A 35kg box moves up a ramp inclined at 12 degrees with the horizontal. It is pulled at an angle of 25 degrees with respect to the incline, has a 185 N force, and coefficient of kinetic friction is 0.27. What is the acceleration up the ramp?

You want the acceleration up a ramp inclined 12° of a 35 kg box pulled with 185 N force at an angle of 25° to the ramp. The coefficient of kinetic friction is 0.27.

Acceleration

The acceleration up the ramp is the difference between that due to the applied force and the acceleration due to gravity and friction in the direction down the ramp. The normal force between the box and the ramp is reduced by the upward component of the applied force.

a = F/m·cos(25°) - 9.8sin(12°) -0.27·(9.8cos(12°) -F/m·sin(25°))

a = (185 N)/(35 kg)(cos(25°)+0.27·sin(25°)) -9.8(sin(12°)+0.27·cos(12°))

a ≈ 0.768 m/s²

The acceleration of the box up the ramp is about 0.768 m/s².

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Additional comment

You could figure the forces due to gravity and friction, but when you divide by mass to get acceleration, the mass cancels in that computation. The result is a multiplier of g, as shown above.