Week 4

Read: and The law of the lever (ASGv2 Chap. 6). Chapter 6 is a bit dense. Don't worry if you don't quite follow some of Galileo's geometrical proofs; we'll talk about this in class. Beams, bones and giants (ASGv2 Chap. 7)

Key topics: torque, equilibrium, the law of the lever, strength of materials, beam breaking

PHY 201 lecture: Torque and static equilibrium.
Quiz: Quiz covering week 3 material.

  1. seesaw equilibrium (Ex. 6.1),
  2. achilles tendon (Ex. 6.2),
  3. aligning a support rafter (Ex. 6.4),
  4. Automobile problem: A 1500 kg automobile has a wheel base (distance between wheels) of 3 meters. The center of mass of the automobile is on at the center line at a point 1.2 meters behind the front axle. Find the force exerted by the ground on each wheel. Solution.
  5. transverse fracture (Ex. 6.5),
  6. forestry (Ex. 6.6),
  7. limestone pillar (Ex. 7.1a),
  8. PHY 201: limestone pillar (Ex. 7.1 b),

Beam breaking (Ex. 6.8). In lab this week, we will explore the transverse force required to snap a dry spaghetti noodle! Of interest: there has been some fascinating work on fracture of spaghetti noodles published in scientific journals lately. Also: Here is a 2016 article by French physicists about the critical wind speed at which trees break. These authors cite day two of Galileo's Dialogues.

Chapter 6: Here are seven videos that walk you through chapter 6 of ASG, in which Galileo develops his theory of the strength of beams. That is: how hard is it to break a beam by applying a transverse force?

Chapter 6: Here is an additional video for PHY 201 students. Depending on time, we may walk through Galileo's geometrical proof of the law of the lever. Dust off your geometry textbook! Otherwise, we will probably spend time talking about more complicated problems involving torque and statics.

Chapter 7: In the following two videos, Galileo describes how beams tend to break under their own weight. This puts a limit on the size of both living organisms and man-made structures, such as ships or buildings.

Physics 1