Physics 18 Spring 2010 Midterm 1 For the midterm, you may use one sheet of notes with whatever you want to put on it, front and back. Please sit every other seat, and please don t cheat! If something isn t clear, please ask. You may use calculators. All problems are weighted equally. PLEASE BOX YOUR FINAL ANSWERS! You have the full length of the class. If you attach any additional scratch work, then make sure that your name is on every sheet of your work. Good luck! 1. A 75 kilogram base runner has an initial speed of 8 m/s (almost 18 miles per hour), and he then slides to a stop over 4 m. What is the coefficient of sliding friction between the runner and ground during the slide? 1
2. An accident victim with a broken leg is being placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of 4.0 kg, and the doctor has decided to hang a 6.0 kg mass from the rope. The boot is suspended by the ropes and does not touch the bed. (a) Determine the amount of tension in the rope by using Newton s laws to analyze the hanging mass. (b) The net traction force needs to pull straight out on the leg. What is the proper angle θ for the upper rope? (c) What is the net traction force pulling the leg? Hint: If the pulleys are frictionless, which we will assume, the tension in the rope is constant from one end to the other. 2
3. Astronauts use a centrifuge to simulate the acceleration of a rocket launch. The centrifuge takes 30 seconds to speed up from rest to its top speed of 1 rotation every 1.3 seconds. The astronaut is strapped into a seat 6.0 m from the axis. (a) What is the astronaut s tangential acceleration during the first 30 seconds? (b) How many g s of acceleration does the astronaut experience when the device is rotating at top speed (each 9.8 m/s 2 of acceleration is 1 g)? 3
4. Let s look the maximum safe heights that a person could jump from in two different landing cases. (a) First, suppose a person of mass m jumps from a height h, and lands with straight legs such that they stop in a small distance d, cushioned only by the padding on the bottom of their feet. Using conservation of energy, show that the force acting back up on them from the ground is F = mgh d. (b) Upon compression bones typical break when subjected to a force per area above about 1.7 10 8 N/m 2. If the tibia near the ankle has a radius of about 1 cm, estimate the maximum height from which a 70 kg person could just land without breaking any bones if the padding on the soles of their feet is about 1 cm. (c) Now, suppose the person lands at the end of the jump using the muscles in his knees to help cushion the collision. Now his center of mass falls a height h before his feet make contact with the ground, but then he bends down, dropping his center of mass a further distance s (we can ignore the padding on his feet now, since it s small compared to how much he bends). Show that the required force is now ( F = mg 1 + h ). s (d) If he bends down 0.5 meters, what is the maximum height that he could just land from without breaking any bones? (Kids - don t try this at home!) 4
The potential energy between a pair of neutral atoms or molecules is very well-approximated by the Lennard-Jones Potential, given by the expression [ (σ ) 12 ( σ ) ] 6 P E(r) = 4ɛ, r r where ɛ and σ are constants, and r is the distance between the molecules. The potential energy is plotted in the figure to the right. The vertical axis is in units of ɛ, while the horizontal axis is in units of σ. Extra Credit Question!! The following is worth 10 extra credit points! Energy 8 7 6 5 4 3 2 1 0-2 -3-4 Molcular Bond Energy 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25-1 Distance (a) Why does the potential energy approach zero as the distance gets bigger? (b) At what separation distance, in terms of σ and ɛ, is the potential energy zero? (c) At approximately what distance is the system in equilibrium? What is the potential energy at that distance? (Express your answers in terms of σ and ɛ.) (d) How much energy would you need to add to the system at equilibrium in order to break the molecular bonds holding it together? Why? (e) How much energy is released in the breaking of those molecular bonds? Why? Note - no calculation is needed to answer these problems! 5