Physics 157 Homework 2 Due in your tutorial the Week October 5-9 For all questions write a few sentences (point form is acceptable) describing the approach and identifying the concepts you will use to solve the problem. Also comment on whether or not your answer makes sense based on what you know about the physical description of the problem or your everyday experience (eg. order of magnitude). Use the physical and material constants from your book unless given in the problem. 1. In order to obtain materials with a desired expansion coefficient, it is sometimes necessary to combine multiple materials together. A simple such composite bar is formed by placing two bars end to end as shown. Bar$1$ Bar$2$ The bars have lengths L1 and L2 and the composite bar has a length L = L1 + L2 . An engineer is asked to design a composite bar of length 52.4cm with coefficient of linear expansion 13.0 ⇥ 10 6 K 1 . If the bars are steel and brass, determine L1 and L2 . 2. A fine steel wire is attached to an aluminum cylinder in parallel (see picture). The structure is assembled at 10.0 C under negligible stress. The initial length of the system is wire$ Cylinder$ 85.0 cm long. The system is heated to 120 C. Calculate the resulting stress in the wire, assuming that the rod expands freely. Justify the assumption that the rod freely expands. 3. An insulated cup is filled with 200 grams of cherry cola soda which was stored at 25 C and 100 grams of crushed ice from a freezer at 15 C. (The thermal properties of the cherry cola soda are the same as water.) Find the temperature of the drink when it reaches reaches thermal equilibrium. (Neglect the heat capacity of the cup and heat exchange with the environment.) 4. In winter, people play hockey on Alta Lake in Whistler. However, it is not considered safe to play hockey on ice until the ice is 20 cm thick. On a winter day with a temperature 10 C, it is observed that the lake has a 1cm thick layer of ice over the entire surface. Assuming the temperature stays constant, find how long it will take for the ice to be safe: (a) If the air temperature remains at 10 C, find the rate in cm per hour at which ice is added to the layer. The thermal conductivity of ice is 2.18W/m · K. (b) Find the time that the ice layer reaches a thickness of 20 cm. 5. Three cubes of equal side length of steel, lead, and copper, are arranged between heat reservoirs at 150 C and 0 C as shown in the diagram. The heat current between the reservoirs is 175 W. a) What is the length of the side of a cube? b) What is the temperature at the junction between the steel and lead cubes? hot$ Steel$ Lead$ copper$ cold$ Copyright: Copyright Don Witt 2015. Not to be copied, used, or revised without explicit written permission from the copyright owner. 1
These tutorials focus not just on concept building but also on development of student epistemology -- their physical intuition, the understanding of scientific reasoning, and relating physics to their everyday experience. They are appropriate for most introductory physics classes, but especially for those with a qualitative and conceptual emphasis. The tutorials are open-source (MS-Word "doc" files) so they can be modified to fit a class's particular notation and needs.
This complete set of materials, interlinked and also accompanied by video clips of students using the materials and by "video workshops" intended to help teaching assistants learn about teaching in a tutorial environment, is available at http://www.spu.edu/depts/physics/tcp/tadevelopment.asp
Here are some guidelines that we have developed to help Tutorial Facilitators.
1 -- Catching mistakes: The case of motion graphs
2 -- The meaning of speed
2 -- Interpreting graphs and equations
3 -- Competing arguments: Backwards acceleration
1 -- Reconciling common sense and Newton's laws
2 -- Counterintuitive ideas: Newton's third law
3 -- What's the purpose of Free-Body Diagrams?
Momentum and Energy
1 -- Relating equations to common sense: "Oomph"
2 -- Work and energy
1 -- Spreading forces over surfaces
1 -- Working from a model: Static electricity
2 -- Abstract concepts: Fields
3 -- Electrostatic potential
Currents and Circuits
1 -- Electric Circuits: I
2 -- Electric Circuits: II
Oscillations and Waves
1-- Harmonic oscillation
2 -- Finding mechanism: Pulses
1 -- A model for light
2 -- Mirrors: How to tell where things are by looking
3 -- Lenses: Can an image float in empty space?
1 -- Two-source interference
2 -- Wave properties of light