(a) Find the resultant of a force of 4N Northward and a force of xN Eastward
(b) A force on a body is 100N, 60 degrees West of South. Find the north and east components of the force
a. they are at 90 deg, so Force=sqrt(4^2+x^2)
b. N: 100cos240 E: 100sin240
(a) To find the resultant of two forces, we need to use vector addition. In this case, we have a force of 4N directed northward and a force of xN directed eastward.
To find the resultant, we need to find the sum of the two forces. Since they are directed at right angles to each other, we can use the Pythagorean theorem and trigonometry to find the magnitude and direction of the resultant.
Let's denote the resultant force as R and its magnitude as Rn. Using the Pythagorean theorem, we can write:
R^2 = (4N)^2 + (xN)^2
Simplifying this equation gives us:
R^2 = 16N^2 + x^2N^2
To find the value of x, we need more information about the force directed eastward. Please provide the value of x to proceed with the calculation of the resultant.
(b) To find the north and east components of a force, we need to break down the force into its vector components. This can be done using trigonometry.
Let's denote the force as F and its magnitude as Fm. We are given that the force is 100N, and it is directed 60 degrees west of south.
To find the north component, we need to find the projection of the force onto the north direction. This can be done using the sine function:
North Component (N) = Fm * sin(60 degrees) = 100N * sin(60 degrees)
To find the east component, we need to find the projection of the force onto the east direction. This can be done using the cosine function:
East Component (E) = Fm * cos(60 degrees) = 100N * cos(60 degrees)
Now you can calculate the north and east components of the force using the given values.