A block of mass 0.500 kg is pushed against a horizontal spring of negligible mas

Question

A block of mass 0.500 kg is pushed against a horizontal spring of negligible mass until the spring is compressed a distance x. The force constant of the spring is 450 N/m. When it is released, the block travels along a frictionless, horizontal surface to point A, the bottom of a vertical circular track of Radius R = 1.00 m, and continues to move up the track. The block's speed at the bottom of the track is Va = 12.0 m/s , and the block experiences an average friction force of 7.00 N while sliding up the track.

a.) What is x?
b.) If the block were to reach the top of the track, what would be its speed at that point?
c.) Does the block actually reach the top of the track? Or does it fall of before reaching the top?

Explanation / Answer

a) put 1/2 kx^2 = 1/2 m vA^2 and solve for x b) Ui + Ki +WD = Kf + Uf 0 + 1/2 mvA^2 - 7.00(Pi r) = 1/2 mvtop^2 + mg(2) 36.47 - 22.0 = 1/2mvtop^2 + 9.8 solve for vtop c) yes it will, Kf is positive.

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