3. (24 points) Spring slope. Show your work and explain your reasoning. An 1.16-

Question

3. (24 points) Spring slope. Show your work and explain your reasoning. An 1.16-kg block is held in place against the spring by a 62-N horizontal external force (see figure). The external force is removed, and the block is projected with a velocity V1 1.3 m/s upon separation from the spring. The block descends a ramp and has a velocity v2 2.1 m/s at the bottom. The track is frictionless between points A and B. Find the spring constant of the spring and the height h of the ramp, each to at least two significant figures. V4 v2

Explanation / Answer

for spring mass - system:

F = k x = > 62 = k x

and k x^2 /2 = m v^2 /2

k x^2 = (1.16)(1.3)^2 = 1.96

k x^2 / kx = x = 1.96 / 62 = 0.0316

k = 62 / x = 1961 N / m ........Ans (Spring constant)

Applying energy conservation from A to B:

Pei + KEi = PEf + Kef

m g h + m v1^2 /2 = 0 + m v2^2 /2

2 x 9.8 x h + 1.3^2 = 2.1^2

h = 0.139 m

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