Physics Education Research and Development Group
Here are some examples of context rich problems. For your convience we have included the physics concepts important for each problem. This is never done for the students.
One-Dimensional, Constant Velocity
You are writing a short adventure story for your English class. In your story, two submarines on a secret mission need to arrive at a place in the middle of the Atlantic ocean at the same time. They start out at the same time from positions equally distant from the rendezvous point. They travel at different velocities but both go in a straight line. The first submarine travels at an average velocity of 20 km/hr for the first 500 km, 40 km/hr for the next 500 km, 30 km/hr for the next 500 km and 50 km/hr for the final 500 km. In the plot, the second submarine is required to travel at a constant velocity, so the captain needs to determine the magnitude of that velocity.
Weight and Normal Force, No Radial Force Components
Just before finals you decide to visit an amusement park set up in the Metrodome. Since it is a weekend, you invite your favorite niece along. She loves to ride on a Ferris wheel, and there is one at the amusement park. The Ferris wheel has seats on the rim of a circle with a radius of 25 m. The Ferris wheel rotates at a constant speed and makes one complete revolution every 20 seconds. While you wait, your niece who has a mass of 42 kg, rides the Ferris wheel. To kill time you decide to calculate the total force (both magnitude and direction) on her when she is one quarter revolution past the highest point. Because the Ferris wheel can be run at different speeds, you also decide to make a graph which gives the magnitude of the force on her at that point as a function of the period of the Ferris wheel.
Electrical Energy (Ohm's Law)
Because of your physics background, you landed a summer job as an assistant technician for a telephone company in California. During a recent earthquake, a 1.0 mile long underground telephone line is crushed at some point. This telephone line is made up of two parallel copper wires of the same diameter and same length which are normally not connected. At the place where the line is crushed, the two wires make contact. Your boss wants you to find this place so that the wire can be dug up and fixed. You disconnect the line from the telephone system by disconnecting both wires of the line at both ends. You then go to one end of the line and connect one terminal of a 6.0-V battery to one wire, and the other terminal of the battery to one terminal of an ammeter (which has essentially zero resistance). When the other terminal of the ammeter is connected to the other wire, the ammeter shows that the current through the wire is 1 A. You then disconnect everything and travel to the other end of the telephone line, where you repeat the process and finds a current of 1/3 A.
Conservation of Energy (Mechanical, Gravitational)
You are watching a National Geographic Special on television. One segment of the program is about archer fish, which inhabit streams in southeast Asia. This fish actually "shoots" water at insects to knock them into the water so it can eat them. The commentator states that the archer fish keeps its mouth at the surface of the stream and squirts a jet of water from its mouth at 13 feet/second. You watch an archer fish shoot a juicy moth off a leaf into the water. You estimate that the leaf was about 2.5 feet above a stream. You wonder at what minimum angle from the horizontal the water can be ejected from the fish's mouth to hit the moth. Since you have time during the commercial, you quickly calculate this angle.
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