Question

As shown in the figure below, a 2.25-kg block is released from rest on a ramp of height h.


As shown in the figure below, a 2.25-kg block is released from rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 15.0 cm that has a coefficient of kinetic friction μk = 0.520. Find h such that the block's speed after crossing the rough patch is 4.20 m/s. 

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An object with a mass m = 4.00 kg is attached to the end of a spring, and the spring is stretched an amount xi = 4.60 cm and then released. If the force constant for the spring is k = 520 N/m, determine the speed of the mass as it passes through the equilibrium position the first time for the following two cases. 

(a) The horizontal surface the object is sliding along is frictionless. 

(b) The coefficient of kinetic friction between the horizontal surface and the object is μk = 0.250. 

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