Force needed to push box down incline plane

[Physics_girl1]

Homework Statement

a) if a force of 86N parallel to the surface of a 20 degree incline plane will push a 120N block up the plane at constant speed, what force parallel to the plane will push it down at constant speed?

Homework Equations

$$\Sigma$$F(X)=F(A)-F(fr)-mgcos$$\vartheta$$=0
$$\Sigma$$F(Y)=F(n)-mgsin$$\vartheta$$=o
where F(A)= force applied, F(fr)= friction force, F(n)= normal force, mg=weight, F(X)= sum of forces in x direction, and F(Y)- sum of forces in y direction

The Attempt at a Solution

normal force=41.0424
friction force=26.73
my answer is -86.0331

 

[Physics_girl1]

my coefficient of friction for this problem=.652

 

[Physics_girl1]

could someone please check my answers?

 

[ritwik06]

Homework Statement

a) if a force of 86N parallel to the surface of a 20 degree incline plane will push a 120N block up the plane at constant speed, what force parallel to the plane will push it down at constant speed?

Homework Equations

$$\Sigma$$F(X)=F(A)-F(fr)-mgcos$$\vartheta$$=0
$$\Sigma$$F(Y)=F(n)-mgsin$$\vartheta$$=o
where F(A)= force applied, F(fr)= friction force, F(n)= normal force, mg=weight, F(X)= sum of forces in x direction, and F(Y)- sum of forces in y direction

The Attempt at a Solution

normal force=41.0424
friction force=26.73
my answer is -86.0331

my coefficient of friction for this problem=.652

could someone please check my answers?

Hi
Writing out the equation for the force to push up the block with constant speed, i.e. net force is zero.
120 sin 20(component of weight along incline) +120 cos 20 * u(Force of friction, u is the coefficient)=86
solve for u
u=0.399
Now for the second part:
120 sin 20 +F=120 cos 20 *u
F=120 sin 20-120 cos 20 *u
F=3.9 N
dos this help?