Question

Two forces, F? 1 and F? 2, act at a point, as shown in the picture. (Figure 1) F? 1 has a magnitude of 9.20 N and is directed at an angle of ? = 65.0 ? above the negative xaxis in the second quadrant. F? 2 has a magnitudeof 5.80 N and is directed at an angle of ? = 53.9 ? below the negative x axis in the third quadrant.A.What is the x component Fx of the resultant force?Express your answer in newtons.B.What is the y component Fy of the resultant force?Express your answer in newtons.C. What is the magnitude F of the resultant force?Express your answer in newtons.D.What is the angle ? that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.Express your answer in degrees.

Answer 1

Answer 1: x-component of forces is 7.297N

Explanation: for x-component FX;

FX = F1cos65 + F2 lcos53.9

FX = 9.20cos65 + 5.8cos53.9

NB both forces are positive if resolved along the x-axis.

FX = 3.88 + 3.417 = 7.297N

Answer 2: 6-component of forces is -3.654N

Explanation: for y-component FY

FY = -F1sin65 + F2sin53. 9

FY = - 9.2sin65 + 5.8sin53.9

NB F1 is negative along y-axis

FY = - 8.34 + 4.686 = - 3.654N

Answer 3: the magnitude of the resultant force is 8.16N

Explanation: magnitude = (FX^2 + FY^2)^0.5

(7.297^2 + (-3.654)^2)^0.5 = 8.16N

Answer 4: angle made with negative x-axis is 26.56°

Explanation: Tan^-1 of FY/FX gives the angle of the resultant force.

= tan^-1 of -3.654/7.297

=tan^-1 of -0.5

= -26.56°

I.e 26.55° from the negative x-axis in a clockwise direction.