A

What is the sliding distance S?

**1.0 kg**block is held in place against a spring with spring constant**k = 100 N/m**(see the figure, below) by a horizontal external force. The spring is compressed**20 cm**. The external force is removed, and the block is projected with some (horizontal) velocity upon separation from the spring. The block descends a ramp with height**h = 2.0 m**. The track is frictionless between points A and B. The block enters a rough section at B, extending to E. The coefficient of kinetic friction over this section is**0.30**. The block slides through this rough section a distance S, and comes to a stop at point D.What is the sliding distance S?

*Can someone please tell me if my below attempt is the correct answer?*

*Find velocity after reaches bottom of hill (by conservation of mechanical energy)*

( 1/2 * k * x^{2} ) + ( 1/2 * m * g ) = 1/2 * m * v^{2}

(1/2 * 100 * .20) + (1/2 * 1 * 9.8) = 1/2 * 1 * v^{2}

14.9 = 1/2 * v^{2}

v ≈ 5.4589 m/s

*Find the acceleration once it hits the rough spot*

μmg = F_{net}

0.30 * 1 * 9.8 = 2.94 N

2.94 N = m * a

2.94 N = 1 * a

a = -2.94 m/s^{2}

*Kinematics to find distance of S*

v_{f}^{2} = v_{i}^{2} + 2ax

0 = 5.4589^{2} + ( 2 * -2.94 * x)

**x = 5.068 m**

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