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An object with a mass of #8 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?

Answer 1

Sebastian Acosta

The coefficient of static friction is #=-0.22#

Taking the direction up and parallel to the plane as positive #↗^+#

The coefficient of static friction is #mu_s=F_r/N#

Consequently, the object's net force is

#F=F_r+Wsintheta#

#=F_r+mgsintheta#

#=mu_sN+mgsintheta#

#=mmu_sgcostheta+mgsintheta#

#=mg(mu_scostheta+sintheta)#

Thus,

#F/(mg)=(mu_scostheta+sintheta)#

#mu_scostheta=F/(mg)-sintheta#

#mu_s=1/costheta*(F/(mg)-sintheta)#

#=1/cos(pi/12)*(4/(8*9.8)-sin(pi/12))#

#=-0.22#

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Answer 2

Olivia Askew

The minimum coefficient of static friction needed is 0.5.

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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.