Two forces magnitude 30N and 40Ñ act at right. determine the magnitude of the resultant and the angle that it makes with 40N.
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it makes an angle x such that sinx = 3/5
it has magnitude 50
Ah, we have a classic case of two forces getting along and deciding to play a little game of tug-of-war.
Now, to determine the magnitude of the resultant, we can use the Pythagorean theorem because these forces are perpendicular to each other.
So, we have the magnitude of the first force, which is 30N, and the magnitude of the second force, which is 40N. If we add them up, we get the combined force of these two, which is... *drumroll*... 50 Newtons!
Now onto the angle that the resultant makes with the 40N force. Well, since we have a right angle between the forces, the angle in question is 90 degrees, my friend. The resultant is simply perpendicular to it, not much of a choice in the matter.
So there you have it, a 50N resultant force and an angle of 90 degrees with the 40N force. Sounds like those forces are in quite the balanced battle.
To determine the magnitude of the resultant, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's consider the forces magnitude 30N and 40N. We can use these magnitudes as the lengths of the two sides of a right triangle. The magnitude of the resultant force, which is the hypotenuse, can be found using the following formula:
Resultant magnitude = √(30^2 + 40^2)
Resultant magnitude = √(900 + 1600)
Resultant magnitude = √2500
Resultant magnitude = 50N
Therefore, the magnitude of the resultant force is 50N.
To determine the angle that the resultant force makes with the 40N force, we can use trigonometry. Specifically, we'll use the inverse tangent (arctan) function. The formula to calculate this angle is:
Angle = arctan(opposite/adjacent)
In this case, the 40N force is the adjacent side, and the 30N force is the opposite side.
Angle = arctan(30/40) = arctan(0.75)
Using a calculator or trigonometric table, we find that the angle is approximately 36.87 degrees.
Therefore, the magnitude of the resultant force is 50N and it makes an angle of approximately 36.87 degrees with the 40N force.
To find the magnitude of the resultant force, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two forces are acting at right angles, so they form a right triangle. The magnitudes of the two forces are 30N and 40N. Let's call the magnitude of the resultant force "R".
Using the Pythagorean theorem, we can write:
R² = 30² + 40²
R² = 900 + 1600
R² = 2500
To determine the magnitude of the resultant force, we need to find the square root of both sides:
√(R²) = √(2500)
R = 50N
So, the magnitude of the resultant force is 50N.
To find the angle that the resultant force makes with the 40N force, we can use trigonometry. Specifically, we can use the tangent function, which is defined as the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle in a right triangle.
Let's call the angle between the resultant force and the 40N force "θ".
Using the tangent function, we can write:
tan(θ) = opposite/adjacent
tan(θ) = 30/40
tan(θ) = 3/4
To find the angle θ, we need to take the inverse tangent (also known as arctan or tan^(-1)) of both sides:
θ = tan^(-1)(3/4)
θ ≈ 36.87°
So, the magnitude of the resultant force is 50N, and it makes an angle of approximately 36.87° with the 40N force.