Unformatted text preview:

PHY 2060 Spring 2006 — 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 algebraic answers in terms of variables defined in the problemand/or g, the acceleration due to gravity near the Earth’s surface. For numerical problems,take g =10m/s2. Please try to write neatly!During this exam, you may use one formula sheet and an electronic calculator. You arenot permitted (a) to consult any other books, notes, or papers, (b) to use any other electronicdevice, or (c) to communicate with anyone other than the proctor. In accordance with theUF Honor Code, by turning in this exam to be graded, you affirm the following pledge: Onmy honor, I have neither given nor received unauthorized aid in doing this assignment.1. The position of a water boatman (an aquatic insect) on the surface of a pond at timet is described by the coordinates x =4− 6t +3t2, y = −2 − t3.(a) Find the water boatman’s velocity and acceleration at time t.(b) Find the insect’s average velocity over the interval between t =0andt =3.(c) At what time 0 <t<3 is the insect’s instantaneous velocity parallel to theaverage velocity defined in (b)?2. A boy stands on a balcony and throws a ball horizontally from a height of 20 m abovethe flat ground. The pebble hits the ground a horizontal distance 30 m from the pointwhere the pebble was released. Air resistance is negligible.(a) What is the pebble’s initial speed?(b) With what velocity (magnitude and direction) does the pebble strike the ground?3. A 20-kg mass is suspended at rest using three ideal stringsattached to two rigid walls, as shown in the diagram. Findthe string tensions T1, T2,andT3.45oT1T3T214. A pendulum consists of a bob of mass m swinging the end of an ideal string of lengthL.Letθ denote the angle of the string measured from the vertical. The bob’s speedvaries between v = 0 at the ends of the swing (θ = ±θmax)andv = vmaxat the bottomof the swing (θ =0).(a) Find the bob’s acceleration (magnitude and direction) at the bottom of the swing(θ =0).(b) Find the bob’s acceleration (magnitude and direction) at one end of the swing(θ =+θ0).5. Three blocks, with masses m1=15kg,m2=5kg,andm3=30 kg, are connected by two ideal strings as shown in thediagram. The pulleys are massless and frictionless. Find thenet force on the mass m1.m3m1m26. Two PHY 2060 students want to swim across a straight, 50-m-wide river to a divingplatform directly opposite them on the other side. Ina Rush impetuously sets outswimming at right angles to the riverbanks, but is swept downstream by the 0.3-m/scurrent. When she reaches the far side, Ina finds the riverbank is too steep to climb, soshe has to swim upstream parallel to the bank until she reaches the platform. PatiencePersonified gets out her calculator and protractor, figures out the correct direction toswim to ensure she travels straight across the river, and enters the water 45 secondsafter Ina. Assuming that both students swim at 0.5 m/s through the water, determinewhich one reaches the platform first, and how much later the other student arrives.7. Two blocks 1 and 2, of mass m1and m2, respectively,slide down a long ramp making an angle θ with the hori-zontal. The blocks are connected by an ideal string thatruns parallel to the slope. The coefficient of kinetic fric-tion between the slope and block 1 is µ1. The coefficientof kinetic friction between the slope and block 2 is µ2.Assume that µ2>µ1. Find the magnitude of the blocks’acceleration.θ128. A passenger train is traveling at 50 m/s when the engineer sees that a freight train isonly 1.6 km ahead on the same track. The freight train is moving at a constant speedof 10 m/s in the same direction as the passenger train. The engineer immediatelyapplies the passenger train’s brakes. What is the minimum magnitude of the resultingacceleration (in m/s2) if a collision is just to be avoided?Hint: Consider the freight train’s position relative to the passenger train.29. A big-money archery challenge requires thecontestants to fire a single arrow through twosmall rings located at the same height h abovethe firing point. The horizontal distance fromthe firing point to the first ring is d1, whilethat to the second ring is d2(see diagram). Atwhat angle φ0to the horizontal must an ar-row be fired to win the prize? Assume thatair resistance is negligible.d1d2hhφ0Hint: It may be useful to recall that a2− b2=(a + b)(a − b).10. A highway curve of radius R is banked to allow a vehicle moving at speed v0to traversethe curve without any sideways frictional force between the tires and the road. Supposethat a car instead traverses the curve at a constant speed v (which may be greater orless than v0). Find an expression for the minimum coefficient of static friction betweenthe tires and the road necessary to prevent slippage.Hint: Apply Newton’s second law in the radial and vertical


View Full Document

UF PHY 2060 - Exam 1

Documents in this Course
Load more
Download Exam 1
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Exam 1 and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Exam 1 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?