AP Physics Spiderman Problem with Solutions Today I would like to give solutions to the AP level free response physics question I gave you yesterday: AP Physics Spiderman Problem Spiderman Free Response Question with Solutions As you know, Spiderman saves a runaway subway by standing at the front of the train and attaching his web to nearby buildings. After five city blocks the train comes to a halt. Assume that the mass of the train is 3.2 × 105 kg and its initial velocity is 90 km/h. Assume also that the web is unstretched when initially attached to the building. If the distance to the buildings is 10 m on each side of the track, and a city block is 50 m long, estimate the spring constant of Spiderman’s web. Quick solution: The situation looks something like the below figure, where the dark rectangle on the left is the initial position of the train, and the light rectangle on the right is the final position. If a city block is 50 m, then the train has moved 250 m before halting. This is much greater than the 10 meters to the buildings, so for a quick approximation, one can merely say that the web has stretched 250 m. The initial energy of the train is its kinetic energy E0 = 1/2 mv2. By energy conservation, the initial kinetic energy must be the energy stored in the web when the train has finally halted. Assuming that the web acts like a spring, we have 1/2 mv2 = kx2, where x = 250 m and k is the spring constant. (We have not put a 1/2 before the expression on the right because there are two strands of web.) Converting km/h to m/s and plugging in the numbers gives k = 1600 N/m, which is high, but not inconceivable. Rigorous solution: If s is the hypotenuse of the right triangle, the energy in the web is actually k(s – s0)2, where s – s0 is the amount it has stretched from its initial position, s0 = 10 m. With the Pythagorean theorem, we get s = 250.2 m, almost exactly the previous answer, and (s – s0) = 240.2 m. Setting mv2/2(s – s0)2 = k yields k = 1733 N/m, which is only 7.6% from the Quick solution, all of which shows the value of making approximations. More Practice for the AP Physics Exams If you are preparing for the AP Physics 1 or 2 exams, you may want to check out Physics Mastery. Click the image below to see the book’s Amazon page. If you think your friends might be interested in this article, please share it with them on Facebook: Thank you all for your continued support! Comments comments