A box which has a mass of 32.8 kg is placed on a plane which is inclined at 40.0°above the horizontal. The sliding friction force acting between the box and the plane is 36.4 N. What is the acceleration of the box as it slides down the plane? (Ans: 5.19m/s2) Explain why isn't acceleration negative and why isn't the Fg -x component down the slope negative as well.

Question

A box which has a mass of 32.8 kg is placed on a plane which is inclined at 40.0°above the horizontal.  The sliding friction force acting between the box and the plane is 36.4 N. What is the acceleration of the box as it slides down the plane? (Ans: 5.19m/s2) Explain why isn't acceleration negative and why isn't the Fg -x component down the slope negative as well.

Damon · Accepted Answer

You can draw your coordinate system with x pointing down the slope and y up perpendicular to the slope if you wish.
Then component of m g perpendicular to slope = m g cos 40
and component of mg down slope in x direction = m g sin 40
= 32.8 * 9.8* sin 40
= 206.6 Newtons
net force down slope = 206.6 - 36.4 = 170.2 N
a = F/m = 170.1/32.8 = 5.19 m/s^2