Abstract question- solving for acceleration up an inclined plane

[will5656]

Homework Statement

Burglars are pushing, with a horizontal force Fpush, a safe of mass m and coefficient of kinetic friction μk up a slope of angle θ. What is the safe's acceleration (in abstract terms)?

Homework Equations

as= +/-gsinθ (natural accl down a slope)
friction on a slope= μmgcosθ

The Attempt at a Solution

Fnet= Force up the slope- natural accl down - kinetic friction
Fnet= Fcosθ - mgsinθ - μmgcosθ
ma= Fcosθ - mgsinθ - μmgcosθ
a= Fcosθ/m - gsinθ - μgcosθ

I thought this was right but we have numbers to plug into check for correctness:
fpush= 4000N
m= 500kg
θ= 20°
coeff of kf= 0.20

and acceleration is supposed to be 1.777 m/s2

I can't seem to arrive at this answer.

 

[gneill]

Hi will5656, Welcome to Physics Forums.

When you draw your free body diagram for the safe, be sure to include the portion of the applied force Fpush which is adding to the normal force...

You've accounted for the "uphill" portion of the force with Fcosθ, but another component of that force is acting to push the safe against the slope. There will be consequences...

 

[nil1996]

Remember that the vertical component of the pushing force is increasing the safe's normal force!