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.
Part A
What is the x component Fx of the resultant force?
Express your answer in newtons.
Part B
What is the y component Fy of the resultant force?
Express your answer in newtons.
Part C
What is the magnitude F of the resultant force?
Express your answer in newtons.
Part 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.
The concept required to solve the problem are resolution of vectors and calculation of resultant vector. We have been given two force vectors with their angle with x axis. The two vectors can be resolved into their resultant components. Further, addition of their components along the respective axis will give the resultant vector’s components.
The vector can be resolved into its components along the x and y axis as follow
The resultant vector can be given by
Here, is the magnitude of force vector and is the angle made by the vector with axis.
The magnitude of the resultant vector from the component is vector is given by
The angle made by the vector with the x axis is given by
(A)
The component of in x direction is
Substitute 9.20 N for
The component of in x direction is
Substitute 5.80 N for
Therefore, the x component of resultant force is
Substitute 3.88 N for and 3.417 for
(B)
The component of in y direction is
Substitute 9.20 N for
The component of in y direction is
Substitute 5.80 N for
Therefore, the y component of resultant force is
(C)
The resultant vector is given by
Substitute 7.297 N for and 3.65 N for
Therefore, the magnitude of Resultant vector is
Substitute 7.297 N for and 3.65 N for
(D)
The resultant vector is
Therefore, the angle made with -x axis
Substitute 7.297 N for and 3.65 N for
It is positive since the resultant vector is in the second quadrant and the angle measured in clockwise direction from -x is taken positive as per the question.
Ans: Part AThe x component of resultant force is
Part BThe y component of resultant force is
Part CThe magnitude of the resultant vector is
Part DThe angle of inclination with the -x axis is
Two forces, F? 1 and F? 2, act at a point, as shown in the picture....
Two forces, F1 and F2, act at a point, as shown in the picture. (Figure 1) F1 has a magnitude of 8.40 N and is directed at an angle of a = 59.0 ? above the negative xaxis in the second quadrant. F2 has a magnitude of 6.40 N and is directed at an angle of b = 54.1 ? below the negative x axis in the third quadrant. a) What is the x component Fx of the resultant force? Express...
Two forces, F1 and F2, act at a point, as shown in the picture. F1 has a magnitude of 9.60 N and is directed at an angle of α = 58.0° above the negative x axis in the second quadrant. F2 has a magnitude of 5.80 N and is directed at an angle of β = 52.5° below the negative x axis in the third quadrant.Part A What is the x component Fx of the resultant force? Part B What is...
Two forces, F⃗ 1 and F⃗ 2, act at a point. F⃗ 1 has a magnitude of 8.00 N and is directed at an angle of 65.0 ∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 7.00 N and is directed at an angle of 53.9 ∘ below the negative x axis in the third quadrant. Part A What is the x component of the resultant force? Express your answer in newtons. N...
Two forces, F⃗ 1 and F⃗ 2, act at a point, as shown in the picture. (Figure 1) F⃗ 1 has a magnitude of 9.00 N and is directed at an angle of α = 58.0 ∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 7.00 N and is directed at an angle of β = 52.9 ∘ below the negative x axis in the third quadrant. PART A: What is the x...
Two forces, F⃗ 1 and F⃗ 2, act at a point, as shown in the picture. (Figure 1) F⃗ 1 has a magnitude of 8.00 N and is directed at an angle of α = 61.0 ∘∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 5.20 N and is directed at an angle of β = 54.1 ∘∘ below the negative x axis in the third quadrant. What is the x component Fx...
Two forces, F1 and F2, act at a point. F1 has a magnitude of 8.20 N and is directed at an angle of 61.0° above, the negative x axis in the second quadrant. F2 has a magnitude of 5.60 N and is directed at an angle of 53.4° below the negative x axis in the third quadrant.Part A What is the x component of the resultant force? Part B What is the y component of the resultant force? Part C What is the...
Two forces, F⃗1 and F⃗2, act at a point, as shown in the picture. (Figure 1) F⃗1 has a magnitude of 8.80 N and is directed at an angle of α = 62.0 ∘ above the negative x axis in the second quadrant. F⃗2 has a magnitude of 7.00 N and is directed at an angle of β = 52.3 ∘ below the negative x axis in the third quadrant. Part A What is the x component Fx of the resultant force? Part...
Two forces, F⃗ 1 and F⃗ 2, act at a point. F⃗ 1 has a magnitude of 9.60 N and is directed at an angle of 59.0 ∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 5.40 N and is directed at an angle of 53.6 ∘ below the negative x axis in the third quadrant. What is the x component of the resultant force? Express your answer in newtons. What is the...
Two forces, F⃗ 1 and F⃗ 2, act at a point. F⃗ 1 has a magnitude of 9.80 N and is directed at an angle of 60.0 ∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 6.00 N and is directed at an angle of 52.1 ∘ below the negative x axis in the third quadrant. What is the x component of the resultant force? What is the y component of the resultant...
Two forces, F⃗ 1 and F⃗ 2, act at a point. F⃗ 1 has a magnitude of 9.40 N and is directed at an angle of 58.0 ∘ above the negative x axis in the second quadrant. F⃗ 2 has a magnitude of 6.20 N and is directed at an angle of 53.1 ∘ below the negative x axis in the third quadrant. A)What is the x component of the resultant force? B)What is the y component of the resultant...