applications of newton's laws?

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Dongyao X

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A spring with a force constant of 120N/M is used to push a 0.27 kg block of wood against a wall. Find the minimum compression of the spring needed to keep the block from falling, given that the coefficient of static friction between the block and the wall is 0.46

how do i get the answer 4.8cm?
 
The Force of gravity acting on the block is Fg=mg=.27(9.81)=2.65 N. Thus, the same amount of force is required to keep the block up. This force will have to come from friction. The friction equation can be used to calculate the Fn needed on the block to keep it from falling. (Ffr=UsFn or Coefficient of static friction times normal force. 2.65=.46Fn, Fn=5.75 N.) Since 5.75 N must be applied to the block to keep it from falling, we can now calculate the minimum compression. (Fsp=Kd, 5.75=120d, d=.0479=~.048=4 M= 4.8 cm.) Therefore, the minimum compression on the string must be 4.8 cm.
I hope this helps!
 
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