To pull a box up a rough slope, the force required will be least when it is applied : a) horizontaly
b) vertically
c) perpendicular to the plane
d) parallel to the plane

The correct option is;

d) Parallel to the plane

Explanation:

The forces acting on the box of mass, m are;

Weight of the box acting an angle, θ, equal to the inclination of the plane to the perpendicular of the plane

Weight of the box acting along the plane = m×g×sin(θ)

The force of friction along the plane = μ×m×g×cos(θ)

The total force acting downward along the plane , = m×g×sin(θ) + μ×m×g×cos(θ)

The Force needed to pull the box up along the plane F = The total force acting downward along the plane

F = m×g×sin(θ) + μ×m×g×cos(θ) = m×g×(sin(θ) + μ×cos(θ))

When the force, Fₐ is applied vertically, the force acting along the plane = Fₐ×cos(θ)

When the force is applied perpendicular, the force acting along the plane = Fₐ×sin(θ)

When the force is applied horizontally, the force acting along the plane = Fₐ×cos(θ)

When the force is applied parallel to the plane, the force acting along the plane = Fₐ

Therefore, since Fₐ > Fₐ×cos(θ) and Fₐ > Fₐ×sin(θ), for acute angles, we have that the least force is required when the force is acting parallel to the plane.

when insulating materials rub against each other, they may become electrically charged . electrons , which are negatively charged, may be 'rubbed off' one material and on to the other. the material that gains electrons becomes negatively charged. the material that loses electrons is left with a positive charge.