A 1kg box starts at rest and slides 4m down the ramp shown in the figure, then c

Question

A 1kg box starts at rest and slides 4m down the ramp shown in the figure, then collides with a spring whose spring constant is k = 2 N/m. The ramp has a coefficient of kinetic friction of mu_k= 0.5. At what compression of the spring does the box have its maximum speed? [Assume the spring is long enough and remains linear]. 0m 0.335m 0.67m 1.667m The block stops before reaching the spring This is a continuation of question 19. At what speed does the block hit the spring? The block stops before reaching the spring. The block stops just as it reaches the spring. 2.315 m/s 5.359 m/s 6.324 m/s

Explanation / Answer

19) let the required compression be y

then conserving the energy

mgsin30(4+y) = umg(4+y)cos30 + 0.5 ky2 + 0.5mv2

(4.9 - 4.2435)(4+y) x 2 = 2y2 + v2

5.2518 +1.313y = 2y2 + v2

now for v max dv/dy = 0

y = 0.32825 m

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