November 18, 1996 Physics 201

EXAM 3

Print your name and section clearly on all five pages. (If you do not know your section number, write your TA's name.) Show all work in the space immediately below each problem. Your final answer must be placed in the box provided. Problems will be graded on reasoning and intermediate steps as well as on the final answer. Be sure to include units wherever necessary, and the direction of vectors. Each problem is worth 25 points. In doing the problems, try to be neat. Check your answers to see that they have the correct dimensions (units) and are the right order of magnitude. You are allowed one 5" x 8" note card and no other references. The exam lasts exactly one hour.

(Do not write below)

SCORE:

Problem 1: __________

Problem 2: __________

Problem 3: __________

Problem 4: __________

TOTAL: ___________

Possibly useful information:

Acceleration due to gravity at the earth's surface: g = 9.80 m/s2

Gravitational constant: G = 6.67 x 10-11 N·m2/kg2

r(water) = 1.00 x 103 kg/m3 = 1.00 g/cm3

1 Liter = 10-3 m3

PROBLEM 1

A 580 kg uniform horizontal beam 8.2 m long is attached by a frictionless pivot to a wall. A steel cable (Young’s modulus = 2.0 x 1011 N/m2) of cross sectional area 1.6 cm2 makes an angle of 45° with the wall, supports the beam at point 4.8 m from the wall. The cable will stretch elastically until it breaks suddenly when tension exceeds 8000 N. At the start no one is on the beam.

a. What is tension in the cable? (5 pts.)

b. What is the change in length of the cable due to tension? (5 pts.)

c. What is the horizontal component of the force on the pivot? (5 pts.)

d. What is the vertical component of the force on the pivot? (5 pts.)

e. How far along the beam can a 95 kg man walk before the cable breaks? (5 pts.)

PROBLEM 2

A torsion pendulum with torsion constant k = 1.0 x 104 g·cm2/s2 consists of a dumbell composed of 2 equal masses m = 50 g separated by a massless rod of length l = 20 cm suspended from its center by a wire that resists being twisted by an angle q.

a. What is the period of oscillation? (5 pts.)

b. The wire is twisted q = 0.05 rad and released. What is the total energy? (5 pts.)

c. What is the maximum linear velocity of either mass after the release in part b? (5 pts.)

d. Find the total system maximum angular momentum after the release in part b? (5 pts.)

e. Find the maximum angular acceleration of either mass after the release in part b. (5 pts.)

PROBLEM 3

A satellite of mass 500 kg is in circular orbit 1000 km above the surface of the earth.

(ME = 6.0 x 1024 kg, rE = 6370 km).

a. What is the orbital (linear) speed of the satellite? (5 pts.)

b. What is the angular momentum of the satellite ? (5 pts.)

c. What is the total energy of the satellite ? (5 pts.)

d. What speed would the satellite need at this orbit to escape from the earth? (5 pts.)

e. A rocket engine on the satellite fires directly towards the earth until the satellite is 1500 km above the earth’s surface. Find the new orbital (linear) speed of the satellite at the instant when the engine shuts off. (5 pts.)

PROBLEM 4

A small garden fountain shoots a vertical jet of water at 0.10 liters/sec to a height of 0.50 m.

a. What is the speed of the water when it emerges from the fountain outlet? (5 pts.)

b. What is the radius of the outlet out of which the water passes? (5 pts.)

c. What is the gauge pressure in Pascals just below the water outlet? (5 pts.)

d. At a height of 0.25 m, what is the speed of the water jet ? (5 pts.)

e. A rubber duck of average density 0.68 g/cm3 floats in the fountain. What percentage of it is submerged (5 pts.)