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Q. Draw a free body diagram of the plank as the man pulls the block with constant...

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user8235304 | Student, Grade 11 | (Level 1) Valedictorian

Posted July 30, 2013 at 3:43 PM via web

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Q. Draw a free body diagram of the plank as the man pulls the block with constant velocity.There is sufficient friction between man and the plank so that the man doesn't slip on the plank,but there is no friction between the plank and the ground.

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valentin68 | College Teacher | (Level 3) Associate Educator

Posted October 30, 2013 at 8:41 AM (Answer #1)

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The diagram is below. The man is standing because of friction forces on the plank. The force is the string `F` on the men is having the direction of the string (making an angle `alpha` with the horizontal). The friction force on the man `Ff` is opposing the horizontal component of the force in string. The weight of the man `G` is directed downwards and the reaction of the plank `N` is directed upwards . There is no friction between the plank and the ground so tat the plank accelerates toward the right. The final force on the plank is its inertia `m*a` opposing to the accelerated motion.

On the x and y axis the sum of the forces need to be the same.

For the man:

`F*cos(alpha) =Ff`  on the x axis

`F*sin(alpha)+N =G`  on the y axis

For the plank

`Ff =m*a`

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