A truck pulls boxes up an incline plane. The truck can exert a maximum force of #5,600 N#. If the plane's incline is #(2 pi )/3 # and the coefficient of friction is #7/6 #, what is the maximum mass that can be pulled up at one time?

1 Answer
May 1, 2016

Answer:

979 kg

Explanation:

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Note, by definition, an inclined plane cannot have an inclination more than #pi/2#. I take the angle is measured from positive x-axis, so it is just #theta = pi/3# the other way.

here #f# is the applied force, NOT the frictional force.

So, as we can easily observe in the picture, the forces that oppose will be (m is expressed in #kg#):

  1. gravitational pull: #mgsintheta = 9.8xxsqrt3/2 m=8.49mN #

  2. frictional force, opposite to the direction of tendency of movement: # mumgcostheta = 7/6xx9.8xx1/2 mN = 5.72m N#

Hence total is: #(8.49+5.72)m N=14.21m N#

So, for the truck the to be able to pull it up, the maximum force it can exert must be more than this:

#5600N>5.72m N => m<979 kg#