PH 314 Homework Set #1
Spring 2008

Assigned: Monday 03/31/2008

Due: Monday 04/07/2008 3:00 PM

When writing a solution, you must explain carefully and concisely, and demonstrate that you understand. When writing in English, you must use complete sentences. (A complete sentence has both a subject and a predicate.) When writing in mathematics, you must use complete equations. (A complete equation has a right-hand-side, an equal sign and a left-hand-side). When grading the homework and exams, the points awarded will be broken down into three main categories: 1) translate (translating the problem from English sentences to mathematical equations, drawing a diagram and explicitly converting prefixes), 2) equate (identifying the relevant relationships between the physical quantities) and 3) solve (using algebra, geometry, trigonometry and/or calculus to solve for the unknown quantity or quantities.) For full credit, the answer must include the units and three significant digits. The answer itself is only worth 10 to 20% of the points. How well you write down how you got the answer is worth 80 to 90% of the points.

1) (a) According to classical physics, if the kinetic energy of an electron is 1.60 x 10^-19 J, then what is the magnitude of its momentum? (b) According to classical physics, if the kinetic energy of a proton is 1.60 x 10^-19 J, then what is the magnitude of its momentum? (c) According to classical physics, if the kinetic energy of a neutron is 1.60 x 10^-19 J, then what is the magnitude of its momentum?

2) (a) According to classical physics, if an electron is accelerated from rest through a potential difference of 1.00 V, then what is its final speed? (b) According to classical physics, if a proton is accelerated from rest through a potential difference of 1.00 V, then what is its final speed? Give both answers in meters per second.

3) A clock moves along the y-axis and reads 8:10 AM as it passes the origin and 8:11 AM as it passes y = 2.50 x 10¹⁰ m. (a) Is the clock running fast or slow according to an observer who is stationary with respect to the y-axis? (b) How much time elapses on a clock which is stationary with respect to the y-axis during the same time? Give the answer in seconds.

4) According to an observer on Earth, the Federation starship Enterprise moves at a constant velocity of 0.800c up and to the right at an angle of 30.0 degrees above the horizontal. According to the same observer, the Klingon cruiser Patah moves at a constant velocity of 0.800c up and to the left at an angle of 30.0 degrees above the horizontal. In this problem, assume that the observer on the Earth is not accelerating and give all speeds in terms of c. (a) According to classical relativity, what would be the speed of the Patah according to an observer on the Enterprise? Given Einstein's theory of relativity, would this speed be possible? (b) According to classical relativity, what would be the speed of the Enterprise according to an observer on the Patah? Given Einstein's theory of relativity, would this speed be possible? (c) According to Einstein's theory of relativity, what would be the speed of the Patah according to an observer on the Enterprise? (d) According to Einstein's theory of relativity, what would be the speed of the Enterprise according to an observer on the Patah?