An object with a mass of #14 kg# is on a plane with an incline of # -(5 pi)/12 #. If it takes #12 N# to start pushing the object down the plane and #7 N# to keep pushing it, what are the coefficients of static and kinetic friction?
Similarly, the force (F) needed to maintain the object's motion on the plane once it begins is given as
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The coefficient of static friction is 0.857 and the coefficient of kinetic friction is 0.5.
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The coefficient of static friction is ( \mu_s = \frac{F_{\text{start}}}{N} ), where ( F_{\text{start}} ) is the force required to start pushing the object and ( N ) is the normal force. The coefficient of kinetic friction is ( \mu_k = \frac{F_{\text{keep}}}{N} ), where ( F_{\text{keep}} ) is the force required to keep pushing the object.
Given:
- Mass of the object (( m )) = 14 kg
- Incline angle (( \theta )) = ( -\frac{5\pi}{12} )
- Force to start pushing (( F_{\text{start}} )) = 12 N
- Force to keep pushing (( F_{\text{keep}} )) = 7 N
First, we need to calculate the normal force (( N )) using the force components along the incline:
[ N = mg \cos(\theta) ]
Then, we can use the formulae for coefficients of friction:
[ \mu_s = \frac{F_{\text{start}}}{N} ] [ \mu_k = \frac{F_{\text{keep}}}{N} ]
After calculating ( \mu_s ) and ( \mu_k ), we'll have the coefficients of static and kinetic friction, respectively.
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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.
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