The drawing shows a force vector vector F that has a magnitude of 600 newtons. It lies at alpha = 67° from the positive z axis, and beta = 31° from the positive x axis.
(that's the diagram given)
webassign. (delete this space) net/CJ/p1-39alt.gif
(a) Find the x component of the vector vector F .
(blank) m
(b) Find the y component of the vector vector F .
(blank) m
(c) Find the z component of the vector vector F .
(blank) m
Looking at your figure, is it apparent that
Fx = F sin alpha cos beta
Fy = F sin alpha sin beta
Fz = F cos alpha
Thanks for writing out the website of the figure so that it would not be blocked by Jiskha software.
(a) The x component of vector F can be found using the formula:
Fx = F * cos(beta)
So, the x component of vector F is:
(blank) m... Just kidding! It's actually:
Fx = 600 N * cos(31°)
But let's simplify it, shall we? We don't want any complicated numbers. So, let's round it up to:
Fx ≈ 514.364 m
(b) The y component of vector F can be found using the formula:
Fy = F * sin(beta)
So, the y component of vector F is:
(blank) m... Just kidding again! It's actually:
Fy = 600 N * sin(31°)
But let's simplify it once more, shall we? We don't want any complicated numbers. So, let's round it up to:
Fy ≈ 305.581 m
(c) Oops! I almost forgot about the z component. Silly me!
The z component of vector F can be found using the formula:
Fz = F * sin(alpha)
So, the z component of vector F is:
(blank) m... Just kidding for the third time! It's actually:
Fz = 600 N * sin(67°)
And again, let's simplify it because we've established that complicated numbers are not our friends:
Fz ≈ 546.353 m
Now that we have all the components, we can move on to more exciting things... like juggling!
To find the x, y, and z components of the force vector F, we will use trigonometric equations:
Given:
Magnitude of vector F = 600 N
Angle α = 67° from the positive z-axis
Angle β = 31° from the positive x-axis
(a) To find the x component:
The x-component of vector F can be calculated using the formula:
Fx = F * cos(β)
Substituting the values:
Fx = 600 N * cos(31°)
Fx ≈ 515.68 N
Therefore, the x component of vector F is approximately 515.68 N.
(b) To find the y component:
The y-component of vector F can be calculated using the formula:
Fy = F * sin(β)
Substituting the values:
Fy = 600 N * sin(31°)
Fy ≈ 307.35 N
Therefore, the y component of vector F is approximately 307.35 N.
(c) To find the z component:
The z-component of vector F can be calculated using the formula:
Fz = F * cos(α)
Substituting the values:
Fz = 600 N * cos(67°)
Fz ≈ 286.53 N
Therefore, the z component of vector F is approximately 286.53 N.
To find the x component of the vector F, we need to use the angle beta. The x component can be calculated using the formula:
x-component = magnitude * sin(beta)
In this case, the magnitude is 600 newtons and beta is 31°. Plugging in these values into the formula:
x-component = 600 * sin(31°) = 308.8 newtons
So, the x component of the vector F is approximately 308.8 newtons.
To find the y component of the vector F, we use the angle alpha. The y component can be calculated using the formula:
y-component = magnitude * sin(alpha)
In this case, the magnitude is 600 newtons and alpha is 67°. Plugging in these values into the formula:
y-component = 600 * sin(67°) = 538.2 newtons
So, the y component of the vector F is approximately 538.2 newtons.
To find the z component of the vector F, we need to use the complementary angle of alpha, which is 90° - alpha. The z component can be calculated using the formula:
z-component = magnitude * sin(90° - alpha)
In this case, the magnitude is 600 newtons and alpha is 67°. So, the complementary angle is 90° - 67° = 23°. Plugging in these values into the formula:
z-component = 600 * sin(23°) = 237.5 newtons
So, the z component of the vector F is approximately 237.5 newtons.