A disembodied frictionless hand exerts a 6 N horizontal force on a block weighin

Question

A disembodied frictionless hand exerts a 6 N horizontal force on a block weighing 14.0 N against a vertical wall. The coefficient of static friction between the wall and the block is 0.59, and the coefficient of kinetic friction is 0.39. Assume that the block is not moving initially. Determine the normal force that the wall exerts against the block Determine the block's acceleration ("+y" axis is upward!) Determine the minimum amount of horizontal force F necessary for the blocks to remain motionless. Determine the minimum amount of horizontal force F necessary for the block to slide down the wall with a constant velocity.

Explanation / Answer

a) the normal force that the wall exerts against the block is 6N

B) The block will move if mg>static friction

==> mg>(mu_s)(N)

==> mg>(mu_s)(F)

==> 14.0>(0.59)(6)

==> 14>3.54 THE BLOCK WILL MOVE LET THE ACCELERATION BE a

so, 14 = 3.54 + ma

or, a = 10.46/m [mg = 14 so, m = 14/9.8 = 1.428 kg]

= 10.46/1.428 = 7.325 m/s^2 .........................................................................ans

c) minimum amount of horizontal force necessary for the block to remain motionless is

= 14 - 3.54 = 10.46 N

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