A force vector points at an angle of 50.8° above the +x axis. It has a y component of +282 newtons. Calculate the magnitude of the force vector.
282/sin50.8
To calculate the magnitude of the force vector, we can use the Pythagorean theorem. The Pythagorean theorem relates the lengths of the sides of a right triangle, where the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the force vector has two components, the x-component and the y-component. We are given the y-component (+282 newtons), and we need to find the magnitude, which is the length of the hypotenuse.
The x-component can be determined by using trigonometry, specifically the cosine function. Since the angle is above the +x axis, the x-component will be positive. We can use the cosine function to calculate the x-component:
x = magnitude * cos(angle)
Substituting the given values into the equation:
x = magnitude * cos(50.8°)
We are given the y-component (+282 newtons), which is equal to the magnitude of the force vector times the sine of the angle. We can rearrange this equation to solve for the magnitude:
magnitude * sin(angle) = y
Substituting the given values into the equation:
magnitude * sin(50.8°) = +282
Now, we have two equations involving the magnitude and angle. We can solve these equations simultaneously to find the magnitude.
By dividing the second equation by the first equation, we can eliminate the magnitude:
(magnitude * sin(50.8°)) / (magnitude * cos(50.8°)) = +282 / magnitude
Simplifying the equation:
tan(50.8°) = +282 / magnitude
Now, we can solve for the magnitude:
magnitude = +282 / tan(50.8°)
Using a calculator, we can evaluate the right side of the equation:
magnitude ≈ +282 / 1.1917
magnitude ≈ 236.9 newtons
Therefore, the magnitude of the force vector is approximately 236.9 newtons.