1. A student, standing on a scale in an elevator at rest, sees that the scale reads 840 N. As the elevator rises, the scale reading increases to 945 N for 2 seconds, then returns to 840 N for 10 seconds. When the elevator slows to a stop at the 10th floor, the scale reading drops to 735 N for 2 seconds while coming to a stop.
(a) Explain why the apparent weight of the student increased at the beginning of the motion.
(b) Draw the free body diagram for the student while the student is accelerating upward, then moving at a constant velocity, and finally accelerating downward at the end. Draw the length of the force vectors to show when forces are balanced or unbalanced.
(c) Sketch acceleration vs. time, velocity vs. time, and displacement vs. time graphs of the student during the elevator ride.
2. A dart of mass m is accelerated horizontally through a tube of length L situated a height h above the ground by a constant force F. Upon exiting the tube, the dart travels a horizontal distance Δx before striking the ground, as depicted in the diagram below.
(a) Develop an expression for the velocity of the dart, v, as it leaves the tube in terms of Δx, h, and any fundamental constants.
(b) Derive an expression for the kinetic energy of the dart as it leaves the tube in terms of m, Δx, h, and any fundamental constants.
(c) Derive an expression for the work done on the dart in the tube in terms of F and L.
(d) Derive an expression for the height of the tube above the ground in terms of m, Δx, L, F, and any fundamental constants.
An experiment is then performed in which the length of the tube, L, is varied, resulting in the dart traveling various horizontal distances Δx which are recorded in the table below.
(e) Use the grid below to plot a linear graph of Δx2 as a function of L. Use the empty boxes in the data table, as appropriate, to record the calculated values you are graphing. Label the axes as appropriate, and place numbers on both axes.
(f) From the graph, obtain the height of the tube given the mass of the dart is 20 grams and the constant force applied in the tube is 2 newtons.
3. Four static charges of identical magnitude are arranged at the corners of a square of side-length 3.00 cm.
All four charges have magnitude of 5.00 micro-coulombs. The top two charges are positive, and the bottom two charges are negative. Assume a positive 1.00-coulomb test charge is placed at the center of the square, and calculate the net force on it due to the four corner charges. (Essentially you are calculating the electric field at the center of the square.) Be sure to include a free-body diagram and show all necessary calculations.
4. The circuit shows a light bulb of resistance 2R connected to a battery with no internal resistance and two resistors, each with a resistance R.
(a) Which component has more current passing through it, the light bulb or either of the resistors? Give a detailed explanation with supporting equations if necessary.
(b) Develop an expression for the voltage drop across the light bulb as a fraction of the battery voltage, V. Give detailed support.
(c) Suppose one of the resistors, R is removed from the circuit, without reconnecting the wires. Which component will develop more power, the remaining resistor or the light bulb? Justify your answer.
5. Students are attempting to determine the speed of sound in air using tuning forks and tubes which are closed at one end. In this procedure, the tube is filled with water, and a tuning fork of known frequency is struck. The vibrating tuning fork is then held over the tube filled with water, and the water is slowly drained out of the tube while students listen for the loudest possible sound at the first resonant condition. Once the loudest possible sound is heard (the first harmonic), the distance from the top of the tube to the water’s surface (L) is measured and recorded. This procedure is repeated for five tuning forks of varying frequencies. Data is recorded in the table below.
(a) Determine the period of oscillation (T) for each of the five trials and fill in the data table above.
(b) Write an equation for the wavelength of the sound wave (λ) as a function of L.
(c) Use the grid below to plot a linear graph of wavelength (λ) as a function of period (T). Use the empty boxes in the data table to record any calculated values you are graphing. Label the axes as appropriate.
(d) Draw a best-fit line on your graph. Using your best-fit line, determine the speed of the sound waves in air.
(e) Describe how your procedure and analysis would change if you used the third harmonic instead of the first harmonic to determine the speed of sound. Indicate specifically any changes in calculations.
5