Question

a mass of 25kg on a ramp at an angle of inclination 30 degrees to the horizontal, is oulled with a force of 75 kg an angle of 20 degrees to the ramp what is the frictional force if it is pulled up the ramp at constant speed

Answer 1

Decompose the forces into components that are parallel or perpendicular to the plane. Then the fricitional force (magnitude f ) is only included in the net force parallel to the surface. The other two are the parallel components of the box's weight (mag. w ) and the pulling force (mag. p)

The box is moving at constant speed, so there is no acceleration and the box is in equilibrium. By Newton's second law,

∑ F = p cos(20º) - w sin(30º) - f = 0

We're given p = 75 N, and

w = m g = (25 kg) (9.80 m/s²)

so

f = (75 N) cos(20º) - (25 kg) (9.80 m/s²) sin(30º)

f ≈ -52 N

That the magnitude is negative makes me think there's a mistake in the question.