Physics 8 Spring 2012 Midterm 1

Transcription

1 Physics 8 Spring 2012 NAME: TA: Physics 8 Spring 2012 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. Wile E. Coyote (Carnivorus hungribilus) is chasing the Roadrunner (Speedibus cantcatchmi) yet again. While running down the road, they come to a deep gorge, 15.0 m straight across and 100 m deep. The Roadrunner launches himself across the gorge at a launch angle of 15 above the horizontal, and lands with 1.5 m to spare. (a) What was the Roadrunner s launch speed? (b) Wile E. Coyote launches himself across the gorge with the same initial speed, but at a different launch angle. To his horror, he is short of the other lip by 0.50 m. What was his launch angle? (Assume that it was less than 15.) 1

2 2. When visiting Yosemite, campers staying in Curry Village are warned by park rangers to store food in lockers outside the cabins to keep bears from getting into your supplies (and never leave food in your car - bears have broken in to get at a single candy bar wrapper). However, bear lockers are not available when camping in the wilderness and the next best alternative is to hang up your pack. Consider a 26 kilogram pack seen the two circumstances in the figures below. (a) In the first case, the ropes were of different lengths and the pack hangs at the angles seen. Calculate the tension in the two ropes. (b) The first situation hung too low, making the pack accessible to the bear. So, you ve shortened the longer rope to hang the pack as seen in the second case. Now what is the tension in the ropes? 2

3 3. Consider two displacement vectors, r 1 = 16î + 31ĵ meters and r 2 = 21î + 10ĵ + 14ˆk meters. (a) What is the length of each vector, r 1 = r 1, and r 2 = r 2? (b) What is the angle, θ, between the two vectors, r 1 and r 2? (c) How much work does a force F = 67î+23ĵ +55ˆk Newtons do as it acts on a body moving in a straight line from r 1 to r 2 (i.e., along r = r 2 r 1 )? 3

4 4. A 190 gram block is launched by compressing a spring of constant k = 200 N/m by 15 cm. The spring is mounted horizontally, and the surface directly under it is frictionless. But, beyond the equilibrium position of the spring end, the surface has frictional coefficient µ k = This frictional surface extends 85 cm, followed by a frictionless curved rise, as shown in the figure to the right. (a) If there was no frictional part, how high up the ramp would the block slide? (b) If we now include the frictional part, how high up the ramp does the block slide? (c) After the block reaches the top of the ramp, it slides back down, over the frictional surface, compressing the spring. The spring then pushes the block back to do the same trip over, again. However, each during each trip, the block slows down when passing over the rough patch. How many times does the block slide over the frictional surface? (Note: you ll get a decimal, meaning that it doesn t make it all the way. Just give the whole number actual completed trips.) (d) How far along the rough patch (measured from the left-hand-side) does the block ultimately stop? 4

5 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 Molcular Bond Energy 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