Question

Two forces of 70 and 110 pounds are acting on an object. The object is standing in a vertical position and the forces are acting at a 40° angle to each side, left and right. Find the magnitude and direction (with respect to the horizonal axis) of the resultant force.

Answer 1

To solve this problem, we can use vector addition to find the magnitude and direction of the resultant force.

First, we need to resolve the forces into their horizontal and vertical components. We can do this using trigonometry, as follows:

Horizontal component of 70 lb force = 70 cos(40°) = 53.58 lb
Vertical component of 70 lb force = 70 sin(40°) = 45.02 lb

Horizontal component of 110 lb force = 110 cos(40°) = 83.97 lb
Vertical component of 110 lb force = 110 sin(40°) = 74.05 lb

Next, we can add the horizontal and vertical components separately to find the resultant force:

Horizontal component of resultant force = 53.58 lb + 83.97 lb = 137.55 lb
Vertical component of resultant force = 74.05 lb - 45.02 lb = 29.03 lb

Using the Pythagorean theorem, we can find the magnitude of the resultant force:

Magnitude of resultant force = sqrt((137.55 lb)^2 + (29.03 lb)^2) = 141.92 lb

Finally, we can use trigonometry to find the direction of the resultant force with respect to the horizontal axis:

Direction of resultant force = arctan(29.03 lb / 137.55 lb) = 11.98°

Therefore, the magnitude of the resultant force is approximately 141.92 pounds and its direction with respect to the horizontal axis is approximately 11.98 degrees.