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

a) acceleration , a = g sin 30°, a = 9.8 * 0.5 = 4.9 m /s2

kx = mu*m g sin(theta)

x=mu*m g sin(theta) /k=0.5*1 kg x 9.8m/s^2 sin 30/2N/m =1.225 m

b) s = 1/2 a * t^2

t^2 = 2s / a = 2*4 / 4.9 = 4.1134

t = 1.633 s
v = a * t = 4.9 * 1.633 = 8.0017 m /s

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