Let's assume that the force required to move the body up the inclined plane is F1, and the force required to prevent the body from sliding down is F2.
When the body is being moved up the inclined plane, the force required is equal to the component of the weight of the body acting along the incline, which is given by:
F1 = m * g * sin(theta),
where m is the mass of the body, g is the acceleration due to gravity, and theta is the angle of inclination of the plane.
When the body is prevented from sliding down the inclined plane, the force of friction acting up the incline is given by:
F_f = mu * N,
where mu is the coefficient of friction and N is the normal force acting on the body, which is equal to m * g * cos(theta).
Since F2 is twice F1, we can write:
2 * F1 = F2,
2 * (m * g * sin(theta)) = mu * (m * g * cos(theta)).
Simplifying the equation:
2 * sin(theta) = mu * cos(theta).
Substituting the given coefficient of friction (mu = 0.25) into the equation:
2 * sin(theta) = 0.25 * cos(theta).
Dividing both sides of the equation by cos(theta):
2 * tan(theta) = 0.25.
Taking the inverse tangent of both sides:
tan(theta) = 0.25 / 2,
tan(theta) = 0.125.
Taking the inverse tangent (arctan) of both sides to find the angle theta:
theta = arctan(0.125).
Using a calculator, we find that theta is approximately 7.125 degrees.
Therefore, the angle of inclination of the plane is approximately 7.125 degrees.