# An object with a mass of #24 kg# is on a ramp at an incline of #pi/12 #. If the object is being pushed up the ramp with a force of # 4 N#, what is the minimum coefficient of static friction needed for the object to remain put?

0.0175

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The minimum coefficient of static friction needed for the object to remain put is approximately 0.286.

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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.

- A truck pulls boxes up an incline plane. The truck can exert a maximum force of #3,500 N#. If the plane's incline is #(3 pi )/8 # and the coefficient of friction is #9/4 #, what is the maximum mass that can be pulled up at one time?
- An object with a mass of #4 kg# is lying still on a surface and is compressing a horizontal spring by #1/4 m#. If the spring's constant is # 8 (kg)/s^2#, what is the minimum value of the surface's coefficient of static friction?
- A box with an initial speed of #7 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #3/2 # and an incline of #(2 pi )/3 #. How far along the ramp will the box go?
- If an object is moving at #15 m/s# over a surface with a kinetic friction coefficient of #u_k=225 /g#, how much time will it take for the object to stop moving?
- An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= < 3 N , 5 N># and the second is #F_2 = < 7 N, -6 N>#. What is the object's rate and direction of acceleration?

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