Question

Work out the highlighted questions (3-6) clearly and with units, please. Thanks!

4/5 a the minimum kinetic energy at the apping point? (C) Use conservation of energy to determine the minimum angular velocity of the block just after the collision, (d) then use conservation of angular momentum during the collision to find the initial speed of the bullet vo. (Hint: Ignore the mass of the bullet after the collision. The moment of inertia of the cube about its bottom-right edge is M.2-/3) A flywheel is made from a steel disk 0.8 m in diameter with a mass of 250 kg, and is mounted on frictionless bearings. A motor connected to the flywheel accelerates it from rest to co= 120 rad/sec. (a) How much energy does the engine give the flywheel? (b) After is achieved, the motor is disengaged and the flywheel is connected to a saw blade used for cutting wood. The saw blade weighs 80 kg and is 1.0 m in diameter. A lightweight flexible belt is used to transfer momentum from the flywheel to the saw blade until they end up at the same final angular speed. How fast are they spinning after being connected? (c) How much energy is lost during the collision (express as a percent)? Both blade and wheel have their masses evenly distributed throughout the disks. Assume that the "collision" time is short. A light string is wound around a ring (a thin walled hollow cylinder with R-5 cm, M = 100 g). The ring is released from rest with the string vertical and its top end tied to a fixed support. As the ring descends and rolls" down the string, find the (a) tension in the string, (b) the acceleration of the center of mass, and (c) the velocity of the center of mass as a function of h, the distance fallen. (If you're having trouble visualizing this problem, think of a Yo-Yo falling. This is similar. Note that the only force which causes the ring to rotate is the tension.) A force F = (5i + 121) N is applied at the point r= (-31 +47) m on the surface of a 2 kg spherical object whose axis of rotation is aligned with the z-axis. (a) What is the moment of inertia of the sphere? (b) What is the magnitude and direction of the net torque on the object? (c) What are the magnitudes of F and /? Use them and the tor determine the angle o between F and r. (d) What is the angular momentum of the sphere after 5 seconds? (e) What is the sphere's angular velocity after 5 s? (t) Through what total angle 0 does it rotate during the 5 s? 6. (a) What is the angular momentumt of a particle located at r-(3.4) m and with linear momentum p-(-8,6) kg-m/s? (b) What about if r(2,6) m and p=(-1,-3) kg-m/s? Does this last answer surprise you? 7. A 54 kg board, of length 7 m, rests on a table with 3 m of its length hanging over the edge of the table. (a) Is it possible for a 10 kg child to stand on the overhanging end of the board without tipping the board? Explain. (b) What is the heaviest object that you could safely place on the end so that it wouldn't fall?

Answer 1

Patley, M =250kg radius, R = 0.8 = 0.4m. i = 0 - s = 12orad/s. al to Energe given by motor flywheel, = KE of totation Of flycaheed - E = 1 T W I = M. R² = (250)(0,1%) = 201 m2

E = L (20) (1202) b) E = 144000J Sawblade, m= 80kg 8 = 1 = 0.5m w Let Speedo, be - common angular momentum is Angular conserved Initial, Li = I was Final Le = I'w It = It mra

T = 20 + 180l6o.s . = 30 kg m? L = Ls 2 Iws = I'w = 20% 120 30 w = 80 8ad/s Initial KE Ki= l I wa K. = 1.44X 105 J

Final RE, Kg = 1 I wa Ks = Į (3010801 Ks = 9.64104 T Loss of cnergy, AK = Ki - Ks. AR= 1.444105 - 9.6 4104 = 4.8x10t J. 4. doss = AK Xloo X 100 4,8 x 10T 1.44x105 = 33.33%

X = (3.47 p = (-8,6 Kg m/s 8 = 3it4j m = - 8it Gj Kg m/s Angular momentum T = 3i+j) *(-3i+j) = 0 - 0 + KK 346 - (-8x4)] I a 50 k Kg ma/

2 = (2,6lm P = (-1,-3) Agnols = (21 +6; ) x ( - 1h 37 = 1 i j 1- -3 0 1 = 0 - 0 +K(-676) It is reapsising to see that angular momentum is zero here.