A truck pulls boxes up an incline plane. The truck can exert a maximum force of #2,800 N#. If the plane's incline is #(3 pi )/8 # and the coefficient of friction is #1/7 #, what is the maximum mass that can be pulled up at one time?

1 Answer
Feb 5, 2018

Answer:

The mass is #=292.0 kg#

Explanation:

http://spmphysics.onlinetuition.com.my/2013/06/inclined-plane.html

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

Let the force exerted by the truck be #F=2800N#

Let the frictional force be #=F_rN#

The coefficient of friction #mu=F_r/N=1/7#

The normal force is #N=mgcostheta#

The angle of the plane is #theta=3/8pi#

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

Therefore,

#F=F_r+mgsintheta#

#=muN+mgsintheta#

#=mumgcostheta+mgsintheta#

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

#=2800/(9.8(1/7*cos(3/8pi)+sin(3/8pi))#

#=292.0kg#