Two forces whose resultant is 100N are per pendicular to each other.if one of them makes an angle of 60•with the resultant, calculate the magnitude
cosine60=R/100
solve for R
To solve this problem, we can use vector addition and trigonometry.
Let's assume the two forces are F1 and F2, with F1 making an angle of 60 degrees with the resultant.
Using this information, we can calculate F1 and F2.
Step 1: Find F1:
Since F1 makes an angle of 60 degrees with the resultant, we can use the trigonometric formula to find F1:
F1 = Resultant / cos(60)
F1 = 100N / cos(60)
Step 2: Find F2:
Since the resultant is the sum of F1 and F2, we can use vector addition to find F2:
Resultant^2 = F1^2 + F2^2
100^2 = F1^2 + F2^2
F2^2 = 100^2 - F1^2
F2^2 = 100^2 - (100N / cos(60))^2
Finally, we can calculate the magnitude of F2 by taking the square root:
F2 = sqrt[F2^2]
This will give us the magnitude of F2.
To solve this problem, we can use vector addition and trigonometry.
Let's assume the magnitude of one of the forces is F1, and the other force is F2. As per the question, the resultant R has a magnitude of 100N.
The forces F1 and F2 are perpendicular to each other, so we can use the Pythagorean theorem to find the magnitude of the resultant:
R^2 = F1^2 + F2^2
Since R = 100N, we have:
100^2 = F1^2 + F2^2
10000 = F1^2 + F2^2
Now, let's consider the force F1 that makes an angle of 60° with the resultant. We can use trigonometry to find its magnitude.
We can use the trigonometric relationship:
cos(60°) = F1/R
Substituting the known values:
cos(60°) = F1/100
We can rearrange the equation to solve for F1:
F1 = cos(60°) * 100
F1 = 0.5 * 100
F1 = 50N
Now that we know F1, we can substitute it back into the equation we derived earlier:
10000 = (50)^2 + F2^2
10000 = 2500 + F2^2
F2^2 = 7500
F2 = sqrt(7500)
F2 ≈ 86.60N (rounded to two decimal places)
Therefore, the magnitude of the second force, F2, is approximately 86.60N.