1) a 2.0 Kg Mass Is Located at (4.0 M, 0.0 M, 0.0 M) and a 4.0 Kg Mass Is Located at (0.0

Chapter 8

1) A 2.0 kg mass is located at (4.0 m, 0.0 m, 0.0 m) and a 4.0 kg mass is located at (0.0 m, 3.0 m, 0.0 m). If this system of masses rotated about the Z-axis perpendicular to the X-Y plane, then the moment of inertia of this system is a) 50 kg m 2 b) 55 kg m 2 c) 58 kg m 2 d) 62 kg m 2 e) 68 kg m 2 Ans: e

2) A 2.0 kg mass is located at (4.0 m, 0.0 m, 0.0 m) and a 4.0 kg mass is located at (0.0 m, 3.0 m, 0.0 m). If this system of masses rotated about the X-axis perpendicular to the Z-Y plane, then the moment of inertia of this system is a) 23 kg m 2 b) 28 kg m 2 c) 33 kg m 2 d) 36 kg m 2 e) 41 kg m 2 Ans: d

3) A 2.0 kg mass is located at (4.0 m, 0.0 m, 0.0 m) and a 4.0 kg mass is located at (0.0 m, 3.0 m, 0.0 m). If this system of masses rotated about the Y-axis perpendicular to the Z-X plane, then the moment of inertia of this system is a) 27 kg m 2 b) 32 kg m 2 c) 38 kg m 2 d) 42 kg m 2 e) 48 kg m 2 Ans: b

144 4) A 4.0 kg mass is located at (2.0 m, 2.0 m, 0.0 m) and a 3.0 kg mass is located at ( - 1.0 m, 3.0 m, 0.0 m). If this system of masses rotated about the Z-axis perpendicular to the X-Y plane, then the moment of inertia of this system is a) 62 kg m 2 b) 70 kg m 2 c) 75 kg m 2 d) 81 kg m 2 e) 88 kg m 2 Ans: a

5) A 4.0 kg mass is located at (2.0 m, 2.0 m, 0.0 m) and a 3.0 kg mass is located at ( - 1.0 m, 3.0 m, 0.0 m). If this system of masses rotated about the X-axis perpendicular to the Z-Y plane, then the moment of inertia of this system is a) 24 kg m 2 b) 36 kg m 2 c) 43 kg m 2 d) 56 kg m 2 e) 62 kg m 2 Ans: c

6) A 4.0 kg mass is located at (2.0 m, 2.0 m, 0.0 m) and a 3.0 kg mass is located at ( - 1 m, 3.0 m, 0.0 m). If this system of masses rotated about the Y-axis perpendicular to the X-Z plane, then the moment of inertia of this system is a) 40 kg m 2 b) 32 kg m 2 c) 29 kg m 2 d) 24 kg m 2 e) 19 kg m 2 Ans: e

7) A 6.0 kg mass is located at (2.0 m, 2.0 m, 2.0 m) and a 5.0 kg mass is located at ( - 1.0 m, 3.0 m, - 2.0 m). If this system of masses rotated about the Z-axis perpendicular to the X-Y plane, then the moment of inertia of this system is a) 60 kg m 2 b) 79 kg m 2 c) 85 kg m 2 d) 98 kg m 2 e) 112 kg m 2 Ans: d

145 8) A 6.0 kg mass is located at (2.0 m, 2.0 m, 2.0 m) and a 5.0 kg mass is located at ( - 1.0 m, 3.0 m, - 2.0 m). If this system of masses rotated about the X-axis perpendicular to the Z-Y plane, then the moment of inertia of this system is a) 281 kg m 2 b) 167 kg m 2 c) 113 kg m 2 d) 85 kg m 2 e) 69 kg m 2 Ans: c

9) A 6.0 kg mass is located at (2.0 m, 2.0 m, 2.0 m) and a 5.0 kg mass is located at ( - 1.0 m, 3.0 m, - 2.0 m). If this system of masses rotated about the Y-axis perpendicular to the Z-X plane, then the moment of inertia of this system is a) 73 kg m 2 b) 66 kg m 2 c) 60 kg m 2 d) 55 kg m 2 e) 48 kg m 2 Ans: a

10) A 20 cm wrench is used to generate a torque at a bolt. A force of 50 N is applied perpendicularly at the end of the wrench. The torque generated at the bolt is, a) 8 Nm b) 10 Nm c) 14 Nm d) 22 Nm e) 37 Nm Ans: b

11) A 30 cm wrench is used to generate a torque at a bolt. A force of 40 N is applied perpendicularly at the end of the wrench. The torque generated at the bolt is, a) 5 Nm b) 7 Nm c) 9 Nm d) 12 Nm e) 20 Nm Ans: d

146 12) A 20 cm wrench is used to generate a torque at a bolt. A force of 50 N is applied at the end of the wrench at an angle of 60 degrees to the wrench. The torque generated at the bolt is, a) 4.9 Nm b) 5.7 Nm c) 6.0 Nm d) 7.5 Nm e) 8.7 Nm Ans: e

13) A 30 cm wrench is used to generate a torque at a bolt. A force of 50 N is applied at the end of the wrench at an angle of 70 degrees. The torque generated at the bolt is, a) 10.4 Nm b) 14.1 Nm c) 19.7 Nm d) 21.5 Nm e) 26.2 Nm Ans: b

14) A 2.0 kg mass is located at (4.0 m, 0.0 m, 0.0 m) and a 4.0 kg mass is located at (0.0 m, 3.0 m, 0.0 m). The center of gravity of the system of masses is, a) (1.33m, 2.00m, 0) b) (1.33m, 1.00m ,0) c) (1.50m, 1.33m ,0) d) (2.00m, 1.33m ,0) e) (1.33m, 1.50m ,0) Ans: a

15) A 5.0 kg mass is located at (2.0 m, 0.0 m, 0.0 m) and a 3.0 kg mass is located at (0.0 m, 4.0 m, 0.0 m). The center of gravity of the system of masses is, a) (1.25m, 1.25m, 0) b) (1.50m, 1.50m, 0) c) (1.25m, 1.50m, 0) d) (1.50m, 1.25m, 0) e) (1.00m, 1.00m, 0) Ans: c

147 16) A 5.0 kg mass is located at (2.0 m, 0.0 m, 3.0 m) and a 2.0 kg mass is located at (0.0 m, 4.0 m, - 2.0 m). The center of gravity of the system of masses is, a) (10/7m, 8/7m, 11/7m) b) (11/7m, 7/7m, 8/7m) c) (7/7m, 10/7m, 11/7m) d) (10/7m, 7/7m, 8/7m) e) (8/7m, 7/7m, 10/7m) Ans: a

17) A 5.0 kg mass is located at (1.0 m, 0.0 m, 3.0 m), a 2.0 kg mass is located at (0.0 m, 3.0 m, - 2.0 m), and a 3.0 kg mass is located at ( - 1.0 m, - 2.0 m , 0.0 m). The center of gravity of the system of masses is, a) (1/10m, 10/10m, 1/10m) b) (2/10m, 0m, 11/10m) c) (3/10m, 2/10m, 10/10m) d) (10/10m, 2/10m, 3/10m) e) (2/10m, 10/10m, 0m) Ans: b

18) A 6.0 kg mass is located at (1.0 m, - 2.0 m, 3.0 m), a 5.0 kg mass is located at (1.0 m, 3.0 m, - 2.0 m), and a 4.0 kg mass is located at ( - 1.0 m, - 2.0 m, 2.0 m). The center of gravity of the system of masses is, a) ( 5/15m, -1/15m, 17/15m) b) ( 5/15m, -17/15m, 5/15m) c) (12/15m, -5/15m, 16/15m) d) (17/15m, -5/15m, 16/15m) e) (16/15m, -1/15m, 17/15m) Ans: d

19) A 10 kg object has a moment of inertia of 1.25 kg m 2 . If a torque of 2.5 Nm is applied to the object, the angular acceleration is, a) 10 rad/s 2 b) 8 rad/s 2 c) 6 rad/s 2 d) 4 rad/s 2 e) 2 rad/s 2 Ans: e

148 20) An 8.0 kg object has a moment of inertia of 1.00 kg m 2 . What torque is needed to give the object an angular acceleration of 1.5 rad/s 2 ? a) 3.0 Nm b) 2.5 Nm c) 2.0 Nm d) 1.5 Nm e) 1.0 Nm Ans: d

21) A 10 kg sphere with a 25 cm radius has a moment of inertia of 2/5MR 2 . If a torque of 2.0 Nm is applied to the object, the angular acceleration is, a) 1 rad/s 2 b) 2 rad/s 2 c) 4 rad/s 2 d) 6 rad/s 2 e) 8 rad/s 2 Ans: e

22) An 8.0 kg object has a moment of inertia of 1.5 kg m 2 . If a torque of 2.0 Nm is applied to the object, the angular acceleration is, a) 0.75 rad/s 2 b) 1.00 rad/s 2 c) 1.33 rad/s 2 d) 2.01 rad/s 2 e) 2.67 rad/s 2 Ans: c

23) A 5.0 kg object has a moment of inertia of 1.2 kg m 2 . What torque is needed to give the object an angular acceleration of 2.0 rad/s 2 ? a) 2.4 Nm b) 2.6 Nm c) 2.8 Nm d) 3.0 Nm e) 3.2 Nm Ans: a

149 24) A 10 kg solid cylinder with a 50 cm radius has a moment of inertia of 1/2MR 2 . If a torque of 2.0 Nm is applied to the object, the angular acceleration is, a) 1.0 rad/s 2 b) 1.6 rad/s 2 c) 1.8 rad/s 2 d) 2.1 rad/s 2 e) 2.3 rad/s 2 Ans: b

25) A torque of 2.0 Nm is applied to a 10 kg object to give it an angular acceleration. If the angular acceleration is 1.75 rad/s 2 , then the moment of inertia is, a) 0.95 kg m 2 b) 1.05 kg m 2 c) 1.14 kg m 2 d) 1.20 kg m 2 e) 1.35 kg m 2 Ans: c

26) The moment of inertia of a rod being rotated about one end is 1/3 M L 2 . What is the moment of inertia of a rod of length L and mass M being rotated about a point located .30 L? a) 0.123 ML 2 b) 0.198 ML 2 c) 0.205 ML 2 d) 0.240 ML 2 e) 0.300 ML 2 Ans: a

27) The moment of inertia of a rod being rotated about one end is 1/3 M L 2 . What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.40 L? a) 0.080 ML 2 b) 0.072 ML 2 c) 0.068 ML 2 d) 0.060 ML 2 e) 0.056 ML 2 Ans: b

150 28) A 4.0 kg hollow sphere of radius 5.0 cm starts from rest and rolls without slipping down a 30 degree incline. The acceleration of the center of mass of the hollow sphere is, a) 2.00 m/s 2 b) 2.22 m/s 2 c) 2.50 m/s 2 d) 2.64 m/s 2 e) 2.94 m/s 2 Ans: e

29) A 4.0 kg hollow sphere of radius 5.0 cm starts from rest and rolls without slipping down a 30 degree incline. . If the length of the incline is 50 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is, a) 1.28 m/s b) 1.44 m/s c) 1.65 m/s d) 1.72 m/s e) 1.98 m/s Ans: d

30) A 2.0 kg hollow sphere of radius 6.0 cm starts from rest and rolls without slipping down a 10 degree incline. . If the length of the incline is 50 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is, a) 1.51 m/s b) 1.47 m/s c) 1.22 m/s d) 1.01 m/s e) 0.95 m/s Ans: d

31) A 3.0 kg hollow sphere of radius 5.0 cm starts from rest and rolls without slipping down a 15 degree incline. . If the length of the incline is 100 cm, then the velocity of the center of mass of the hollow sphere at the bottom of the incline is, a) 3.02 m/s b) 2.59 m/s c) 2.37 m/s d) 2.02 m/s e) 1.75 m/s Ans: e

32)A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of ½ M*R 2 . If m1 is 1.0 kg, m2 is 2.0 kg, and M is 4.0 kg, then what is the acceleration of m1? a) 1.55 m/s 2 b) 1.96 m/s 2 c) 2.06 m/s 2 d) 2.33 m/s 2 e) 2.72 m/s 2 Ans: b

33) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of ½ MR 2 . If m1 is 1.0 kg, m2 is 2.0 kg, and M is 4.0 kg, then what is the tension in the string attached to m1? a) 6.83 N b) 7.03 N c) 7.84 N d) 8.02 N e) 8.33 N Ans: c

34) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a 152 moment of inertia of ½ MR 2 . If m1 is 1.0 kg, m2 is 2.0 kg, and M is 4.0 kg, then what is the tension in the string attached to m2? a) 3.92 m/s 2 b) 3.65 m/s 2 c) 3.23 m/s 2 d) 3.02 m/s 2 e) 2.98 m/s 2 Ans: a

35) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of ½ MR 2 . If m1 is 4.0 kg, m2 is 2.0 kg, and M is 4.0 kg, then what is the acceleration of m1? a) 4.9 m/s 2 b) 4.5 m/s 2 c) 4.1 m/s 2 d) 3.9 m/s 2 e) 3.7 m/s 2 Ans: a

36) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of ½ MR 2 . If m1 is 4.0 kg, m2 is 4.0 kg, and M is 4.0 kg, then what is the acceleration of m1? a) 4.42 m/s 2 b) 3.92 m/s 2

153 c) 3.42 m/s 2 d) 3.04 m/s 2 e) 2.96 m/s 2 Ans: b

37) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of ½ MR 2 . If m1 is 4.0 kg, m2 is 4.0 kg, and M is 4.0 kg, then what is the tension in the string attached to m1? a) 35.6 N b) 32.7 N c) 31.0 N d) 29.0 N e) 23.5 N Ans: e

38) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless horizontal surface as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of ½ MR 2 . If m1 is 4.0 kg, m2 is 4.0 kg, and M is 4.0 kg, then what is the tension in the string attached to m2? a) 10.4 N b) 12.6 N c) 15.7 N d) 17.6 N e) 19.8 N Ans: c

154 36) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 30 cm and a moment of inertia of MR 2 . If m1 is 4.0 kg, m2 is 3.0 kg and M is 6.0 kg, then what is the acceleration of the masses? a) 0.695 m/s 2 b) 0.703 m/s 2 c) 0.731 m/s 2 d) 0.754 m/s 2 e) 0.805 m/s 2 Ans: d

37) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 30 cm and a moment of inertia of MR 2 . If m1 is 4.0 kg, m2 is 3.0 kg and M is 6.0 kg, then what is the tension in the string that is attached to m1? a) 36.2 N b) 44.6 N c) 58.2 N d) 60.6 N e) 74.5 N Ans: a

155 38) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 30 cm and a moment of inertia of MR 2 . If m1 is 4.0 kg, m2 is 3.0 kg and M is 6.0 kg, then what is the tension in the string that is attached to m2? a) 20.7 N b) 25.5 N c) 31.7 N d) 35.2 N e) 41.3 N Ans: c

39) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 20 cm and a moment of inertia of ½ MR 2 . If m1 is 3.0 kg, m2 is 6.0 kg and M is 4.0 kg, then what is the acceleration of the masses? a) 5.05 m/s 2 b) 4.75 m/s 2 c) 4.05 m/s 2 d) 3.44 m/s 2 e) 2.67 m/s 2 Ans: e

156 40) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 20 cm and a moment of inertia of ½ MR 2 . If m1 is 3.0 kg, m2 is 6.0 kg and M is 4.0 kg, then what is the tension in the string that is attached to mass m1? a) 20.8 N b) 27.4 N c) 30.2 N d) 37.4 N e) 43.5 N Ans: d

41) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 as shown in the figure. Both masses move vertically and there is no slippage between the string and the pulley. The pulley has a radius of 20 cm and a moment of inertia of ½ MR 2 . If m1 is 3.0 kg, m2 is 6.0 kg and M is 4.0 kg, then what is the tension in the string that is attached to mass m2? a) 33.6 N b) 42.8 N c) 53.6 N d) 63.4 N e) 75.5 N Ans: b

42) A 4.0 kg hollow cylinder of radius 5.0 cm starts from rest and rolls without slipping down a 30 degree incline. The acceleration of the center of mass of the cylinder is, a) 2.45 m/s 2

157 b) 2.98 m/s 2 c) 3.35 m/s 2 d) 3.98 m/s 2 e) 4.05 m/s 2 Ans: a

43) A 4.0 kg hollow cylinder of radius 5.0 cm starts from rest and rolls without slipping down a 30 degree incline. If the length of the incline is 50 cm, then the velocity of the center of mass of the cylinder at the bottom of the incline is, a) 1.35 m/s b) 1.82 m/s c) 2.21 m/s d) 2.55 m/s e) 3.02 m/s Ans: c

44) A 4.0 kg solid sphere of radius 5.0 cm starts from rest and rolls without slipping down a 30 degree incline. The acceleration of the center of mass of the solid sphere is, a) 1.5 m/s 2 b) 2.0 m/s 2 c) 2.5 m/s 2 d) 3.0 m/s 2 e) 3.5 m/s 2 Ans: e

45) A 4.0 kg solid sphere of radius 5.0 cm starts from rest and rolls without slipping down a 30 degree incline. . If the length of the incline is 50 cm, then the velocity of the center of mass of the solid sphere at the bottom of the incline is, a) 1.69 m/s b) 1.87 m/s c) 2.33 m/s d) 2.75 m/s e) 3.22 m/s Ans: b

158 46) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless incline as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25cm and a moment of inertia of ½ MR 2 . If m1 is 2.0 kg, m2 is 1.0 kg, M is 4.0 kg, and the angle is 60 degrees, then what is the acceleration of m1? a) 3.98 m/s 2 down b) 3.27 m/s 2 down c) 3.15 m/s 2 down d) 2.94 m/s 2 down e) 1.64 m/s 2 down Ans: d

47) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless incline as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 25 cm and a moment of inertia of ½ MR 2 . If m1 is 1.0 kg, m2 is 2.0 kg, M is 4.0 kg, and the angle is 60 degrees, then what is the acceleration of m1? a) 0.0 m/s 2 b) 1.2 m/s 2 c) 1.8 m/s 2 d) 2.2 m/s 2 e) 2.8 m/s 2 Ans: b

159 48) A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless incline as shown in the figure. There is no slippage between the string and the pulley. The pulley has a radius of 30 cm and a moment of inertia of MR 2 . If m1 is 4.0 kg, m2 is 4.0 kg, M is 4.0 kg, and the angle is 70 degrees, then what is the acceleration of m1? a) 3.10 m/s 2 b) 2.89 m/s 2 c) 2.43 m/s 2 d) 2.15 m/s 2 e) 1.49 m/s 2 Ans: d

49) A torque of 20 Nm is applied to a bolt. The bolt rotates through an angle of 180 degrees. The work done in turning the bolt is, a) 2,103 J b) 1,750 J c) 1,146 J d) 956 J e) 826 J Ans: c

50) A torque of 15 Nm is applied to a bolt. The bolt rotates through an angle of 360 degrees. The work done in turning the bolt is, a) 1,720 J b) 2,040 J c) 2,290 J d) 2,400 J e) 2,650 J Ans: a

160 51) A 4.0 kg solid sphere (I = 2/5 MR 2 ) is spinning with an angular velocity of 23 rad/s. The diameter of the sphere is 20 cm. The angular kinetic energy of the spinning sphere is, a) 3.02 J b) 3.52 J c) 3.75 J d) 4.02 J e) 4.23 J Ans: e

52) A 20 kg hollow cylinder (I= MR 2 ) has a diameter of 50 cm. The cylinder is rolling down a hill with a velocity of 5 m/s. The angular kinetic energy of the rolling cylinder is, a) 225 J b) 200 J c) 175 J d) 150 J e) 125 J Ans: e

53) A 4.0 kg hollow sphere (I = 2/3 MR 2 ) is spinning with an angular velocity of 10 rad/s. The diameter of the sphere is 20 cm. The angular kinetic energy of the spinning sphere is, a) 1.75 J b) 1.50 J c) 1.33 J d) 0.90 J e) 0.75 J Ans: c

54) A 100 kg solid spherical rock (I=2/5 MR 2 ) has a diameter of 50 cm. The rock is rolling down a hill with a velocity of 5.0 m/s. The total kinetic energy ( angular + translational ) of the rolling rock is, a) 1,750 J b) 2,000 J c) 2,250 J d) 2,670 J e) 2,900 J Ans: a

161 55) Chris and Jamie are carrying Wayne on a horizontal stretcher. The uniform stretcher is 2.0 m long and weighs 100 N. Wayne weighs 800 N. Wayne’s center of gravity is 75 cm from Chris. Chris and Jamie are at the ends of the stretcher. The force that Chris is exerting to support the stretcher with Wayne on it, is a) 250 N b) 350 N c) 400 N d) 550 N e) 650 N Ans: d

56) Chris and Jamie are carrying Wayne on a horizontal stretcher. The uniform stretcher is 2.0 m long and weighs 100 N. Wayne weighs 800 N. Wayne’s center of gravity is 75 cm from Chris. Chris and Jamie are at the ends of the stretcher. The force that Jamie is exerting to support the stretcher with Wayne on it, is a) 250 N b) 300 N c) 350 N d) 400 N e) 550 N Ans: c

57) Jim and Mary are carrying Bob on a horizontal stretcher. The uniform stretcher is 2.0 m long and weighs 80 N. Bob weighs 600 N. Bob’s center of gravity is 80 cm from Mary. Jim and Mary are at the ends of the stretcher. The force that Mary is exerting to support the stretcher with Bob on it, is a) 550 N b) 400 N c) 300 N d) 280 N e) 200 N Ans: b

58) Jim and Mary are carrying Bob on a horizontal stretcher. The uniform stretcher is 2.0 m long and weighs 80 N. Bob weighs 600 N. Bob’s center of gravity is 80 cm from Mary. Jim and Mary are at the ends of the stretcher. The force that Jim is exerting to support the stretcher with Bob on it, is a) 280 N b) 320 N c) 380 N d) 400 N

162 e) 520 N Ans: a

59) A 2.0 m long horizontal uniform beam of mass 20 kg is supported by a wire as shown in the figure. The wire makes an angle of 20 degrees with the beam. Attached to the beam 1.2 m from the wall is a ball with a mass of 40 kg. What is the tension in the string? a) 1,000 N b) 1,090 N c) 2,100 N d) 2,250 N e) 2,680 N Ans: b

60) A 2.0 m long horizontal uniform beam of mass 20 kg is supported by a wire as shown in the figure. The wire makes an angle of 20 degrees with the beam. Attached to the beam 1.2 m from the wall is a ball with a mass of 40 kg. What are the vertical and horizontal components of the force of the wall on the beam at the hinge? a) V = 175.6 N, H = 2,023 N b) V = 186.6 N, H = 1,805 N c) V = 195.4 N, H = 1,750 N d) V = 200.6 N, H = 1,323 N e) V = 215.6 N, H = 1,023 N Ans: e

163 61) A 1.5 m long uniform beam of mass 30 kg is supported by a wire as shown in the figure. The beam makes an angle of 10 degrees with the horizontal and the wire makes and angle of 30 degrees with the beam. A 50 kg mass, m, is attached to the end of the beam. What is the tension in the wire? a) 2,034 N b) 1,855 N c) 1,435 N d) 1,255 N e) 1,035 N Ans: d

62) A 1.5 m long uniform beam of mass 30 kg is supported by a wire as shown in the figure. The beam makes an angle of 10 degrees with the horizontal and the wire makes and angle of 30 degrees with the beam. A 50 kg mass, m, is attached to the end of the beam. What are the vertical and horizontal components of the force of the wall on the beam at the hinge? a) H = 1,458 N, V = 454.0 N b) H = 1,300 N, V = 403.4 N c) H = 1,179 N, V = 354.9 N d) H = 979 N, V = 324.5 N e) H = 750 N, V = 297.3 N Ans: c

164 63) A 75 kg ladder that is 3.0 m in length is placed against a wall at an angle theta. The center of gravity of the ladder is at a point 1.2 m from the base of the ladder. The coefficient of static friction at the base of the ladder is 0.8. There is no friction between the wall and the ladder. What is the vertical force of the ground on the ladder? a) 625 N b) 640 N c) 735 N d) 832 N e) 900 N Ans: c

64) A 75 kg ladder that is 3.0 m in length is placed against a wall at an angle theta. The center of gravity of the ladder is at a point 1.2 m from the base of the ladder. The coefficient of static friction at the base of the ladder is 0.8. There is no friction between the wall and the ladder. What is the minimum angle the ladder makes with the horizontal for the ladder not to slip and fall? a) 26.57 degrees b) 30.34 degrees c) 36.35 degrees d) 40.55 degrees e) 46.52 degrees Ans: a

165 65) A 75 kg ladder that is 3.0 m in length is placed against a wall at an angle theta. The center of gravity of the ladder is at a point 1.2 m from the base of the ladder. The coefficient of static friction at the base of the ladder is 0.4. There is no friction between the wall and the ladder. What is the minimum angle the ladder makes with the horizontal for the ladder not to slip and fall? a) 35 degrees b) 45 degrees c) 53 degrees d) 60 degrees e) 65 degrees Ans: b

66)A solid cylinder with a moment of inertia of 4.2 kg m 2 is rotating with an angular velocity of 2.3 rad/s about a shaft pointed in the direction (0.866, 0.500, 0.0). What is the angular momentum vector? a) ( 4.83 kg m 2 /s, 8.37 kg m 2 /s, 0.0 kg m 2 /s) b) ( 5.56 kg m 2 /s, 3.83 kg m 2 /s, 0.0 kg m 2 /s) c) ( 7.56 kg m 2 /s, 2.03 kg m 2 /s, 0.0 kg m 2 /s) d) ( 8.37 kg m 2 /s, 4.83 kg m 2 /s, 0.0 kg m 2 /s) e) ( 8.56 kg m 2 /s, 2.83 kg m 2 /s, 0.0 kg m 2 /s) Ans: d

67) A solid sphere with a moment of inertia of 6.1 kg m 2 is rotating with an angular velocity of 10 rad/s about a shaft pointed in the direction (cos(45) sin(30), sin(45) sin(30), cos(30)). What is the angular momentum vector? a) (11.57 kg m 2 /s, 14.57 kg m 2 /s, 12.83 kg m 2 /s) b) (52.83 kg m 2 /s, 11.57 kg m 2 /s, 14.73 kg m 2 /s) c) (11.57 kg m 2 /s, 52.83 kg m 2 /s, 12.40 kg m 2 /s) d) (12.57 kg m 2 /s, 11.57 kg m 2 /s, 21.57 kg m 2 /s) e) (21.57 kg m 2 /s, 21.57 kg m 2 /s, 52.83 kg m 2 /s) Ans: e

166 68) A solid cylinder with a moment of inertia of 4.2 kg m 2 is rotating with an angular velocity of 2.3 rad/s about a shaft pointed in the direction (cos(35), sin(35), 0). What is the omega vector? a) (2.05 rad/s, 2.02 rad/s, 0) b) (4.80 rad/s, 4.32 rad/s, 0) c) (2.54 rad/s, 2.72 rad/s, 0) d) (1.88 rad/s, 1.32 rad/s, 0) e) (5.88 rad/s, 3.32 rad/s, 0) Ans: d

69) A solid sphere with a moment of inertia of 6.1 kg m 2 is rotating with an angular velocity of 10 rad/s about a shaft pointed in the direction (cos(30) sin(45), sin(30) sin(45), cos(45)). What is the omega vector? a) 10 rad/s (0.612, 0.354, 0.707) b) 12 rad/s (0.354, 0.612, 0.707) c) 14 rad/s (0.612, 0.707, 0.354) d) 16 rad/s (0.707, 0.354, 0.612) e) 18 rad/s (0.612, 0.354, 0.707) Ans: a

70) A 2.0 kg solid sphere (I = 2/5 MR 2 ) with a diameter of 50 cm is rotating at an angular velocity of 5.0 rad/s. The angular momentum of the rotating sphere is, a) 0.55 kg m 2 /s b) 0.48 kg m 2 /s c) 0.37 kg m 2 /s d) 0.25 kg m 2 /s e) 0.20 kg m 2 /s Ans: d

71) An ice dancer with her arms stretched out starts into a spin with an angular velocity of 1.0 rad/s. Her moment of inertia with her arms stretched out is ½ 70 kg(0.2) 2 + 1/3 4 kg (.9) 2 = 1.4 +1.08 = 2.48 kg m 2 . What is her angular velocity when she pulls in her arms to make her moment of inertia 1.4 kg m 2 ? a) 2.67 rad/s b) 2.45 rad/s c) 2.03 rad/s d) 1.90 rad/s e) 1.77 rad/s Ans: e 167 72) An ice dancer with her arms stretched out starts into a spin with an angular velocity of 1.0 rad/s. Her moment of inertia with her arms stretched out is ½ 70 kg(0.2) 2 + 1/3 4 kg (.9) 2 = 1.4 +1.08 = 2.48 kg m 2 . What is the increase in her rotational kinetic energy when she pulls in her arms to make her moment of inertia 1.4 kg m 2 ? a) 0.957 J b) 0.902 J c) 0.870 J d) 0.750 J e) 0.690 J Ans: a

73) A grinding wheel has a mass of 250 kg and moment of inertia of 500 kg m 2 . A torque of 100 Nm is applied to the grinding wheel. If the wheel starts from rest, what is the angular momentum of the wheel after 5.0 seconds? a) 650 kg m 2 /s b) 500 kg m 2 /s c) 450 kg m 2 /s d) 300 kg m 2 /s e) 250 kg m 2 /s Ans: b

74) A 10 kg solid cylinder (I = 1/2 MR 2 ) with a radius of 30 cm is rotating about a vertical axis through its center. If the angular momentum is increasing at the rate of 25 kg m 2 /s, then what is the torque? a) 70 Nm b) 45 Nm c) 37 Nm d) 25 Nm e) 12 Nm Ans: d

168 75) A 10 kg solid cylinder (I = 1/2 MR 2 ) with a radius of 30 cm is rotating about a vertical axis through its center. If the angular momentum is increasing at the rate of 25 kg m 2 /s, then what is the angular acceleration? a) 75.3 rad/s 2 b) 65.9 rad/s 2 c) 55.6 rad/s 2 d) 40.5 rad/s 2 e) 35.2 rad/s 2 Ans: c