Question

Two forces are applied to a tree stump to pull it out of the ground. Force A has a magnitude of 2580 newtons (N) and points 36.0 ° south of east, while force B has a magnitude of 2270 N and points due south. Using the component method, find the (a) magnitude and (b) direction of the resultant force A + B that is applied to the stump. Specify the direction as a positive angle with respect to due east.

Answer 1

(a) 4323.67 N

(b) 421.13 degree

Step-by-step explanation:

A = 2580 N 36 degree South of east

B = 2270 N due South

A = 2580 ( Cos 36 i - Sin 36 j) = 2087.26 i - 1516.49 j

B = 2270 (-j) = - 2270 j

A + B = 2087.26 i - 1516.49 j - 2270 j

A + B = 2087.26 i - 3786.49 j

(a) Magnitude of A + B =
`\sqrt{2087.26^(2)+(-3786.49)^(2)}`

Magnitude of A + B = 4323.67 N

(b) Direction of A + B

Tan theta = - 3786.49 / 2087.26

theta = - 61.13 degree

Angle from ast = 360 - 61.13 = 421.13 degree.