Question

Help please!! im really struggling with these force questions, hoping someone could help and give me an explanation on how to solve them!!

question: Three forces with magnitudes of 80 pounds, 95 pounds, and 125 pounds act on an object at angles of 30°, 45°, and 120°, respectively, with the x-axis. Find the direction and magnitude of the resultant of these forces. (Round your answers to one decimal place.)

Answer 1

Answer: To find the direction and magnitude of the resultant of these three forces, we will use the law of cosines and law of sines.

First, we will find the horizontal and vertical components of each force using trigonometry:

F1x = 80 * cos(30) = 69.28 pounds

F1y = 80 * sin(30) = 40 pounds

F2x = 95 * cos(45) = 67.08 pounds

F2y = 95 * sin(45) = 67.08 pounds

F3x = 125 * cos(120) = -62.5 pounds

F3y = 125 * sin(120) = -106.57 pounds

Next, we will add the horizontal and vertical components of each force together to find the overall horizontal and vertical components of the resultant force:

Rx = F1x + F2x + F3x = 69.28 + 67.08 + (-62.5) = 72.86 pounds

Ry = F1y + F2y + F3y = 40 + 67.08 + (-106.57) = 0.51 pounds

Finally, we can use the law of cosines to find the magnitude of the resultant force, and the law of sines to find the direction of the resultant force:

R = sqrt(Rx^2 + Ry^2) = sqrt(72.86^2 + 0.51^2) ≈ 114.66 pounds

theta = atan(Ry/Rx) = atan(0.51/72.86) = 0.0068 radians ≈ 0.39 degrees

So, the direction of the resultant force is 0.39 degrees counter-clockwise from the positive x-axis, and the magnitude of the resultant force is 114.66 pounds.

Note: Keep in mind that angle given in the question is in degree and the trigonometric functions in most programming languages accept the angle in radians, so you have to convert the angle to radians before using the trigonometric functions.

Explanation: