XF.10 205PHYS-205(10) (Kaldon-18454) Name ______________________________________________WMU-Winter 2002 Final Exam - 200,000 points + 40,000 ¶ points Check-Out: Q X3 Grades T ___4/21/2002•Rev.A7State Any Assumptions You Need To Make – Show All Work – Circle Any Final AnswersUse Your Time Wisely – Work on What You Can – Be Sure to Write Down EquationsFeel Free to Ask Any Questions¶2a ¶2b ¶2c ¶2eSafety First (50,000 points)1.) (a) A small car, m = 1350 kg, is moving at only 5.00 mph (2.23 m/s). How much kinetic energy Kdoes it have?(b) The small car is equipped with 5 mph safety bumpers, basically a rigid piece of steel on a spring withconstant k. The spring is compressed 4.00 cm when the car runs into a brick wall at 5.00 mph (2.23 m/s).Find the spring constant k.(c) If the car didn’t have the safety bumper, find the average acceleration a needed to bring the car to astop from 5.00 mph (2.23 m/s) in a distance of 4.00 cm.(d) Smashing the 5.00 kg of steel of the front of the car will result not just in bending and making a noise,but raising its temperature. Find the temperature change DT of 5.00 kg of steel when it absorbs a heatenergy Q = 2250 J. The specific heat of steel is csteel = 448 J/kg·°C-1.(e) A shelf of width D is made from a uniform slab of wood with massm. It is attached to the wall at Point 1 with a force rF1 and is proppedup at the end by another piece of wood which exerts a force rF2 on theshelf at Point 2. Draw the Free Body Diagram and Free RotationDiagram of the shelf. Identify which way all the components of rF1 andrF2 point. Hint: Should the prop piece be in tension or compression?Physics 205 / Final Exam [Form-A] Winter 2002 Page 2Star Points – The Tasty New Breakfast Sensation (50,000 points)2.) ¶(a) An experimental high speed car (m=4100. kg) is traveling at 400. mph (179 m/s) and needs to bestopped. But the car tends to flip if the brakes are applied too hard too early. So the driver uses a forceequal to F1 = C x³, where x is how far the car has traveled while braking, and brings the car to a stop in2450 m. Set up an integral to find the work done by the force and solve for the constant C.¶(b) The speed of an object can be described by the following equation. Find the position of the objectat the time t = 1.23 sec.vt ms ms ms()././ ./=+ +7 00 7 00 7 00243tt¶(c) The angular speed of an object can be described by the following equation. Find the angularacceleration of the object at the time t = 1.23 sec.w ()./././t rad s rad s rad s=+ +700 700 700243tt(d) Vector rrroCAB m=+=1315 35.@ and Vector rB has components Bmix= 62 3.$ and Bmjy=-42 7.$.What is the standard angle q of Vector rA ?¶(e) The wreck of the RMS Titanic lies 3821 meters below the surface of the ocean, where the pressureon it is 48,240,000 Pa. We can’s just use P = r g h because r is not constant. While water is fairlyincompressible, it does increase somewhat from its surface value of r0 = 1030 kg/m³. If we let the mass-to-volume ratio for sea water to be rr()yChy=+FHGIKJ01 , then integrate Pygdyh=zr ()0 where h = 3821 mto find the constant C. To eliminate minus signs, we are defining y-positive as down.Physics 205 / Final Exam [Form-A] Winter 2002 Page 3Dr. Phil Marvels That ANYONE Can Afford a Boat! (50,000 points)3.) The $114,121 Hydra-Sports 2796 Vector cc uses twin Evinrude outboard motors, eachwith 250 h.p., to move a 6900 pound boat (m = 3130 kg) at speeds up to 54.5 mph (24.4 m/s).At top speed, the engines are generating 500. h.p. total. That’s 373,000 W. (a) If weneglected all air and water resistance forces, how long (time) would it take for this boat to getto 54.5 mph (24.4 m/s) using the power of 373,000 W?(b) However there are resistive forces, and it would not only take longer, but limit the top speed. Find theconstant force that a power of 500. h.p. generates at 54.5 mph (24.4 m/s).(c) At 54.5 mph (24.4 m/s), the boat can’t go any faster due to hydrodynamic resistance – water drag.This is similar to the drag due to air resistance. Use the high speed drag equation, F = c v², and find theconstant c. If you didn’t get an answer to (b), then use F = 10,000 N.(d) How many Joules/second of Useful Work (per time) is 500. h.p.?The fuel economy at top speed is 1.23 miles per gallon, since the boat can travel 333 miles on 270 gallonsof gas, when traveling at 54.5 mph for 6.11 hours. This results in 1.62 × 106 J of total energy available persecond. (e) Find the Actual Efficiency, eactual , of the engines.Physics 205 / Final Exam [Form-A] Winter 2002 Page 4Whirling Physicists (50,000 points)4.) Consider a merry-go-round on a children’s playground, mass M = 277 kg andradius R = 3.00 m, that we can treat as a uniform solid disk to find it’s moment ofinertia I. The merry-go-round is spinning at a constant w = 1.50 rad/sec with fourlarge adult men (m1 = m2 = m3 = m4 = 175 kg) having just hopped onto the edgeof the merry-go-round. (a) What was the men’s linear speed just before theyjumped onto the merry-go-round?(b) Find the frequency f and the period T of the merry-go-round is spinning at a constant w = 1.50 rad/sec.(c) If the men all move 2.00 meters closer to the central pivot point, what is the new angular velocity ofthe merry-go-round? Hint: What rotational quantity can we conserve in this problem?(d) A squirrel in a tree 15.0 meters above the ground watches this show, and laughing, rushes to go tell hisbrothers about these stupid humans. Leaping from one branch with v0x = 7.80 m/s, the squirrelunfortunately misses the next branch and falls all the way to the ground. How far away from his releasepoint does he hit the ground? Assume he begins to free-fall immediately.(e) Lying on the ground, catching his breath, the surprised squirrel contemplates that his weight and hisnormal force exactly cancel each other, so that he doesn’t move. What principle of Physics is in playhere? Short