# 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, (pi)/4]#, where x is in meters?

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[ W = \int_{(-5\pi)/12}^{(\pi)/4} \left( \mu_k \cdot m \cdot g \cdot \cos(x) + m \cdot g \cdot \sin(x) \right) ,dx ]

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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.

- If the length of a #13 cm# spring increases to #40 cm# when a #7 kg# weight is hanging from it, what is the spring's constant?
- An object with a mass of #2 kg# is on a surface with a kinetic friction coefficient of # 2 #. How much force is necessary to accelerate the object horizontally at #8 m/s^2#?
- If a #3 kg# object moving at #20 m/s# slows to a halt after moving #500 m#, what is the coefficient of kinetic friction of the surface that the object was moving over?
- If the length of a #47# #cm# spring increases to #89# #cm# when a #2# #kg# weight is hanging from it, what is the spring's constant?
- Sand is deposited at a uniform rate of 20g/s and with negligeable kinetic energy unto an empty convergor belt moving horizontally at a constant speed of 10m/s. Calculate the force required to maintain the constant velocity?

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