A box weighing 50N was placed on a sloping plane inclined at 30degree to the horizontal. It was acted on by the force 50n. Find the perpendicular and parallel compönent
And your thinking is?
To find the perpendicular and parallel components of the force acting on the box, we can break down the force vector into its components.
The force acting on the box can be resolved into two components: the perpendicular component (F_perpendicular) and the parallel component (F_parallel).
The perpendicular component (F_perpendicular) is the force acting perpendicular to the incline. It can be calculated using the formula:
F_perpendicular = F × sin(θ)
where F is the magnitude of the force (50 N) and θ is the angle between the force vector and the incline (30 degrees in this case).
Substituting the values into the formula:
F_perpendicular = 50 N × sin(30°)
F_perpendicular = 50 N × 0.5
F_perpendicular = 25 N
Therefore, the perpendicular component of the force acting on the box is 25 N.
The parallel component (F_parallel) is the force acting parallel to the incline. It can be calculated using the formula:
F_parallel = F × cos(θ)
Using the same values as before:
F_parallel = 50 N × cos(30°)
F_parallel = 50 N × 0.866
F_parallel = 43.3 N
Therefore, the parallel component of the force acting on the box is approximately 43.3 N.