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Consider a 3.0 kg mass on a spring on a horizontal surface. The spring has sprin

ID: 1532084 • Letter: C

Question

Consider a 3.0 kg mass on a spring on a horizontal surface. The spring has spring constant 45 N/m. The static coefficient of friction between the mass and the surface is mu_s = 0.30 and the kinetic coefficient of friction is mu_k = 0.20 (a) When the mass is at x_0 = 20 cm it is moving to the right with speed 50 cm/s. Where does it first come to a stop? (b) Once the mass stops, docs it remain at rest or docs it move back to the left? If it moves to the left, what is its initial acceleration? Justify your answer

Explanation / Answer

A) 0.5kx^2 = 0.5kxo^2 + 0.5mv^2 - 0.2 mg(x-xo)

22.5*(x^2 - 0.2^2) = 1.5*0.5^2 - 0.6*9.8 (x - 0.2)

22.5x^2 - 0.9 = 0.375 - 5.88x + 1.176

22.5x^2 + 5.88x - 2.45 =0

x = 0.224m

= 22.4 cm

B) kx = 0.224*45 = 10.08 N

Which is more than umg =0.3*3*9.8

So block will move back

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