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31 A solid cube of side 2a and mass M is sliding on a frictionless surface with uniform velocity v with arrow, as shown in Figure a. It hits a small obstacle at the end of the table that causes the cube to tilt as shown in Figure b. Find the minimum value of the magnitude of v with arrow such that the cube tips over and falls off the table. Note: The cube undergoes an inelastic collision at the edge. (Use the following as necessary: M, a, and g.1

Answer 1

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when the cube hits the obstacie at end of table its comer sticks to it so, the colision is completely inelastic Energy and momentum are not conservette during such a collision because there are external forces acting on cube at obstacie. only angular momentum is conserved. 92 A BA at pointa, from, consenation of angrar momentum hi=hf molx h = lf In = { ma? + m (222) Ia:- Sma. mva - Iaw ma = 8maºu = : total total mechanical en During cottision mechanical energy is conserved. There fore, for the cube to tip over & fall off, its ko€ > PE. Ja W; 2 = mg (Jaa -a). $ 8ma? () = mg (aa-a) ..V de 25 a-a) = 4 . (-1. - Minirowen vawe of (v)= 4 . CE-1). .: Minimum value of (V) = 1