An elastic cube sliding without friction along a horizontal floor hits a vertical wall with one of its faces parallel to the wall. The coefficient of friction between the wall and the cube is μ . The

Question

An elastic cube sliding without friction along a horizontal floor hits a vertical wall with one of its faces parallel to the wall. The coefficient of friction between the wall and the cube is μ . The angle between the direction of the velocity v of the cube and the wall is α . (see figure for a bird's - eye view of the collision). Choose the correct option(s) :-

TestHub · Accepted Answer

Elastic bounce perpendicular to the wall: $v_{x}^{'} = - v sin α$ , so the normal impulse has magnitude $2 m v sin α$ for any $μ$ - (A).

Friction acts until sliding along the wall stops. If $v_{y}^{'} = v (cos α - 2 μ sin α) > 0$ , i.e. $tan α < \frac{1}{2 μ}$ : $tan β = \frac{t a n α}{1 - 2 μ t a n α}$ - (C)

If $tan α \geq \frac{1}{2 μ}$ , $v_{y}$ reaches zero during contact and the cube leaves perpendicular to the wall: $β = \frac{π}{2}$ - (B)

Friction changes the parallel component, so $β \neq = α$ in general - (D) wrong.

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Options:(select one or more)

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