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101e301 - 9'”ng r KENS Physics 171.101 Exam3 Nov 20 2001...

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Unformatted text preview: 9'”ng r\ KENS Physics 171.101 Exam3 Nov. 20, 2001 Prof. Barnett Do all FOUR problems. You may use anything written on the front and back of ONE 37’X5” index card. Everything should be written in ink and no “snow paint” should be used. Use g = 10 m/sec2, 7r 2 3.0, Sin(370):0.6, Cos(370):0.8, Tan(370):0.75. 1. At t=0 seconds a 0.3 kg firecracker is shot straight up (3 direction) from a gun located at (X20, y:0, 2:0) with a speed of 50 m/second. Four seconds later (at t : 4 seconds) it explodes into 2 parts of unequal mass. The smaller part, 1111, has a mass of 0.1 kg. The larger part, M2, has a mass of 0.2 kg. One second after the explosion, (at t:5 seconds), the smaller mass, 1%, is located at the position E1(:r,y, 2,15 = 5 seconds) = 61 + 125} + 8k meters. A) (5 pts) What is the location of the center of mass for the system at t: 5 seconds? Rcm— — 125 j meters he #65 \° B) (5 pts) What 15 the location of mass .Mg at t: 5 seconds? C952 «*3 T 00w 5 ~ 13 “('05 R203, y,z z,—-t — 5 seconds): —3i +125j + —4k meters 5'3"?“ V“ T 2' l}: I I C) (5 pts) What is the velocity of mass 1% at t: 5 seconds? V1(.r, y, z, t— — 5 seconds)— — 62' + 8k meters/second. D) (5 pts) What is the velocity of mass Mg at t: 5 seconds? V2(2:, y,z 2,152 5 seconds): —31—4k meters/second. E) (5 pts) How much chemical energy was turned into mechanical energy in the explosion? The energy relative to the center of mass is ($) NIH/12 + (é) 1%gi : 7.5J 2. A mass All of 50 kg is hung using a massless cord with tension T from the outer edge of a pulley made of a uniform density disk with total mass Mdisk : 100 kg. The radius of the disk/pulley is 1 meter. Liz-5,, : (g) MdiskR? A) (5 pts) Draw a figure showing all the forces acting 011 Ml Tj and —mgj with j pointing‘ ‘”up. B) (10 pts) What is the torque applied to the disk? "F = 250 Newton-meters directed into the page. C) (10 pts) What is the acceleration of the mass Ml. 51’: —5 771/5602 j 5? E333 (mow-em News; [Ti Rf: Li‘f; {Jig/bloc mm H~ 35’ 3. A cubical empty box with sides of length 1 meter has a mass of 200 kg. It floats in water with density of pwatsr : 1 g/cm3. It has a massless rope dangling down to and wrapped around a rock of density mek = 5 g/cm3. A) (10 pts) At low tide the rope has slack in it, i.e. the rope is not pulling on the rock, (Figure a). What percentage of the box is below the water (a) surface? 20% Low tide B) (10 pts) At high tide the rope becomes taut and the box lifts the rock frOm the bottom of the water, (Figure b). What is the maximum mass rock that the barrel can lift? 103 kg C) (5 pts) For the situation in part (B) what is the tension in the rope? 8000 Newtons High tide 4. liour grams of a thin wire is 100 meters long. A wave of the form A 1/2(:r,t) : (3.00 X 10—2771) sin[(8.0 7r radians/m) x + (4.0 7r radians/second) t] j propagates along a piece of the wire. A) (4 pts) What are the maximum and minimum values of 1/7? i3 cm - B) (4 pts) What are the wavelength and frequency (cycles per second) of the wave? : 1/4 meters f = 2 cycles per second C) (2 pts) Does the wave propagate toward smaller or larger values of x as as time increases? Smaller values of x. D) (5 pts) What is the tension in the wire? The phase velocity is 0.5 m/second : (/T/n. ,u = 4 X 10‘5 kg/m. Tension = 10—5 newtons. E) (5 pts) Draw a graph of the wire displacement at X20 for time period t:0 to 1:24 seconds. 2,0(x,t) : (3.00 X 10—2m) sm[(4.0 7r radians/second) t] j ' F) (5 pts) Draw a graph of the velocity of the wire (not the phase velocity) at X20 for the time period t:O to t=4 seconds. #(znfi) = (12.007T X 10—2m) cos[(4.0 7r m/second) t] ] Refine ERAMPLE‘J‘ [213) 12,9 {2,3/ / H'W I’flCDBLF’I‘x 12.(5“ J l2, (Ci ...
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