1. (10 points, suggested time 20 minutes)
Two students observe water flowing from left to right through the section of pipe shown above, which decreases in diameter and increases in elevation. The pipe ends on the right, where the water exits vertically. At point A the water is known to have a speed of 0.5 m/s and a pressure of 2.0*105Pa. The density of water is 1000kg/m3.
(a) The students disagree about the water pressure and speed at point B. They make the following claims.Student Y claims that the pressure at point B is greater than that at point A because the water is moving faster at point B.
Student Z claims the speed of the water is less at point B than that at point A because by conservation of energy, some of the water’s kinetic energy has been converted to potential energy of the Earth-water system.
i. Indicate any aspects of student Y’s claim that are correct.
ii. Indicate any aspects of student Y’s claim that are incorrect. Support your answer using appropriate physics principles.
iii. Indicate any aspects of student Z’s claim that are correct.
iv. Indicate any aspects of student Z’s claim that are incorrect. Support your answer using appropriate physics principles.
(b) Calculate the following at point B.
i. The speed of the water
ii. The pressure in the pipe
(c) A valve to the left of point A now closes off that end of the pipe. The section of pipe shown is still full of water, but the water is no longer flowing.
i. Calculate the absolute pressure at point A (the pressure that includes the effect of the atmosphere).
ii. An air bubble forms at point A. On the figure below, where the dot represents the air bubble, draw a free-body diagram showing and labeling the forces (not components) exerted on the bubble. Draw the relative lengths of all vectors to reflect the relative magnitudes of the forces.
2. (12 points, suggested time 25 minutes)
A group of students is given several long, thick, cylindrical conducting rods of the same unknown material with various lengths and diameters and asked to experimentally determine the resistivity of the material using a graph.The available equipment includes a voltmeter, an ammeter, connecting wires, a variable-output DC power supply, and a metric ruler.
i. Describe a procedure the students could use to collect the data needed to create the graph, including the measurements to be taken and a labeled diagram of the circuit to be used. Include enough detail that another student could follow the procedure and obtain similar data.
Draw a labeled diagram here.
Write your procedure here.
ii. Describe how the data could be graphed in a way that is useful for determining the resistivity of the material. Describe how the graph could be analyzed to calculate the resistivity.
The students are now given a rectangular rod of the material, as shown below, whose dimensions are not known.The students are asked to experimentally determine the resistance of the rod. They obtain the data in the table below for the potential difference △V across the rod and the current I in it.
(b) On the axes below, plot the data so that the resistance of the rectangular rod can be determined from a best-fit line. Label and scale the axes. Use the best-fit line to determine the resistance of the rod, clearly showing your calculations.
(c) After completing their calculations, the students begin to consider the factors that might have produced uncertainties in their results.
i. The students realize that they did not take into account the internal resistance of the power supply.Briefly describe how this would affect their value of the resistance of the rectangular rod. Explain your reasoning.
ii. The students realize that they did not take into account a possible change in the temperature of the cylindrical rods. Should the students be concerned about this? Explain why or why not.