PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 8 HOMEWORK PROBLEMS Chapter 8 ROTATIONAL EQUILIBRIUM AND ROTATIONAL DYNAMICS PART A Hand in your answers in class on scantron on Monday 08 November 2010 Write your name class 1401 and HW 8 on the scantron 1 A wrench 0 500 m long is applied to a nut with a force of 80 0 N Because of the cramped space the force must be exerted upward at an angle of 60 0 with respect to a line from the bolt through the end of the wrench How much torque is applied to the nut a 34 6 N m b 4 56 N m c 11 8 N m d 14 2 N m e 20 0 N m t rF sin q 0 500 m 80 0 N sin 60 0 36 4 N m which is choice a 2 A horizontal plank 4 00 m long and having mass 20 0 kg rests on two pivots one at the left end and a second 1 00 m from the right end Find the magnitude of the force exerted on the plank by the second pivot a 32 0 N b 45 2 N c 112 N d 131 N e 98 2 N Using the left end of the plank as a pivot and requiring that St 0 gives mg 2 00 m F2 3 00 m 0 or 2 20 0 kg 9 80 m s2 2mg 3 3 so choice d is the correct response F2 131 N 3 What is the magnitude of the angular acceleration of a 25 0 kg disk of radius 0 800 m when a torque of magnitude 40 0 N m is applied to it a 2 50 rad s2 b 5 00 rad s2 c 7 50 rad s2 d 10 0 rad s2 e 12 5 rad s2 Assuming a uniform solid disk its moment of inertia about a perpendicular axis through its center is I MR 2 2 so t I a gives a 2 40 0 N m 2t 5 00 rad s2 2 MR 25 0 kg 0 800 m 2 and the correct answer is b 4 Estimate the rotational kinetic energy of Earth by treating it as a solid sphere with uniform density a 3 X 1029 kg m2 s2 b 5 X 1027 kg m2 s2 c 7 X 1030 kg m2 s2 d 4 X 1028 kg m2 s2 e 2 X 1025 kg m2 s2 For a uniform solid sphere I 2 MR 2 5 2p rad 1d 7 27 10 5 rad s and wE 1 d 8 64 10 4 s so 24 6 1 2 1 2 5 98 10 kg 6 38 10 m KEr IwE 2 2 5 yielding KEr 3 1029 2 7 27 10 5 J making a the correct choice 1 rad s 2 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 8 5 Two forces are acting on an object Which of the following statements is correct a The object is in equilibrium if the forces are equal in magnitude and opposite in direction b The object is in equilibrium if the net torque on the object is zero c The object is in equilibrium if the forces act at the same point on the object d The object is in equilibrium if the net force and the net torque on the object are both zero e The object cannot be in equilibrium because more than one force acts on it In order for an object to be in equilibrium it must be in both translational equilibrium and rotational r ur equilibrium Thus it must meet two conditions of equilibrium namely F net 0 and t net 0 The correct answer is therefore choice d 6 A disk rotates about a fixed axis that is perpendicular to the disk and passes through its center At any instant does every point on the disk have the same a centripetal acceleration b angular velocity c tangential acceleration d linear velocity or e total acceleration In a rigid rotating body all points in that body rotate about the axis at the same rate or have the same angular velocity The centripetal acceleration tangential acceleration linear velocity and total acceleration of a point in the body all vary with the distance that point is from the axis of rotation Thus the only correct choice is b 7 BLANK 8 A block slides down a frictionless ramp while a hollow sphere and a solid ball roll without slipping down a second ramp with the same height and slope Rank the arrival times at the bottom from shortest to longest a sphere ball block b ball block sphere c ball sphere block d block sphere ball e block ball sphere When objects travel down ramps of the same length the one with the greatest translational kinetic energy at the bottom will have the greatest final translational speed and hence greatest average translational speed This means that it will require less time to travel the length of the ramp Of the objects listed all will have the same total kinetic energy at the bottom since they have the same decrease in gravitational potential energy due to the ramps having the same vertical drop and no energy has been spent overcoming friction All of the block s kinetic energy is in the form of translational kinetic energy Of the rolling bodies the fraction of their total kinetic energy that is in the translational form is 1 M v2 KEt 1 1 2 f 1 1 2 2 2 KEt KEr Mv 2 Iw 1 I MR2 1 I M w v 2 Since the ratio I MR equals 2 5 for a solid ball and 2 3 for a hollow sphere the ball has the larger translational kinetic energy at the bottom and will arrive before the hollow sphere The correct rankings of arrival times from shortest to longest is then block ball sphere and choice e is the correct response 2 9 A solid disk and a hoop are simultaneously released from rest at the top of an incline and roll down without slipping Which object reaches the bottom first a The one that has the largest mass arrives first b The one that has the largest radius arrives first c The hoop arrives first d The disk arrives first e The hoop and the disk arrive at the same time 2 PHYS 1401 College Physics I CRN 55178 Khalid Bukhari HW 8 Please read the answer to Question 8 above since most of what is said there also applies to this question The total kinetic energy of either the disk or the hoop at the bottom of the ramp will be KEtotal Mgh where M is the mass of the body in question and h is the vertical drop of the ramp The translational kinetic energy of this body will then be KEt f KEtotal fMgh where f is the fraction discussed in Question 8 Hence M v2 2 f M gh and the translational …