I have yet to see any problem, however complicated, which, when you looked at in the right way, did not become still more complicated. |
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-Poul Anderson |
Choose one of these for a brief presentation at the board. YouÕre playing the role of the instructor in a calculus-based introductory physics class. This is not the same as a student's role.
1. Describe how to determine the coefficient of static friction between two objects.
2. A carÕs reliable speedometer reads 20 miles per hour. Hanging from the rear-view mirror is an air freshener on a string. The string hangs towards the left at an angle of 32û with the vertical. Describe the carÕs motion, quantitatively.
3. Starting from rest, a hoop rolls down a hill that makes an angle of 30û with the horizontal. How long does it take to change its elevation by 10 meters?
4. A baseball hit for a home run travels 150 meters. What was its minimum speed upon leaving the bat? (Neglect air resistance.) How much work has the batter done on the baseball?
5. You lean a ladder (length 2.5 m, mass 12 kg) against a wall. You find that if it makes an angle of more than 15û with the vertical it will slide and fall. What information does this give you about what physical quantities, if any?
6. A rock of mass 3 kg is attached to one end of a rope and is swung in a vertical circle of radius 1 m. What minimum tensile strength must this rope have?
7. A clothesline with a tensile strength of 150 N is strung horizontally between two buildings. An object with a weight of 50 N is hung from the middle of this line, and the line promptly breaks. Why does this happen?
8. A rope passes over a pulley. One end is attached to the top of a cage, and the other end dangles into the cage. A student of mass 65 kg is inside the cage, which is initially sitting on the floor below the pulley. The student intends to grab the rope and pull, in order to haul herself and the 30 kg cage upwards. How much force must she apply to the rope? What difficulties may she encounter? How much work will she have done when she has raised the cage through 2 meters? Does this make sense?
9. A vertically oriented, uncompressed spring sits on the floor. A 2 kg mass is initially at rest 2 m above the spring, and is allowed to fall onto it. The spring compresses 3 cm. What is the spring constant?
10. A crate slides across a platform, traveling 2 m in 2 seconds before coming to rest. From this information, determine the minimum angle with respect to the horizontal to which the platform must be tilted to cause the crate to begin sliding again.
11. We have a mass on a frictionless surface and the mass is attached to two springs with different spring constants. One end of each spring is attached to the mass and the other end is attached to a wall. The mass will oscillate at some frequency; does it matter if the two springs are attached to the same wall rather than to two opposite walls? Does the mass act like itÕs attached to only one spring? If so, what is the effective spring constant?
12. Assume all the humans on earth are distributed equally over the surface of the globe. One day we all travel to the equator and hang out there for a week to reminisce about the Harmonic Convergence. During that week, the length of a day differs from its usual length. Calculate that difference.
13. You are dragging a heavy crate across a floor by a rope attached to the top of the crate. Given that the coefficient of kinetic friction between the crate and the floor is mu, what angle should the rope make with the horizontal in order to minimize the force you must apply in order to drag the crate at constant velocity? Will this angle minimize the work you do? If not, what angle will minimize the work?
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