Question

A 25 kg box is being dragged by a gentleman at an angle of 40 degrees above the horizontal with a force of 50N. What is the magnitude of force along the horizontal (X) axis?

a) 38 N
b) 30 N
c) 31.6 N
d) 20 N

Answer 1

The magnitude of the horizontal component of the force is approximately 38 N when a 50 N force is applied at a 40-degree angle above the horizontal.

Step-by-step explanation:

To find the magnitude of the horizontal component of the force, we can use trigonometry, specifically the cosine function, which relates the adjacent side of a right triangle (the horizontal component we are looking for) to the hypotenuse (the 50 N applied force).

The formula to use is:

F

x

= F * cos(θ)

,

where Fx is the horizontal component of the force, F is the applied force, and θ is the angle of the force above the horizontal.

Step-by-Step Calculation

1. Insert the known values into the equation:
   Fx = 50 N * cos(40°).
2. Calculate the cosine of 40 degrees.
3. Multiply 50 N by the cosine of 40 degrees to find the horizontal component.

In this case, the horizontal component of the force (Fx) is:

Fx = 50 N * cos(40°) ≈ 38 N