Midterm II for phy231 Monday November 5 2001 Constants g 9 8 m s2 Moments of inertia I sphere 2 5 M R2 I disk 12 M R2 I hoop M R2 1 Two masses are attached to the end of a rod of length 12 m Each has a mass of m 5 kg The rod is rotated around an axis which is 1 4 of the way from one end What is the moment of inertial I in units of kg m2 Ignore the mass of the rod a 720 b 450 Definition of momentum of inertia I m 4 2 m 34 2 d 180 5 kg 32 92 m2 5 90 kg m2 450 kg m2 c 360 e 90 2 A sphere starts from rest at the top of an inclined plan and rolls down The height of the inclined plane is h 5 m and it makes an angle of 30 with respect to the horizontal What is the translational velocity of the sphere when it reaches the bottom in units of m s Use conservation of energy a 10 0 mgh 12 mv 2 21 I 2 I 25 mR2 v R b 8 4 7 mv 2 12 mv 2 1 52 10 c 7 0 m2 gh 490 Therefore v 2 10 7 7 s2 d 4 2 or v 70 m s 8 4 m s e 2 1 3 An ice skater is spinning with his arms stretched out When the skater brings his arms in which is the following is true There are no external torques a The moment of inertia is increased b The angular momentum is increased c The angular velocity is increased d The angular velocity is constant e Kinetic energy is conserved Angular momentum is conserved in this process i e I const Arms pulled in I is reduce is increased 4 A helium filled blimp is floating at a constant height above the ground The volume of the balloon is 2000 m3 the density of helium is 0 18 kg m3 and the density of air is 1 2 kg m3 What is the buoyancy force in newtons a 360 b 2400 c 3500 d 20000 Buoyancy force weight of air replaced force m g air V g 23500 N e 23500 1 5 A fluid which fills a large pipe with a radius of 2 m flows into a smaller pipe with a radius of 1 m Which of the following is true Assume laminar flow a The volume rate of flow does not change b The velocity of the fluid does not change c The pressure in the fluid does not change d The pressure is smaller in the large pipe e The kinetic energy does not change larger A same smaller same larger Av v p 12 v 2 p smaller A same larger same smaller 6 A pool with a depth of 5 m is filled with water What is the increase in pressure from the top of the pool to the bottom of the pool in Psi pounds per square inch The density of water is 1000 kg m3 1 atm 1 01x105 Pa 14 7 Psi a 49000 b 21 9 Increase in pressure is c 14 7 kg m p w gh 1000 m 3 9 81 s2 5 m d 7 1 e 0 49 4 91 104 P a 14 7 P si 1 01 105 P a 7 1 Psi 7 The temperature of a hot coal is 2000 F What is the temperature in K a 820 b 1093 c 1366 d 2273 T K T C 273 59 T F 32 273 1366 e 3632 8 A container of an ideal gas starts out with a temperature of 50 C and a pressure of 1 atm It is heated to a temperature of 100 C The number of atoms and the volume are constant What it the final pressure in units of atm a 0 5 Pi Ti Pf Tf b 0 67 Ideal gas law c 0 87 which implies Pf Pi Tfi in K d 1 15 e 2 0 T Therefore Pf 1 atm 2 373 273 1 15 atm 9 The temperature of an ideal gas increases from 200 K to 800 K The rms root mean square velocity of the atoms in the gas a Stays the same b Decreases by a factor of two Since 21 mv 2 23 kT c Decreases by a factor of four increasing T by a factor of d Increases by a factor of two will increase v by a factor of 2 800 K 200 K 4 e Increases by a factor of four 10 Andy and Bill collide in bumper cars of mass 50 kg each Andy has a mass of 75 kg and Bill has a mass of 50 kg Bill is at rest when Andy strikes him from the rear at v 8 m s Andy s speed is reduced to 4 m s after collision What is Bill s speed after collision in units of m s a 2 Momentum is conserved in the collision PAndy PBill 0 b 3 PAndy mA vf vi A 125 kg 4 m s 500 kg m s c 4 d 5 e 6 PBill mB vf vi B PAndy 500 kg m s 500 kg m s Thus vfB 5 m s 100 kg Note masses mA B include person car 11 When a free standing rifle is fired a Kinetic energy and linear momentum are conserved b Kinetic energy is conserved and linear momentum increases c Kinetic energy increases and linear momentum is conserved d Neither kinetic energy nor linear momentum are conserved e Kinetic energy increases and linear momentum increases 12 A billiard ball collides in an elastic head on collision with a second stationary identical ball After the collision which of the following conditions applies to the first ball a maintains the same velocity as before b has one half its initial velocity c comes to rest d moves in the opposite direction with half the speed e moves in the opposite direction with the same speed 3 See the solution of this problem in the textbook 13 A record drops onto a turntable which turns at a rate of 33 rpm revolutions per minute and accelerates up to speed in 0 6 seconds What is its angular acceleration during this time a 3 46 rad s b 5 76 rad s c 7 57 rad s2 d 5 76 rad s2 e 3 46 rad s2 33 rpm 33 rev 2 rad 1 min t 0 6 s 0 6 min s rev 60 s rad 2 33 rad 5 76 2 2 36 s s 14 Consider a child playing on a swing As she reaches the lowest point in her swing which is the following is true a The tension in the rope is equal to her weight b The tension in the rope is equal to her mass times her acceleration c Her acceleration is downward and equal to g 9 …
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