(a) How far is the spring compressed, if k = 120 N/m? (b) What minimum value of the coefficient of static friction, us, will assure that the spring remains compressed at the maximum compressed position? (c) If us is less than this, what is the speed of the block when it detaches from the decom- pressing spring?
(a) How far is the spring compressed, if k = 120 N/m? (b) What minimum value of the coefficient of static friction, us, will assure that the spring remains compressed at the maximum compressed position? (c) If us is less than this, what is the speed of the block when it detaches from the decom- pressing spring?
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Transcribed Image Text:2. A 2-kg block slides along a horizontal surface with a coefficient of kinetic friction uk =
0.30. The block has a speed v = 1.3 m/s when it strikes a massless spring head-on.
(a) How far is the spring compressed, if k = 120 N/m?
(b) What minimum value of the coefficient of static friction, us, will assure that the spring
remains compressed at the maximum compressed position?
(c) If us is less than this, what is the speed of the block when it detaches from the decom-
pressing spring?
Expert Solution
Step 1
Ans a) Using the law of conservation of energy
0.5*m*v^2 - umgx = 0.5*k*x^2
0.5*2*(1.3)^2 - 0.30*2*9.8*x = 60*x^2
60*x^2 + 5.88x - 1.69 = 0
Solving for x we get
x = 0.1258
Ans b) Using hookes law
umg = kx
u = 120*0.1258/2*9.8
u = 0.77
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