Physics H131: Problem Set #1

Two-Minute/Short-Answer Problems

Remember to give a good explanation, no longer than two sentences.

• C1T.1: How can you test whether astrologers' predictions are reliable?
• C2T.8: Write down the mathematical expression for the magnitude of a vector and then discuss it.

Chapter C1 Problems

• C1B.2: Picture the puck in your mind sliding over rough ice -- will it always stay in contact with the ice? If not, what brings it back? What keeps it from penetrating into the ice? what slows it down when in contact and when not in contact with the ice? Classify each of these interactions according to long- vs. short-range and according to the macroscopic subcategories in Figure C1.5.
• C1B.3: Use the unit operator technique to make the conversion into minutes.
• C1S.4: This is the same procedure as when drawing a map -- you can think of it as scaling all distances by a common factor, or as preserving all ratios between different distances.
• C1R.1: Use the density of water given on the front inside cover of the textbook in the form of the unit-operator for unit conversion.

Chapter C2 Problems

Remember to always include the correct units with dimensionful numbers! Remember that each component of a vector has the same units as the vector as a whole or as its magnitude.

• C2B.9: Read section C2.6 again if you encounter problems here.
• C2S.3: Hint: Two (non-parallel) vectors define a plane. How can you use this to simplify your algebra? (Think about your choice of reference frame. Try to use planar polar coordinates.) Another hint: It may be easier to compare the squares of the two expressions. (Is this allowed? Why?)
• C2S.4: You are given two vectors -- which ones? You are asked about a third vector; how is it related to the given vectors? Don't forget your units!
• C2A.1: See hints for C2S.3. How can you ensure that theta is the polar angle in a planar polar coordinate representation of the vectors u and w?
  (a) Note the typo -- the vectors p and q at the end of the sentence should really be u and w.
  (b) Again, it's easier to first study the relations between the squares of the given expressions. Think about why it is allowed to argue that if the squares are related to each other in the way stated in the problem, the same is true for the quantities themselves. Think carefully about the origin of the absolute magnitude signs on the left hand side.