What is the length of the inclined plane if a body weighing 75 kg is lifted by 40 cm

What is the length of the inclined plane if a body weighing 75 kg is lifted by 40 cm along it, applying a force of 150 N in the direction of motion. There is no friction.

m = 75 kg.

g = 9.8 m / s2.

h = 40 cm = 0.4 m.

F = 150 N.

L -?

Since the body is lifted evenly along an inclined plane, the effect on its forces is compensated.

The body is acted upon by the force of gravity m * g vertically downward, the force F with which the body is pulled along the inclined plane, the reaction of the plane N is perpendicular to the plane upward.

m * g * sinα = F.

N = m * g * cosα.

sinα is expressed as the ratio of the opposite leg h to the hypotenuse L: sinα = h / L.

m * g * h / L = F.

The formula for determining the length of an inclined plane will take the form: L = m * g * h / F.

L = 75 kg * 9.8 m / s2 * 0.4 m / 150 N = 1.96 m.

Answer: the length of the inclined plane is L = 1.96 m.