Question

i PROBLEM 3. A square block of mass m and side dimension b (as shown to the left) is vo given an initial velocity vo at a distance d b away from a small step at point 0. It slides towards O on a surface with friction m b coefficient u. It strikes the small step at point O and begins to rotate into an upright position. Assume that any impulses delivered are negligible and that the height of d the step is negligible compared to the dimension b of the block. (a) (10 points) Find the velocity of the block just before impact at point 0.(b) (20 points) Find the minimum value of the initial vo such that the block arrives at the final position shown with zero velocity, with its center of gravity pointed along the vertical dashed line (i.e., suspended along its diagonal). The mass moment of inertia for this square block about its mass center is 16 mb?. HINT: Consider work/energy during the sliding 6 portion, then consider the angular momentum about point O before and after the impact, and finally consider energy conservation again after impact. 1 =

Answer 1

Solution NO Wyb ll let vis the velocity Just before gmpact. ubing Works Energy principle, QI Total Work-cone = Change in KE big + hipoiction = 1 mo? I must or ungd = 1 mv²- Imm2 smus ungla 2 mwa v2 = 2.lgd-No V = √2ugd - No Ang (6 BY Conservation of congular momentum, xp OXO E Iolal Ferre Io = Int Ist me%% lub mont more mø +3m83 = 408² 6 12 2 / 2 mg ² lor 3 mo? gmu singo' = 2 mghw wa ms2gdom von 10

9 2 m 6² x tm 12g4d-vo a Ws 9 2526 2 giud-vo Agaion, by energy conservention big KE math = t Iw? angol tag -2) = x upon Bin (29dd-vo-) 0-207 96= 0.8431284d - ) 0:245 88=2g4d - wo² No = √2 guld - 0.24596 Ang