A truck pulls boxes up an incline plane. The truck can exert a maximum force of #4,500 N#. If the plane's incline is #pi/8 # and the coefficient of friction is #4/3 #, what is the maximum mass that can be pulled up at one time?

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Answer 1 · 2018-01-15T15:42:42

The mass is #=284.4kg#

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

Let the force exerted by the truck be #F=4500N#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N=4/3#

The normal force is #N=mgcostheta#

The angle of the plane is #theta=1/8pi#

The acceleration due to gravity is #g=9.8ms^-2#
Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

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

#=4500/(9.8(4/3*cos(1/8pi)+sin(1/8pi))#

#=284.4kg#