# An object with a mass of # 3 kg# is lying on a surface and is compressing a horizontal spring by #25 cm#. If the spring's constant is # 9 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

The coefficient of friction is

The static friction coefficient is

Consequently,

The typical force is

The static friction coefficient is

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The minimum value of the surface's coefficient of static friction is 0.36.

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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 with a mass of #4 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 5+tanx #. How much work would it take to move the object over #x in [(-5pi)/12, (5pi)/12], where x is in meters?
- An object with a mass of # 16 kg# is lying still on a surface and is compressing a horizontal spring by #2/3 m#. If the spring's constant is # 4 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
- An object with a mass of #6 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 2+cscx #. How much work would it take to move the object over #x in [pi/8, (3pi)/4], where x is in meters?
- An object with a mass of #3 kg# is hanging from a spring with a constant of #8 (kg)/s^2#. If the spring is stretched by #8 m#, what is the net force on the object?
- An object with a mass of #10 kg# is lying still on a surface and is compressing a horizontal spring by #5/6 m#. If the spring's constant is #24 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?

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