two forces whose resultant is 80N are perpendicular to each other,if one of them makes an angle 60degree with resultant.calculate its magnitude.
F = 80*Cos60.
f=80*cos60
Well, let's do some clown math, shall we?
Since the two forces are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the unknown force.
Let's call the magnitude of the unknown force "F". According to the Pythagorean theorem, we have:
(Resultant)^2 = (Force1)^2 + (Force2)^2
(80 N)^2 = (F)^2 + (F)^2
6400 N^2 = 2F^2
Dividing both sides of the equation by 2, we get:
3200 N^2 = F^2
Now, taking the square root of both sides, we find:
F = sqrt(3200 N^2) ≈ 56.57 N
So, the magnitude of the unknown force is approximately 56.57 N. And remember, clown math can make even physics fun!
Let's assume that the two forces are F1 and F2, with F1 making an angle of 60 degrees with the resultant.
We know that the resultant force is the vector sum of F1 and F2, and its magnitude is given as 80 N.
Using the Pythagorean theorem, we can calculate the magnitude of F1.
The Pythagorean theorem states that for a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the resultant force is the hypotenuse, and F1 and F2 are the other two sides.
Let's denote the magnitude of F1 as x.
Using trigonometry, we can express F1 and F2 in terms of the angle between them and the resultant force.
sin(60) = F1 / 80
Solving for F1:
F1 = 80 * sin(60)
F1 ≈ 80 * 0.866
F1 ≈ 69.28 N
Therefore, the magnitude of F1 is approximately 69.28 N.
To solve this problem, we need to use trigonometry and vector addition.
Let's call the magnitudes of the two perpendicular forces F1 and F2.
Given that the resultant force is 80N, we can use the Pythagorean theorem to find the relationship between F1 and F2:
(Resultant force)^2 = (F1)^2 + (F2)^2
Substituting the given values:
(80N)^2 = (F1)^2 + (F2)^2
6400N = (F1)^2 + (F2)^2 ....(Equation 1)
Next, we need to consider the angle between the resultant force and one of the forces (we'll choose F1). According to the given information, this angle is 60 degrees.
To find the magnitude of F1, we can use the trigonometric relationship:
cos(angle) = adjacent/hypotenuse
In this case, the adjacent side is F1, and the hypotenuse is the resultant force (80N).
cos(60 degrees) = F1/80N
Taking the cosine of 60 degrees, we have:
1/2 = F1/80N
Simplifying, we get:
F1 = (1/2) * 80N
F1 = 40N
Now, we can substitute this value back into Equation 1:
6400N = (40N)^2 + (F2)^2
6400N = 1600N + (F2)^2
Subtracting 1600N from both sides:
4800N = (F2)^2
Taking the square root of both sides:
F2 = sqrt(4800N)
F2 = 69.28N (rounded to two decimal places)
Therefore, the magnitude of the force making a 60-degree angle with the resultant is approximately 69.28N.