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?

Answer 1

#4.07, 3.93#

The force #F# required to push an object of mass #m=9# kg downward on an inclined plane at an angle #theta=-{5\pi}/12=-75^\circ# & coefficient of static friction #\mu_s# is given as
#F=\mu_s mg\cos\theta-mg\sin\theta#
#\mu_s=\frac{F+mg\sin\theta}{mg\cos\theta}#
#\mu_s=\frac{12+14\times9.81\sin75^\circ}{15\times9.81\cos75^\circ}# #=4.07#

Similarly, the force (F) needed to maintain the object's motion on the plane once it begins is given as

#F=\mu_k mg\cos\theta-mg\sin\theta#
#\mu_k=\frac{F+mg\sin\theta}{mg\cos\theta}#
#\mu_k=\frac{7+14\times9.81\sin75^\circ}{15\times9.81\cos75^\circ}# #=3.93#
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Answer 2

The coefficient of static friction is 0.857 and the coefficient of kinetic friction is 0.5.

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Answer 3

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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Answer from HIX Tutor

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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