EXAM 1                      October 1, 1997                          PHYS 207

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If you need a constant not given here or do not understand a problem, please ask me about it.
No notes, books, etc. may be used during this exam. Do not use math or physics formulas stored in your calculator.

g = 9.8 m/sec2Radius of the earth = 6.38 x 106 m The mass of the electron is 9.11 x 10-31 kg.
Calculus and trig formulas will not be given after this exam:
cos(2x) = cos2 (x) - sin2 (x)sin(2x) = 2 sin(x) cos(x) d xn / dx = n xn-1
d cos(x)/dx = - sin(x) d sin(x)/dx = cos(x) d(fg)/dx = f (dg/dx) + (df/dx) g
For all problems, explain the physics principles you are using in the box on the page. You may quote the general form of the equations expressing the principles or give an explanation in English. If no diagram is applicable to a problem, write "none" in the diagram section.

1. (10 points)

(a) Explain how to remember the equation for the acceleration of a particle which is in circular motion at a constant speed. Draw a diagram showing the velocity and acceleration when the particle is at the top of the circle.
(b) Draw on the diagram below a sketch of the x-component of the velocity of the particle whose position is given by the x(t) on the diagram.

2. (From homework; 30 points) Calculate the acceleration of a person at latitude 40o owing to the rotation of the Earth.

Diagram:
Principles:

3. (30 points) You throw a ball from eye level at a speed v0 and at an angle theta from the horizontal. As the ball flies through the air, you follow it with your eyes. When it reaches its maximum height, your eyes are directed at an angle phi with respect to the horizontal. Find an expression for tan (phi) in terms of v0 and theta.

Diagram:
Principles:
4. A sportscar, Fiasco I, can accelerate uniformly to 120 mi/hr in 30 sec. Its maximum braking rate cannot exceed 0.7g. What is the minimum time required to go 1/2 mi, assuming it begins and ends at rest. (Hint: A graph of velocity vs. time will be very helpful).

Diagram:
Principles:
Use this page if necessary to continue any of the problems. Be sure to label the problem number.