# An object with a mass of #7 kg# is lying still on a surface and is compressing a horizontal spring by #5/4 m#. If the spring's constant is #3 (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

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The minimum value of the surface's coefficient of static friction is 0.48.

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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 # 6 kg# is lying still on a surface and is compressing a horizontal spring by #3/4 m#. If the spring's constant is # 8 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
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- An object with a mass of #5 kg# is pushed along a linear path with a kinetic friction coefficient of #u_k(x)= 1-cos(x/2) #. How much work would it take to move the object over #x in [0, 8pi], where x is in meters?
- A box with an initial speed of #2 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?
- An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < -2 N , -3 N># and the second is #F_2 = < -1 N, 6 N>#. What is the object's rate and direction of acceleration?

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