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.

*(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.)*