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 # 7 m/s^2#?
Consider,
where
Recall Newton's second law,
Hence, That's some serious work we need to do!
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(F_{\text{net}} = m \cdot (a + g \cdot \mu_k))
(F_{\text{net}} = 6 , \text{kg} \cdot (7 , \text{m/s}^2 + 9.8 , \text{m/s}^2 \cdot 0.8))
(F_{\text{net}} = 6 , \text{kg} \cdot 15.24 , \text{m/s}^2)
(F_{\text{net}} = 91.44 , \text{N})
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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.
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 #2 kg# is acted on by two forces. The first is #F_1= < 6 N , 8 N># and the second is #F_2 = < -7 N, 3 N>#. What is the object's rate and direction of acceleration?
- If the length of a #40 cm# spring increases to #64 cm# when a #7 kg# weight is hanging from it, what is the spring's constant?
- If an object is moving at #1 m/s# over a surface with a kinetic friction coefficient of #u_k=5 /g#, how far will the object continue to move?
- An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -2 N , 4 N># and the second is #F_2 = < 3 N, 5 N>#. What is the object's rate and direction of acceleration?
- A box with an initial speed of #5 m/s# is moving up a ramp. The ramp has a kinetic friction coefficient of #3/4 # and an incline of #(5 pi )/12 #. How far along the ramp will the box go?

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