SOLUTION: 5. a) A 70-Kg box is slid along the floor by a 400-N force. The coefficient of friction between the box and the floor is 0.50 when the box is sliding. Calculate acceleration of the

Algebra ->  Test -> SOLUTION: 5. a) A 70-Kg box is slid along the floor by a 400-N force. The coefficient of friction between the box and the floor is 0.50 when the box is sliding. Calculate acceleration of the      Log On


   



Question 1161028: 5. a) A 70-Kg box is slid along the floor by a 400-N force. The coefficient of friction between the box and the floor is 0.50 when the box is sliding. Calculate acceleration of the box?
5. b) Suppose this box (70-Kg) is pulled by a 400-N force at an angle of 30 to the horizontal .
Find the X and the Y components.
5. c) Determine the acceleration of the box

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
NOTE: If you have to "show your work" you may want to use the number of decimal places/significant figures that would make your teacher/instructor/professor happy.
I tend to use more decimal places than needed during intermediate calculations and round at the end, because that is what is required in my line of work.

a) Assuming a horizontal, level floor, the normal force (perpendicular to the surface, pressing the box into the floor) is
%2870kg%29%2A%289.807ms%5E9-2%29=686.49N
The horizontal friction force opposing the movement is
0.50%2A%28686.49N%29=343.245N
The net force on the box is
400N-343.245N=56.755N
The box will accelerate in the direction of the 400N force.
The acceleration will be
56.755N%2F%2270+kg%22=highlight%280.81ms%5E%28-2%29%29

b)

F%5Bx%5D=%28400N%29%2Acos%2830%5Eo%29=%28400N%29%2A0.8660=highlight%28346.4N%29
F%5By%5D=%28400N%29%2Asin%2830%5Eo%29=%28400N%29%2A0.5000=highlight%28200N%29

c) Now the normal force is
686.49N-F%5By%5D=686.49N-200N=486.49N
That will make the friction force opposing the movement
%28486.49N%29%2A0.50=243.245N
The net horizontal force acting on the box will be
346.4N-243.245N=103.155N
Acting on a mass of 70kg, that net horizontal force will produce a horizontal acceleration of
103.155N%2F%2270+kg%22=highlight%281.47ms%5E%28-2%29%29