A man is pulling on a rope with a force of 65 N
directed at an angle of 26◦ to the horizontal.
What is the x-component of this force?
Answer in units of N.
x = hor. = 65 * cos(26) = 58.4N.
To find the x-component of the force, we need to use the concept of trigonometry. The x-component can be found by using the cosine function.
The formula to find the x-component of a force is given by:
F_x = F * cos(θ)
Where:
F_x is the x-component of the force,
F is the magnitude of the force, and
θ is the angle the force makes with the horizontal.
In this case, the magnitude of the force is given as 65 N, and the angle is given as 26°.
Using the formula, we can calculate the x-component of the force:
F_x = 65 N * cos(26°)
To calculate this, you can use a scientific calculator or a calculator with trigonometric functions.
Taking the cosine of 26° gives us approximately 0.894.
Now, we can substitute this value into the formula:
F_x = 65 N * 0.894
Multiplying these two values, we get:
F_x ≈ 58.11 N
Therefore, the x-component of the force is approximately 58.11 N.