A force of 350 lb. is resolved into forces at right angles to one another, the angle of F2 being 67 from the 350 lb. force. Find F2.
322
Construct a rectangle with sides F1 and F2, so that the given force of 350 is the hypotenuse.
and label the angle it makes with F2 as 67°
On mine F2 is the shorter side.
Cos 67° = F2/350
F2 = 350cos67 = ....
btw, F1 = 350sin67 = ...
To find F2, we can use the concept of resolving forces into components. Given that the force of 350 lb is resolved into forces at right angles to one another, we can represent it as the sum of two forces: F1 and F2.
Let's assume that F1 is the force responsible for the 350 lb force in the horizontal direction, and F2 is the force responsible for the 350 lb force in the vertical direction.
To find F2, we need to calculate the vertical component of the 350 lb force.
We have the angle between F2 and the 350 lb force, which is 67 degrees.
Using trigonometry, we can calculate F2 as follows:
F2 = 350 lb * sin(67 degrees)
Using a calculator, we find:
F2 ≈ 350 * sin(67) ≈ 350 * 0.921 ≈ 322.35 lb
Therefore, the force F2 is approximately 322.35 lb.
To find F2, we can use trigonometry. We have a force of 350 lb that is resolved into two forces at right angles to each other. Let's denote the magnitude of F2 as F2 and the angle it makes with the 350 lb force as θ2.
First, we need to find the horizontal component of the 350 lb force, which is F1x. This can be determined using the cosine function:
F1x = 350 lb * cos(θ)
= 350 lb * cos(0 degrees)
= 350 lb
Since the angle between F2 and the 350 lb force is 67 degrees, we know that the angle between the horizontal component of the 350 lb force (F1x) and F2 is 90 degrees - 67 degrees = 23 degrees.
Next, we can find the magnitude of F2 using the sine function:
F2 = F1x / sin(θ2)
= 350 lb / sin(23 degrees)
To get the actual value of F2, we can now calculate it using the given formula:
F2 = 350 lb / sin(23 degrees)
F2 ≈ 849.04 lb
Therefore, the magnitude of F2 is approximately 849.04 lb.