physics help... PLEASE?

Question

A clerk moves a box of cans down an aisle by pulling on a strap attached to the box. The clerk pulls with a force of 184.0 N at an angle of 30° with the horizontal. The box has a mass of 31 kg, and the coefficient of kinetic friction between the box and the floor is 0.45. Find the acceleration of the box.

AND

A 3.10 kg block is pushed along the ceiling with an constant applied force of F = 86.5 N that acts at an angle = 52° with the horizontal, as in the figure below. The block accelerates to the right at 6.02 m/s2. Determine the coefficient of kinetic friction between the block and the ceiling.

and

A 1.1 kg mass starts from rest and slides down an inclined plane 8.8 10-1 m long in 0.62 s. What net force is acting on the mass along the incline?

Answer 1

1) The force of friction is
(31*9.81-184*sin(30))*0.45
95.45 N

setting up F=m*a
184*cos(30)-95.45=31*a
solve for a
a=2.06 m/s^2


2) the force of friction is
(86.5*sin(52)-3.10*9.81)*µk
54.9*µk
setting up F=m*a

86.5*cos(52)-54.9*µk=3.10*6.02
solve for µk
µk=0.630

net force =m*a
and
s(t)=.5*a*t^2
from the givens
0.88=.5*a*0.62^2
solve for a
4.58 m/s^2
so
F=1.1*4.58
F=5.04 N


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