An object with a mass of # 4 kg# is lying on a surface and is compressing a horizontal spring by #8 cm#. If the spring's constant is # 2 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

Answer 1

#mu = 2xx.08/(4xx9.81) = .04/9.81 ~~.004#

Take FBD:
1) y-direction #N = mg #
2) x-direction #F_(ms) = muN#
Insert 1) into 2)
#kx = mumg #
# mu = (kx)/(mg)#
# mu = 2xx.08/(4xx9.81) = .04/9.81 ~~.004#

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Answer 2

Lily Adams

The minimum value of the surface's coefficient of static friction is 0.5.

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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.