PLEASE SOLVE CLEARLY , I NEED HELP !! At right, a small object (mass = 100 kg) s

Question

PLEASE SOLVE CLEARLY , I NEED HELP !!

At right, a small object (mass = 100 kg) starts from rest at point (1) and slides down a curved vertical track until it reaches a horizontal segment between the points (2) and (3). We note that there is a spring (k = 96000 N/m) on the horizontal segment; the spring is initially in equilibrium. We can assume that the entire system is frictionless and that there is no air resistance. If the heights H = 360 m and h = 120 m then what will be the speed of the object after compressing the spring 0.50 m from equilibrium? (in m/sec)

Explanation / Answer

speed of block just before it touches spring ,

mv^2 /2 = mg (H - h)

v =sqrt(2 x 9.8 x (360 - 120)) = 68.59 m/s

after that

m 68.59^2 /2   = 96000* 0.5^2 /2 + mv^2 /2  

100 x 68.59^2 /2   = 12000 + 100v^2 /2

v = 66.82 m/s

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