physics

Name____________________________________________________________

Instructions

 There are 5 multiple choice problems worth 2 points each and 3 written problems worth

30 points each.

 Show all of your work in arriving at an answer, include proper units.

 Box-in your final answer

 Keep numbers out of your equations as much as possible to make your reasoning more

transparent.

 Ask if you do not understand what is being asked for in a given problem.

 All work must be done on these pages, no scrap paper allowed.

 Time for the exam is 1 hour and 25 minutes, budget your time accordingly!

 All parties involved in cheating will receive a zero for the exam.

MC P1 P2 P3 Total

Part I Multiple Choice: Choose the BEST answer. No partial credit. Place answers in the boxes at the end of the

section.

1. A mass attached to a spring oscillates with the following position as a function of time.

𝑦 = 0.5 cos(5𝑡 + 2) where the position, y, is measured in cm and angles in the cos function are measured in radians. How

many oscillations does the mass make per second?

(a) 0.79 (b) 5 (c) 31.4 (d) 1.59 (e) 10

2. For the mass in the previous problem what is its speed at t = 7 s?

(a) 27 cm/s (b) 1.61 cm/s (c) 13.88 cm/s (d) 9.64 cm/s (e) 0 cm/s

3. A banked curve on a race track is designed to operate without friction for a car traveling at a speed of

47 m/s. A driver goes through the curve at a speed of 31 m/s. In which direction does the friction force

on the car tires point (if there is a friction force)?

(a) Banked tracks do not require friction.

(b) The friction force points radially inward towards the center of the circular motion (the friction force

direction is parallel to the ground).

(c) The friction force is parallel to the banked track and points up the slope of the banked track.

(d) The friction force is parallel to the banked track and points down the slope of the banked track.

(e) The friction force points in the direction of the normal force.

4. The density of lead is 11.36 g/cm3 and the mass number of lead is 208 g/mol. Calculate the interatomic

spacing of lead (Avogadro’s number = 6.02 x 1023).

(a) 10.9 nm (b) 1.02 nm (c) 0.31 nm (d)9.77 nm (e) 1194 nm

5. What is the total energy of a proton of mass, m= 1.67 x 10-27 kg, moving at 0.99c.

(a) 7.4 x 10-11 J (b) 3.55 x 10-18 J (c) 1.5 x 10-10 J (d) 8.2 x 10-28 J (e) 1.07 x 10-9 J

Place answers to the multiple choice in the boxes below.

1 2 3 4 5

Part II. All work must be shown for full credit. Answers must have appropriate units.

1. A steel beam of mass 250 kg and length 8 m is attached to a vertical wall by a hinge. The beam is

supported in a horizontal position by a cable that attaches to the beam at a point 6 m from the wall.

The cable makes an angle of 35o to the beam as shown in the figure below. The system is designed to

support a worker of mass 110 kg who walks out to the very end of the beam (see Walter in figure).

(a) Calculate the tension in the cable when Walter (mass = 110 kg) is at the end of the beam. Carefully

show your reasoning. [18 points]

(b) Determine the horizontal and vertical force components that must be applied to the beam at the hinge

point where it meets the wall. (Make sure both magnitude and direction of the components is clear).

[12 points]

2. On a hot wheels track the car of mass 38 g starts at a height of 1.2 m above the level of the table. The loop

has a diameter of 0.38 m. Assume the track is frictionless apart from a rough patch of length x with coefficient

of kinetic friction k=0.91.

(a) Calculate the speed of the car at the top of the loop (point T in the figure). [8 points]

(b) Determine the normal force on the car when it is at the top of the loop (point T). [8 points]

(c) Determine the speed and the normal force on the car at the bottom of the loop after it has gone over

the top. [6 points]

(d) Find the minimum distance x of the rough patch required to just bring the car to a stop. [8 points]

3. A metal wire of length 3 m and diameter 4 mm is attached to the ceiling. The wire extends in length by

6 mm when an 80 kg mass is hung from the wire.

(a) Assuming the wire acts like a spring, determine the effective spring constant, keff, for the wire. [8

points]

(b) The metal from which the wire is made has an interatomic spacing of d=0.14 nm. Using the ball and

interatomic spring model of the atoms in the wire, determine the number of parallel springs, Nparallel,

and the number of springs in series, Nseries, for the wire. [8 points]

(c) Determine the spring constant for the interatomic bonds between atoms. [7 points]

(d) Determine Young’s modulus for the metal. [7 points]

__MACOSX/._P2110Test2Sample p1.pdf

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