Question

Two forces,f¹and f² act at a point. The magnitude of f¹ is 9.50N, and its direction is at an angle of 55.0,

above the negative direction of the x-axis in the second quadrant. The magnitude of f² is 6.00N, and its direction is at an angle of 52.1⁰below the negative direction of the x-axis in the third quadrant. What is the magnitude and direction of the net force R=f¹+f²?
A) Magnitude: 3.29 N, Direction: 157.1⁰ (measured counterclockwise from the negative x-axis)
B) Magnitude: 15.76 N, Direction: 76.9° (measured counterclockwise from the negative x-axis)
C) Magnitude: 5.48 N, Direction: 108.1° (measured counterclockwise from the negative x-axis)
D) Magnitude: 13.48 N, Direction: 128.1° (measured counterclockwise from the negative x-axis)

Answer 1

The magnitude and direction of the net force R=f¹+f² are 8.97 N and 198.1° (measured counterclockwise from the negative x-axis) respectively.

Step-by-step explanation:

To find the net force, we can add the x-components and y-components of the two forces separately.

For the x-components, f¹ has a magnitude of 9.50N and is directed at an angle of 55.0° above the negative x-axis. Therefore, its x-component is 9.50*cos(55.0°) = 4.78N in the negative x-direction.

For the y-components, f¹ has a magnitude of 9.50N and is directed at an angle of 55.0° above the negative x-axis. Therefore, its y-component is 9.50*sin(55.0°) = 7.76N in the positive y-direction.

Similarly, for f², its x-component is 6.00*cos(52.1°) = 3.73N in the positive x-direction and its y-component is 6.00*sin(52.1°) = 4.77N in the negative y-direction.

Adding the x-components together gives 4.78N + 3.73N = 8.51N in the negative x-direction. Adding the y-components together gives 7.76N + (-4.77N) = 2.99N in the positive y-direction.

The magnitude of the net force R=f¹+f² is given by the formula √(Fx² + Fy²) = √(8.51N² + 2.99N²) = 8.97N.

The direction of the net force is given by the formula 0 = tan^(-1)(Fy/Fx) = tan^(-1)(2.99N/8.51N) ≈ 18.1° above the negative x-axis. Since the question specifies that the direction should be measured counterclockwise from the negative x-axis, the actual direction is 180° + 18.1° ≈ 198.1°.