# 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?

Take FBD:

1) y-direction

2) x-direction

Insert 1) into 2)

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

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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 # 14 kg# is lying still on a surface and is compressing a horizontal spring by #1 m#. If the spring's constant is # 2 (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 on a surface with a kinetic friction coefficient of # 8 #. How much force is necessary to accelerate the object horizontally at # 19 m/s^2#?
- A box with an initial speed of #8 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #8/7 # and an incline of #( pi )/4 #. How far along the ramp will the box go?
- What is the net force acting on a yo-yo when it doesn't move?
- How fast will an object with a mass of #8kg# accelerate if a force of #20 N# is constantly applied to it?

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