Consider the incline shown in the figure with inclination angle θ and height h. The coefficient of kinetic friction between a block of mass m and the incline changes along its surface. From A to B it has a value of μ1, and from B to C its value is μ2. The block (not shown) is given an initial velocity up the incline at point A with a magnitude vA. A) What is the value of vA for which the block will reach the top of the incline (point C) with zero kinetic energy? Your answer should be written in terms of the quantities given in the statement. B) Show that for the block to surpass point B, the initial speed at A should satisfy the inequality vA > √[ (2/3)gh(1+μ1cotθ) ]
Consider the incline shown in the figure with inclination angle θ and height h. The coefficient of kinetic friction between a block of mass m and the incline changes along its surface. From A to B it has a value of μ1, and from B to C its value is μ2. The block (not shown) is given an initial velocity up the incline at point A with a magnitude vA.
A) What is the value of vA for which the block will reach the top of the incline (point C) with zero kinetic energy? Your answer should be written in terms of the quantities given in the statement.
B) Show that for the block to surpass point B, the initial speed at A should satisfy the inequality
vA > √[ (2/3)gh(1+μ1cotθ) ]
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