A truck pulls boxes up an incline plane. The truck can exert a maximum force of #4,000 N#. If the plane's incline is #pi/3 # and the coefficient of friction is #2/3 #, what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2017-07-22T06:56:40

The mass is #=340.3kg#

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Resolving in the direction parallel to the plane #↗^+#

Let the force exerted by the truck be #=FN#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N#

The normal force is #N=mgcostheta#

Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

#m=F/(g(mucostheta+sintheta))#

#=4000/(9.8(2/3*cos(1/3pi))+sin(1/3pi))#

#=340.3kg#