Question

two forces act on an object. the first has a magnitutude of 360 newtons and acts at an angle of 30* as measured from the horizontal. the second force has a magnitude of 240 newtons and acts at an angle of 135* as measured from the horizontal. determine the vector v that represents the resultant force

Answer 1

To find the resultant force, we first need to break down both forces into their horizontal and vertical components.

For the first force:
Magnitude = 360 N
Angle = 30 degrees

Horizontal component = 360 * cos(30) = 360 * √3 / 2 = 360 * 1.732 / 2 = 311.04 N
Vertical component = 360 * sin(30) = 360 * 0.5 = 180 N

For the second force:
Magnitude = 240 N
Angle = 135 degrees

Horizontal component = 240 * cos(135) = 240 * (-√2 / 2) = -240 * 0.707 = -169.92 N
Vertical component = 240 * sin(135) = 240 * (-√2 / 2) = -240 * 0.707 = -169.92 N

Now, we can find the total horizontal and vertical components of the resultant force by adding the components of the two forces:

Horizontal component of resultant force = 311.04 N - 169.92 N = 141.12 N
Vertical component of resultant force = 180 N - 169.92 N = 10.08 N

Finally, we can find the magnitude and direction of the resultant force using the Pythagorean theorem and trigonometry:

Magnitude of resultant force = sqrt((141.12)^2 + (10.08)^2) = √(19891.8637 + 101.6064) = √20093.47 = 141.69 N

Angle of resultant force with respect to the horizontal:
tan^−1(10.08 / 141.12) = tan^−1(0.071446) = 4.1 degrees

Therefore, the vector V that represents the resultant force is 141.69 N at an angle of 4.1 degrees with respect to the horizontal.