The sum of two forces, one having a magnitude of 8 N acting due west and other having a magnitude of 6 N acting due north is ___. What is the magnitude of that force?
Answer in units of N
Mag. = sgrt(6^2 + 8^2) = 10N.
Well, aren't those forces quite the couple! It seems like we're dealing with a bit of a Love Triangle of forces here.
Now, let's see how these forces combine. The force in the west direction is 8N, and the force in the north direction is 6N. We have to use some math magic to figure out the total magnitude of their love child.
Now, imagine the forces are on a lovely date night - the force in the west direction is taking them to the west, and the force in the north direction is trying to pull them to the north. But, silly forces, we want to know their total magnitude!
To find this, we can use the Pythagorean theorem (don't worry, it's just math, not love), which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Applying this to our forces, we have:
Magnitude of the total force = √(8^2 + 6^2)
Now let's do some math and solve it! Drum roll, please...
Magnitude of the total force ≈ √(64 + 36) ≈ √100 ≈ 10 N
So, the magnitude of that force is approximately 10 N. Love can be complicated, but math doesn't have to be!
To find the magnitude of the resulting force, we need to use the Pythagorean theorem, which states that in 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 two forces acting are perpendicular to each other, which forms a right-angled triangle. The force acting due west can be considered the horizontal side, and the force acting due north can be considered the vertical side.
By applying the Pythagorean theorem, we can calculate the magnitude of the resulting force:
Magnitude of the resulting force = √((8 N)² + (6 N)²)
Magnitude of the resulting force = √(64 N² + 36 N²)
Magnitude of the resulting force = √100 N²
Hence, the magnitude of the resulting force is 10 N.
To find the magnitude of the force resulting from the sum of two forces, one acting due west and the other acting due north, we can use vector addition.
Let's represent the force due west as F₁ with a magnitude of 8 N, and the force due north as F₂ with a magnitude of 6 N.
To find the magnitude of the resultant force, we can use the Pythagorean theorem. The magnitude of the resultant force (R) is given by:
R = √(F₁² + F₂²)
Substituting the given values into the formula, we have:
R = √(8² + 6²)
= √(64 + 36)
= √100
= 10 N
Therefore, the magnitude of the resultant force is 10 N.