Two forces of 5 lb. and 14 lb. act on a body at right angles to each other. Find the angle their resultant force makes with the force of 14 lb
To find the angle between the resultant force and the 14 lb force, we can use the concept of vector addition.
Given that the two forces are acting at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant force:
Resultant force = √(5 lb)^2 + (14 lb)^2
Resultant force = √25 lb^2 + 196 lb^2
Resultant force = √221 lb^2
Resultant force ≈ 14.87 lb (rounded to two decimal places)
Now that we have the magnitude of the resultant force, we can use trigonometry to find the angle between the resultant force and the 14 lb force.
Let's call this angle θ.
Cos θ = adjacent side / hypotenuse
Cos θ = 14 lb / 14.87 lb
Cos θ ≈ 0.941
To find the value of θ, we need to take the inverse cosine (cos^-1) of 0.941:
θ ≈ cos^-1(0.941)
θ ≈ 19.27° (rounded to two decimal places)
Therefore, the angle between the resultant force and the 14 lb force is approximately 19.27°.
To find the angle between the resultant force and the force of 14 lb, we need to first calculate the magnitude and direction of the resultant force.
The magnitude (R) of the resultant force can be found using the Pythagorean theorem:
R = √(5^2 + 14^2)
R = √(25 + 196)
R = √221
R ≈ 14.87 lb
Next, we need to find the direction of the resultant force. We can use trigonometry to accomplish this. The angle between the resultant force and the force of 14 lb can be found using the following equation:
sinθ = (opposite / hypotenuse)
θ = sin^(-1)(opposite / hypotenuse)
In this case, the opposite side (the side opposite to the angle in question) is 5 lb, and the hypotenuse is 14.87 lb (the magnitude of the resultant force). Plugging these values into the equation, we get:
θ = sin^(-1)(5 / 14.87)
θ ≈ 20.36 degrees
Therefore, the angle between the resultant force and the force of 14 lb is approximately 20.36 degrees.
After you make your sketch you should see that
tanØ = 5/14
Ø = 19.65°