# December 10, 1997

Possibly useful information:

Show all your work! Tell me all the details. Diagrams are important.

Just a comment about the final: As you know, we have discussed (far) more topics and ideas than have been possible to cover on four one-hour exams. The hour exams have covered important topics. But equally important topics have not been covered. The final exam will be about six to nine problems similar to the homework problems. They may include topics already covered and they may cover topics that were not covered on previous exams. This course is filled with interesting and useful and important topics. It is impossible to distill this entire course down to "the nine most important topics".

1. (12.24) A steel piano wire 1.12 m long has a cross-sectional area of 6.0 x 10-3 cm2. When under a tension of 115 N, how much does it stretch?

From Table 12.1, p 346, Young's modulus for steel is 20 x 1010 N / m2.

A = 6.0 x 10-3 cm2 [ 1 m2 / 104 cm2 ] = 6.0 x 10-7 m2

stress = F / A = 115 N / 6.0 x 10-7 m2

F / A = 1.92 x 108 N / m2

2. (13.22) A 50-g mass connected to a spring of force constant 35 N/m oscillates on a horizontal, frictionless surface with an amplitude of 4.0 cm. Find

(a) the total energy of the system and

(b) the speed of the mass when the displacement is 1.0 cm.

When the displacement is 3.0 cm, find

(c) the kinetic energy and

(d) the potential energy.

3. (14.9) If the mass of Mars is 0.107 ME and its radius is 0.53 RE, estimate the gravitational field g at the surface of Mars.

4. (15.43) Old Faithful Geyser in Yellowstone Nat'l Park erupts at approximately 1-hour intervals and the height of the fountain reaches 40 m.

(a) With what speed does the water leave the ground?

(b) What is the pressure (above atmospheric) in the heated underground chamber if its depth is 175 m?