# Abstract question- solving for acceleration up an inclined plane

1. Oct 21, 2013

### will5656

1. The problem statement, all variables and given/known data

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)?

2. Relevant equations

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

3. 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 in to 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Oct 21, 2013

### Staff: Mentor

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...

3. Oct 21, 2013

### nil1996

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