A block (m= 15 kg) is on a flat surface and is being pulled by a spring (k= 1.2

Question

A block (m= 15 kg) is on a flat surface and is being pulled by a spring (k= 1.2 X 10^3 N/m) horizontally. THe coefficient of static friction between the block and table is 0.60, the coefficient of kinetic friction is 0.40. By what amount must the spring be stretched to start the block moving? Also, what is the acceleration of the block is the stretch of the sprin is maintained at a constant value equal to that required to start the motion? A block (m= 15 kg) is on a flat surface and is being pulled by a spring (k= 1.2 X 10^3 N/m) horizontally. THe coefficient of static friction between the block and table is 0.60, the coefficient of kinetic friction is 0.40. By what amount must the spring be stretched to start the block moving? Also, what is the acceleration of the block is the stretch of the sprin is maintained at a constant value equal to that required to start the motion?

Explanation / Answer

the frictional force is calculated as follows:

f = u_smg = 0.6*15*9.8 = 88.2 N

Hence, the stretched length of the spring is,

x = f/k = 88.2 /1200 = 0.0735 m = 7.35 cm

the eacceleration is calculated as follows:

ma = f - u_kmg

18*a = 88.2 - 0.4*15*9.8

a = 1.63 m/s^2

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