A given force F→ is located in the yz-plane. It has a magnitude of 18N and is directed at a 30.0° angle clockwise from the positive y-axis.
(a) Describe F→ using polar notation.
(b) Describe F→ using its y- and z-components.
(c) Describe F→ using cartesian notation.
I have a hard time figuring out this question
For a) I think it's 18m/s[300degrees]
b) Fy= 15.6 degree, Fz= 9 degrees
c) No clue.
Please correct me if I am wrong.
shouldn't the angle be 330deg?
on the force magnitudes, the unit is Newtons
f=fx i + fy j + fz k
fx=0, fy, fz as above
Sorry there was a typo in the question, you're right.
For part (a) - describing F→ using polar notation:
Polar notation represents a vector in terms of its magnitude (r) and the angle (θ) it makes with a reference axis (usually the positive x-axis). In this case, we are given the magnitude of the force (18N) and the angle it makes with the positive y-axis (30° clockwise).
To convert the given angle to the angle measured counterclockwise from the positive x-axis, we subtract the given angle from 90° (since the positive y-axis is perpendicular to the positive x-axis).
So the angle measured counterclockwise from the positive x-axis is 90° - 30° = 60°.
Therefore, in polar notation, F→ is represented as 18N[60°].
For part (b) - describing F→ using its y- and z-components:
Since this force is located in the yz-plane, it means it only has components in the y and z directions.
To determine the y-component, we use the sine of the angle (30°) and multiply it by the magnitude of the force:
Fy = 18N * sin(30°) = 9N.
To determine the z-component, we use the cosine of the angle (30°) and multiply it by the magnitude of the force:
Fz = 18N * cos(30°) = 15.6N.
Therefore, the y-component is 9N and the z-component is 15.6N.
For part (c) - describing F→ using cartesian notation:
Cartesian notation represents a vector in terms of its x, y, and z-components. Since this force is located in the yz-plane, it means it only has components in the y and z directions while the x-component is zero.
So, F→ in cartesian notation is (0, 9N, 15.6N).