1. a force of 30n with a direction of 35 degrees northwest acts on point p. Find:
a) the northward component on the force
b) the westward component of the force
Please show work. Thanks!
"35 degrees northwest" is not a direction. Do you mean 35 degrees north of west?
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again, you have to express directions in standard form. 35 degrees northwest is not a standard direction. Is it 35 degrees North of west, or 35 degrees west of North?
That is just what my homework says but it probably does mean north of west.
To find the northward and westward components of the force, we can use trigonometry.
Given that the force has a magnitude of 30 N and a direction of 35 degrees northwest, we can break down this force into its northward and westward components.
Step 1: Convert the given direction to angles with respect to the positive x and y-axis (east and north).
To find the angle with respect to the positive x-axis (east), we subtract the given angle (35 degrees) from 45 degrees (northwest).
Angle with respect to east = 45 degrees - 35 degrees = 10 degrees.
Step 2: Use trigonometric functions to find the northward and westward components.
a) To find the northward component, we use the sine function.
Northward component = 30 N * sin(10 degrees)
Northward component ≈ 5.16 N
b) To find the westward component, we use the cosine function.
Westward component = 30 N * cos(10 degrees)
Westward component ≈ 29.21 N
Therefore, the northward component of the force is approximately 5.16 N and the westward component is approximately 29.21 N.