Newton's 2nd law, friction

Problem:

A box of mass m slides across a horizontal table with coefficient of friction μ.  The box is connected by a rope which passes over a frictionless pulley to a body of mass M hanging along side the table.  Find the acceleration of the system and the tension in the rope.

Solution:

Problem:

In the figure below the coefficient of friction is the same at the top and the bottom of the 700-g block. 
(a)  Draw a free body diagrams for both the 200-g and the 700-g blocks, considering all forces.
(b)  If the acceleration is a = 70 cm/s2 when F = 1.3 N, how large is the coefficient of friction?

image

Solution:

Problem:

A trunk weighing 500 N is to be pushed up a rough incline by an applied horizontal force F.  The incline makes an angle of 40o with the horizontal.  If a force of 1000 N is sufficient to move the trunk at a constant velocity of 0.200 m/s, what is the coefficient of kinetic friction between the trunk and the incline?

Solution:

Problem:

A block is given a quick push along a horizontal table.  The coefficient of kinetic friction between the block and the table is μk.  It is known that during the time interval t (immediately after the push) the block covers a distance d.  Find the distance that may be covered by the block during the subsequent time interval t'.  Find all possible answers.

Solution:

Problem:

You are going to entertain children by pulling a tablecloth out from under the the cake at a birthday party.  The birthday cake is resting on a tablecloth at the center of a square table.  Each side of the table has length l =  1.84 m.  The tablecloth is the same size as the table top.  You grab the edge of the tablecloth and pull sharply in a direction along one of the sides.  The tablecloth and cake are in contact for time t after you start pulling.  Then the sliding cake is stopped (you hope) by the friction between the cake and table top.  The coefficient of kinetic friction between the cake and tablecloth is μk1 = 0.310 , and that between the cake and table top is μk2 = 0.410.  Calculate the maximum value of t if the cake is not to end up on the floor.  Neglect the size of the cake compared to the size of the table.

Solution: