An object with a mass of # 2 kg# is lying still on a surface and is compressing a horizontal spring by #80 c m#. If the spring's constant is # 9 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

Answer 1

#mu = 3.6/g#

The force due to the static friction is #mu xx m g# and the force exerted by the spring is #K xx Delta x# The equilibrium is mantained as log as

#mu xx m g ge K xx Delta x#

then the minimum value for #mu# is

#mu = ( K xx Delta x)/(mg) = (9 xx 0.80)/(2 xx g) = 3.6/g#

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Answer 2

Adam Arnold

The minimum value of the surface's coefficient of static friction is 0.45.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.