Resultant Vectors and Forces (Physics)?

3.


A 5kg block slides with constant velocity down a 37º inclined plane.





Draw the force diagram and write out the equations for the sum of the forces.





a. What is the weight of the box?





b. What is the normal force?





c. What is the frictional force?





d. What is the coefficient of kinetic friction?








*I know that the weight is 5 X 9.8 = 49N


*Also that Acceleration = 0


But when I try to find the Normal Force this is what I come up with.


Fn – Fg = ma


Fn – (9.8 x 5) = (5)(0)


Fn – 49 = 0


+49


Fn = 49N








That’s how I am solving the problem, but my worksheet says that the normal force is 39.1N…. so I’m totally lost.

Resultant Vectors and Forces (Physics)?
Let:


m be the mass of the block,


g be the acceleration due to gravity,


R be the normal reaction of the plane on the block,


F be the friction acting upward parallel to the plane,


a be the inclination of the plane,


u be the coefficient of kinetic friction.





Your force diagram for the block should show:


R perpendicular to and away from the plane;


F parallel to and up the plane;


mg vertically downward.





Resolving parallel to the plane:


mg sin(a) = F ...(1)





Resolving perpendicular to the plane:


mg cos(a) = R ...(2)





F / R = u ...(3)





(a)


The weight is mg = 49N, as you have found.





(b)


From (2):


F = 49cos(37) = 39.1N.





(c)


From (1):


F = 49sin(37) = 29.5N.





(d)


From (3):


u = tan(37) = 0.75.