A truck pulls boxes up an incline plane. The truck can exert a maximum force of #6,800 N#. If the plane's incline is #(5 pi )/8 # and the coefficient of friction is #4/5 #, what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2017-06-29T12:55:54

The mass is #=1123.3kg#

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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))#

#=6800/(9.8(4/5*cos(5/8pi))+sin(5/8pi))#

#=1123.3kg#