A 25-kg block is connected to a 30-kg block by a light string that passes over a

Question

A 25-kg block is connected to a 30-kg block by a light string that passes over a frictionless pulley. The 30-kg block is connected to a light spring of force constant 175 N/m, as in the figure below. The spring is unscratched when the system is as shown in the figure, and the incline is smooth. The 25-kg block is pulled 30 cm down the incline (so that the 30-kg block is 50 cm above the floor) and is released from rest. Find the speed of each block when the 30-kg block is 20 cm above the floor (that is, when the spring is unscratched). m/s

Explanation / Answer

Approach using energy

E = (30kg)g(30cm) + (1/2)(175N/m)(30cm)2

E' = (25kg)g(30cm)sin40 + (1/2)(30 + 25)v2

E = E'

9g + 7.875 = 4.82g + 27.5v2

v2 = 1.204756

v = 1.097 m/s

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