PHY 2060 Fall 2005 — Exam 1Instructions: Attempt all ten questions, each of which carries a maximum of 10 points.You will receive credit only for knowledge and understanding that you demonstrate in yourwritten solutions. To maximize your score, you should briefly explain your reasoning andshow all working. Give all final answers in terms of variables defined in the problem (andpossibly also g, the acceleration due to gravity). Please try to write neatly!During this exam, you may use a single formula sheet. You are not permitted to consultany other books, notes, or papers, to use calculators or any other electronic device, or tocommunicate with anyone other than the proctor. In accordance with the UF Honor Code,by turning in this exam to be graded, you affirm the following pledge: On my honor, I haveneither given nor received unauthorized aid in doing this assignment.1. An object moving in one dimension is observed to have a position x that varies withtime t according to x(t)=x0cos(2πt/τ), where x0=10cmandτ = 3 seconds.(a) Determine the particle’s velocity v(t) and acceleration a(t).(b) What is the maximum velocity, and at what position(s) does it occur?(c) What is the maximum acceleration, and at what position(s) does it occur?2. Two blocks rest on a horizontal, frictionless surface, and are connected by an idealstring, which is also horizontal. Mass m1is subjected to a force of magnitude F1,andmass m2is subjected to a force of magnitude F2, directed as shown in the figure.(a) What is the accelerationof mass m1?(b) What is the tension inthe string?m12mF2F13. A plane flying at a constant airspeed of 120 km/hr has enough fuel to power the enginefor only another 17 minutes. The pilot hopes to reach a landing strip located 32 kmdue north of the plane’s current position. The pilot is initially unaware that there is a30 km/hr wind heading due west. However, after 12 minutes of steering due north, thepilot realizes that the plane is being blown off course and corrects the plane’s headingto properly take the wind into account.(a) At the moment the plane corrects course, how far is it from the landing strip?(b) Still flying at an airspeed of 120 km/hr, can the plane reach the landing stripbefore the fuel runs out? Explain your answer.You should be able to do all necessary arithmetic without the aid of a calculator. Itmay be helpful to recall that 60 km/hr = 1 km/min and that 32+42=52.14. A construction worker stands in a crane bucket that is being lowered vertically down-ward at a constant speed vb. The worker throws a pebble vertically upward at a speedvprelative to the bucket. If the pebble is released at a height h above the ground, whatis the greatest distance above the ground that the pebble reaches during its subsequentmotion? You may ignore drag forces and the possibility that the pebble hits anythingelse before reaching the ground.5. A block of mass m rests on a plane inclined at anangle θ above the horizontal. To prevent the blocksliding down the incline, a horizontal force of minimummagnitude F must be applied to the block.(a) Find the magnitude of the normal force exertedon the block by the plane.(b) Find the coefficient of static friction between theblock and the plane.θF6. Two beads A and B, of masses mAand mB, are attached at different points to an idealstring, which is then twirled in a horizontal plane so that the beads pursue circularmotion about point O with radii rAand rB, respectively. The outer bead (A)isobserved to have a constant speed vA.(a) Find the tension T1in thestring between A and B.(b) Find the tension T2in thestring between B and O.ABOBrrA1T2T7. Three blocks (A, B, C of masses mA, mB,mC, respectively) are connected by twoideal strings (1, 2) running over masslesspulleys, as shown in the diagram. There isno friction in the system. Find the massmCthat causes block B to ...(a) move up the incline with a constantspeed v.(b) move up the incline with a constantacceleration a = g/2.ABCstring 1string 2θ8. You want to fire a dart from a blowgun pointing at a fixed angle φ0above the horizontalground. Your goal is for the dart to pass over the top of a wall of height h that standswith its base a distance d from the firing point. By blowing harder or more softly, youcan vary the initial speed v0with which the dart leaves the blowgun.2(a) What is the minimum initialspeed with which the dart mustbe launched in order for it to passover the top of the wall?(b) What is the maximum height ofwall that it is possible for the pro-jectile to pass over (for fixed d,φ0,andg)?φ0dhv09. A runaway railway locomotive traveling at a steady speed vris spotted passing througha station. After a delay time T , a pursuit party sets off from the station on a trackparallel to the runaway’s. The pursuit locomotive undergoes a constant accelerationapfrom rest until it reaches its top speed vp(where vp>vr), which it then maintainsuntil it catches up with the runaway. How far along the tracks from the station doesthe pursuit locomotive overhaul the runaway?10. Two identical slabs of polished granite siton top of one another on a concrete ramp,which is inclined at an angle θ to the hori-zontal. The upper slab starts sliding down-ward along the top of the lower slab, whichin turn starts sliding down the ramp. Thecoefficient of kinetic friction between thetwo slabs is µg, while the coefficient of ki-netic friction between the granite and con-crete surfaces is µc(where µc>µg).θaualFind the acceleration (a) auof the upper slab, (b) alof the lower