (Rx < 0)

 

  1. Write your result in terms of unit vectors i and j.

 

  R = (-68.0 i + 30.0 j) m

 

 

 

 

 

 

7. A famous soccer player, Hedley Footy, kicks the ball at a speed of 15.0 m/s when t = 0 s.

The initial velocity vector of the ball makes an angle of 60.0o with the horizontal direction.

 

 

a.       Find the components of the initial velocity.

 

Vi: 15.0 m/s @ 60.0o

 

                        Vix = Vi cos(qi) = 15.0m/s cos(60.0o) = 7.50 m/s

                        Viy = Vi sin(qi) = 15.0m/s sin(60.0o) = 13.0 m/s

 

 

b.      Out of curiosity (and to get the credit, of course) calculate the instant when the velocity vector of the ball makes an angle of  -45.0o with the horizontal direction.

 

tan(q) = Vyf /Vxf

                                   

      Vxf = Vxi = 7.50 m/s

 

Vyf  = tan(q)Vxf

 

Vyf  = tan(-45.0o)7.50 m/s = -7.50 m/s

 

Vyf  = Vyi - gt

 

(Vyi  - Vyf) /g = t

           

                                    t = 2.09 s

 

c.       If the ball lends at the same level as it started, how long is the ball in motion?

 

yi = 0 m

                        yf = 0 m

       

yf = yi + Viy t – ½ g t 2

 

                         0 = t (Viy – ½ g t)       

                        Viy – ½ g t = 0

t = 2 Viy /g       

                        t = 2.65 s

 

 

d.      Find the range of the ball’s trajectory.

 

 

xi = 0 m

                        xf = xi + Vix t

                        xf = (7.50 m/s)(2.65 s) = 19.9 m

 

 

 

8.  Dr. K is trying to move a box full of physics textbooks (total mass of 30 kg) up the incline  by exerting a constant force parallel to the surface of incline. Alas, the surface is rough and the coefficient of friction is 0.300. She very quickly discovers that the best she can do is barely move the box up the incline with a constant speed. The surface is inclined to the horizontal at an angle of 35o.

 

 

    1. Draw a free body diagram including all the forces acting on the box.

 

 

 

 

    1. Find the magnitude of the normal force exerted on the box by the incline.

 

 

            Ax = A cos(0o) = A

            Ay = A sin(0o) = 0

         

            nx = n cos(90.0o) = 0

            ny = n sin(90.0o) = n

 

            fkx = fk cos(-180o) = - fk= -mkn

            fky = fk sin(-180o) = 0

 

            wx = w cos(270 o -35.0o) =  – mg sin(35.0o)

            wy = w sin(270 o -35.0o) = – mg cos(35.0o)

 

S Fx = m ax            ax = 0                  A – mkn – mg sin(35.0o) = 0

            S Fy = m ay                ay = 0                  n – mg cos(35.0o) = 0    n = 241 N

 

 

    1. Find the limit of Dr. K’s physical abilities (magnitude of the force she exerts on the box.)

 

 

                              A – mkn – mg sin(35.0o) = 0

                              A = 241 N

 

 

 

9. Three 2.00 kg decoys on a frictionless table are connected in series by strings as indicated in the figure. The final string passes over an ideal pulley at the edge and suspends the mother of all decoys with a mass of 3.00 kg. The ducks are initially at rest.

 

    1. Which string has the least tension and why?

 

 

 

 

T3 = max           T2 - T3 = max                   T1 - T2 = max       Mg – T1 = Max

 

T3 = max      T2 = 2.00 max            T1 = 3.00 max

 

 

 

 

    1. Which string has the greatest tension? Show that the greatest tension has a magnitude of less than 29.4 N.

  

                                              T1 = 3.00 max

                                               See d.

 

 

    1. Do you expect the magnitude of the acceleration of the ducky system to be less than, greater than, or equal to g?

 

                                                                  LESS than g

 

 

 

    1. Calculate the magnitude of the acceleration of the system of ducks.

 

                                                   Mg – T1 = Max

 

                                                  Mg – 3.00 axm = Max

 

                                                  ax = Mg/(M + 3.00 m) = 1/3 g