Suitcase Ramp

While being unloaded from a moving truck, a bag of 10 kg is placed on a ramp inclined at 37 degrees flat. When released from rest, the bag accelerates the ramp of 0.15 m / s ^ 2. What is the coefficient of kinetic friction between the suitcase and the ramp?

From Newton's 2nd law forces are parallel to the slope component of gravity on the slope and the friction force on the slope (friction building in front of the motion). taking as positive, the equation for the net forces:

ΣF = ma = mgsinθ - μn -----> (1)

The forces acting perpendicular to the slope are the force of gravity perpendicular to the slope and the normal force acting upwards and perpendicular. Their sum is zero, the equation is:

ΣF = 0 = n - mgcosθ
n = mgcosθ -----> (2)

The connection (2) (a) and resolution of μ, you get:

MA = mgsinθ - μmgcosθ
μ = (gsinθ - a) / gcosθ
= (9.8 m / s ² sin37 ° - 0.15 m / s ²) / 9.8 m / s ² ° cos37
= 0.73 (rounded)

Hope this helps.