A cube of side b slides along a flat frictionless table with speed v. The cube t

Question

A cube of side b slides along a flat frictionless table with speed v. The cube then hits a “bump”: a very low step that causes the leading lower edge of the cube to come to an abrupt stop. After our discussion in lecture, the phrase “abrupt stop” should immediately tell you that the cube-bump collision is inelastic in nature. (a) Calculate the cube’s angular velocity immediately after the cube hits the step. (b) Calculate the minimum speed v for which the cube rolls over after hitting the step (instead of falling back to its original position). HINT: This question concerns the situation after the collision with the step, so restart your strategy thinking from the start.

Explanation / Answer

Conservation of angular momentum

Radius if rotation = b/sqrt(2)

Moment of inertia = (1/6)*m*b^2 + m* (b^2/2) = 2mb^2/3

m*v*b/2 = 2*mb^2* w /3

So w = 3v/4b

For the cube to roll over

Normal force should shift to the edge of the cube

Using enegr equations

0.5*m*v^2 = mg*b*0.5*(sqrt(2) -1)

So V min = sqrt(g*b*(sqrt(20-1))

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