# An object with a mass of # 12 kg# is lying on a surface and is compressing a horizontal spring by #40 cm#. If the spring's constant is # 4 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

The coefficient of static friction is

The coefficient of static friction is

Therefore,

The normal force is

The coefficient of static friction is

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The minimum value of the surface's coefficient of static friction is 0.4.

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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.

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.

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.

- An object, previously at rest, slides #9 m# down a ramp, with an incline of #(pi)/3 #, and then slides horizontally on the floor for another #6 m#. If the ramp and floor are made of the same material, what is the material's kinetic friction coefficient?
- An object with a mass of #6 kg# is on a surface with a kinetic friction coefficient of # 8 #. How much force is necessary to accelerate the object horizontally at # 7 m/s^2#?
- If a #3 kg# object moving at #9 m/s# slows down to a halt after moving #27 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?
- How fast will an object with a mass of #3 kg# accelerate if a force of #6 N# is constantly applied to it?
- If an object is moving at #80 m/s# over a surface with a kinetic friction coefficient of #u_k=6 /g#, how far will the object continue to move?

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