Verified answer

Net force = mass * acceleration

The component of the weight of box, which is parallel to the ramp, is causing the box to accelerate. The friction force is causing the box to decelerate.

Force parallel = mass * g * sin θ

Friction force = µ * mass * g * cos θ

Net force down the ramp = Force parallel – Friction force

mass * g * sin θ – µ * mass * g * cos θ = mass * acceleration

Divide both sides by mass

g * sin θ – µ * g * cos θ = acceleration

9.8 * sin 29 – µ * 9.8 * cos 29 = 3.10

Add µ * 9.8 * cos 29 to both sides

9.8 * sin 29 = µ * 9.8 * cos 29 + 3.10

Subtract 3.10 from both sides

9.8 * sin 29 – 3.10 = µ * 9.8 * cos 29

Divide both sides by 9.8 * cos 29

(9.8 * sin 29 – 3.10) ÷ (9.8 * cos 29) = µ

0.1926 = µ

Check

9.8 * sin 29 – 0.1926 * 9.8 * cos 29 = 3.10

OK

except the container has an engine the only acceleration is from gravity. to discover the coefficient of friction you could need;preliminary velocity,length of the ramp traveled and time elapsed. There are 2 forces,one pulling orizontally and the different flattening. resolve with trigonometry for 29 degree and you will have the area coated in the elapsed time. study this with the unique time and the version is via friction.

acceleration = g*(sinө - μ*cosө) = 3.10

=> μ*cosө = sinө - 3.10/g = 0.184

=> μ = 0.184 / cosө = 0.21