PHY–302 K. Final Exam. May 15, 2010, 2 to 5 PM.This exam has 18 problems; make sure you have all 6 pages.Correctly solving any 15 problems out of 18 will give you full credit. You can get extracredit by solving more problems, up to the theoretical maximum of 120% if you solve all 18problems and don’t make any mistakes.You can solve the problems in any order you like. I recommen d you d o them in t h e orderof difficulty, so you don’t get stuck on a h ar d p r ob l em a n d lo se much time while there areeasier problems left unsolved. If you know how to solve a problem, do it, and write down yoursolution. If you don’t, skip to the next problem, or rather to the next problem you know howto solve. Once you have done all the easy problems and written down all the solutions, thenyou can go back to the hard problems and do what you can.1. In one hour, a student walks along 3 sides of a square mile: First 1 mile North, then 1mile East, and then 1 mile Sou t h . Find th e student’s average speed and average velocityduring this wa lk .2. During a post-exam party, a beer bottle flies out of a 7thfloor window, 20 m et er s abovethe ground. The initial velocity of the bottle is 10 m/s directed 30◦above the horizontal.How far from the buildin g does the bottle hit the ground?3. A bee wants to fly to a flower 200 m due North from the beehive. Th e airspeed of thebee is 5 m/s, and the wind blows from East to West at 3 m/s speed.(a) In wh i ch direction shoul d th e bee head to get to the flower?(b) How much time would the flight take?4. When a g u n is fired, the gas pressure in the barrel b ehind the bullet reaches P =500 atm ≈ 50 MPa. The bul l et has mass m = 9 g and diamet er 2R = 9 mm. What is itsacceleration?15. A 2 kg block lies on a ta b l e, and another 2 kg block lies on top of t h e first block. Thetwo blocks are connected by a light unstretchable string which goes over a fixed p u l l ey asshown below:FµµThe pul le y is frictionless and ha s negligible inertia, I ≈ 0. But there is friction betweenthe two blocks, and also between the bottom block and the table; the kinetic frictioncoefficient in bo t h places is µ = 0.25. An external force F pulls th e bottom block to theright an d gives it acceleration a = 2 m/s2. The top b l ock accel er at es to the left.Draw the free-body force diagrams for each block and calculate the external force F .6. A high-sp eed test track for cars has a curved section — a circular arc of radius r = 800 m.The cu r ved section is banked θ = 15◦from the horizontal.r = 800 mθ = 15◦Top Vi ew Rear ViewOne d ay, oil spills on the t r ack making a few meters of th e curved section frictionless.Explain how a car moving at just the right speed v ca n go through this frictionless sectionwithout slipping left or right and calculate that ‘magic’ speed v.27. Pluto — the ninth planet fr om the Sun — has a r a t h er eccentric or bit. At perihelion,Pluto is only 29,658 AU from the Sun, closer than Neptune (the eights planet)! Pluto’sorbital period is 248.09 years. How far does Pluto gets from the Sun at aphelion ?Note: the astronomical unit (AU) is the semi-major axis of the Earth’s orbit around theSun, and the year is the orbital period of Earth. You don ’ t n eed t h ei r numerical valuesin metric units to solve thi s prob l em , bu t if your have to know,1 AU ≈ 1.49598 · 1011m, 1 year ≈ 3.1558 · 107s,MSun≈ 1.98892 · 1030kg, GNewton≈ 6.6674 · 10−11N (m/kg)2.(1)8. A WWI ri fl e could shoot through a big tree and kil l a man hiding behind it. Consideran 11.4 gram bullet going thr ou g h a 60 cm thick tree. It enters the tree with vel ocityv1= 650 m/s and exits it with velocity v2= 350 m/s. The exit velocity is lower becauseof the fric ti o n force between the bullet and the wood. Find this friction force.9. Two 1 kg masses are connected by a light unstretchable string going over a frictionlessI ≈ 0 pu l le y as shown below:30◦The l eft mas s slid es along a frictionless 30◦incline, the right mass moves vertically.The masses are r el eas ed at zero init i al speeds. What are their speeds after the right massmoves down through L = 1 m?10. A 1200 lb cannon shoots a 24 lb ball at 500 MPH speed. The c an non is loose. What isits recoil speed?311. To check the balance of a bicycle wheel, it’s removed from the bike and given a highrotation rate of 3000 revolutions per minute. To stop the wheel’s rotation after the test,a wet rag is pr ess ed against the tire with normal force N = 30 N; the kinetic frictionforce between the tire and the rag is fk= 8.0 N. The wheel has radius R = 33 cm, m assM = 1. 1 kg and moment of inertia I = 0.90MR2.How much time will it take the wet rag to stop the wheel’s rotation ?12. Two space-walking astronauts are connected by a cable of length L = 20 m. Eachastronaut in his spacesuit has gross mass m = 160 kg. The astr on auts rotate aroundtheir common center of mass (loca te d in the middle of the cable) o n ce every minut e.Without firing th ei r jetpacks, they pull on the cable to reduce the distance between themto L′= 10 m.(a) What happens to the rotation rate of the two astronauts?(b) What happens to their net kinetic energy? How much work do the astronauts p er for mwhile pulling on the cable?Hint: the moment of inertia of the two astronaut system about their common center ofmass is I = 2 × M(12L)2=12ML2.13. When you raise your arm , the deltoid muscle in your shoulder pulls on your humerus ( t heshoulder bone) to keep your arm from swinging down. For the sake of definiten ess , let’sassume your arm weighs 8 lb and i t s center of mass is 11 inches distal⋆from the sh ou l d erjoint when the arm is straight. The deltoid muscle is attached to the hume rus bone at apoint 5 inches distal⋆from the shoulder joint; the angle between the muscle — or ra t h erits tendon — and t h e bone is 17◦.Suppose you raise your arm 17◦degrees above the horizontal (so the deltoid muscle’stendon becomes horizontal) and keep it straight. For this position, ca lculate (a) thetension of the deltoi …