# Week 1 (Aug. 14 - 16)

Welcome to General College Physics at Wisconsin Lutheran High School! The sidebar (to the right) has some basic information about this course, such as the Professor's contact information and the textbook we will be using. You might wish to take a look at that first.

**Reading:**PSE Chap 1, Physics and MeasurementIn the first week of class, we will begin by talking about Physics and Measurement. You should read chapter 1 of the textbook: the

__Pocket guide to accompany Physics for Scientists and Engineers__(PSE) for this week.**Topics:**This week, we will be covering some preliminary information on*units*such as length, time and mass. We'll discuss unit conversions and learn the valuable technique of*dimensional analysis***Lab:**To put this into practice, we'll do an experiment on*pendulum motion*during week 2.**Week 1 Homework Problems:**Here are some problems involving the concepts of*dimensional analysis*and*significant figures*. You may work on these with an accomplice, but you must write up and submit your own solutions. To receive full credit, your solutions must be handed in to me by the due date. These problems serve as valuable practice to prepare you for quizzes and tests.**Dimensions and units:**Write down the dimensions of, and the MKS units of, the following quantities: speed, acceleration, density, and force.**Coulomb's law dimensions:***Coulomb's law*allows one to calculate the force that one electrical charge exerts on a second, nearby, electrical charge. The formula for Coulomb's law is: (Force) = (coulomb's constant) * (charge 1) * (charge 2) / (distance between charges)^2. Don't worry if you are not familiar with this formula. Just use the technique of*dimensional analysis*, to determine the*dimension*of coulomb's constant. What might be the*units*of coulomb's constant? Hint: the dimension of charge is Q and the MKS units are Coulombs.**Answer: The units of the coulomb constant in SI are Newton-meter^2/coulomb^2. The dimension is M L^3 / T^2 Q^2****Wave speed dimensions:**The speed of a wave traveling on the surface of the ocean depends only on (i) its*wavelength*and (ii) the*acceleration of gravity.*Using the technique of dimensional analysis, find a*mathematical formula*for the speed of the wave.**Answer: v is proportional to sqrt(g * lambda).****Density and significant figures:**Calculate the*density*(in grams per cubic centimeter) of a solid cube that measures 5.00 cm on each side and has a mass of 351 grams. Pay careful attention to significant figures. How many are there in your answer?**Answer: Density = 351 grams/125 cc = 2.81 g/cc.****Kinetic energy dimensions (additional, optional problem):**When an object is moving, it is said to have "kinetic energy". The kinetic energy, K, depends on two things: the mass of the object and its speed, v. Use the technique of dimensional analysis to find how K depends on m and v. Afterwards, look up the formula for kinetic energy; were you right?**Hydrostatic pressure dimensions (additional, optional problem):**When a submarine descends into the depths of the ocean, the pressure on the hull increases. The pressure is the force per unit area of the water pushing inward on the surface of the submarine. Use the technique of dimensional analysis to find how the pressure, P, depends on three quantities: the depth, y, the density of the water, d, and the acceleration of gravity, g. That is: find P = P(y,d,g). Look up the formula for hydrostatic pressure; were you right?

**Quiz:**not yet (it's the first week!)**Classroom problems:**As a reminder, these are some of the problems we worked out in class…

- Dimensions and units: the universal gravitational constant, G, that appears in Newtons' universal law of gravitation.
- Dimensions and units: energy, E, that appears in Einstein's formula E=mc^2.
- Dimensional analysis: determine how the frequency of a stretched vibrating string depends on its length, tension, and mass per unit length.