Find the angle between the forces given the magnitude of their resultant. (Hint: Write force 1 as a vector in the direction of the positive x-axis and force 2 as a vector at an angle θ with the positive x-axis. Round your answer to one decimal place.)
Force 1: 2700 pounds
Force 2:1100 pounds
Resultant Force:3600 pounds
i got 138.7° as final answer. is it correct?
Yes, that is the angle from the cosine law calculation,
but you wanted the angle between the two forces.
Look at your diagram and see that that angle must be 180 - 138.7
To find the angle between the forces given the magnitude of their resultant, we can use vector addition.
Step 1: Write force 1 as a vector in the direction of the positive x-axis. Since force 1 is given in magnitude only, we can write it as F1 = 2700 pounds * (1, 0). This means that force 1 has a magnitude of 2700 pounds and is purely in the x-direction.
Step 2: Write force 2 as a vector at an angle θ with the positive x-axis. Since force 2 is given in magnitude only, we can write it as F2 = 1100 pounds * (cosθ, sinθ). This means that force 2 has a magnitude of 1100 pounds and is at an angle θ with the positive x-axis.
Step 3: Find the resultant force by adding force 1 and force 2. The resultant force is given as 3600 pounds, so we can write it as R = 3600 pounds * (cosθ + 1, sinθ).
Step 4: Equate the x and y components of the resultant force and solve for θ. The x-component equation is: F1_x + F2_x = R_x, and the y-component equation is: F2_y = R_y.
F1_x = 2700 pounds * 1 = 2700 pounds
F2_x = 1100 pounds * cosθ
R_x = 3600 pounds * (cosθ + 1)
F2_y = 1100 pounds * sinθ
R_y = 3600 pounds * sinθ
Equating the x and y components:
2700 pounds + 1100 pounds * cosθ = 3600 pounds * (cosθ + 1)
1100 pounds * sinθ = 3600 pounds * sinθ
Simplifying the equations:
2700 pounds = 3600 pounds * cosθ + 1100 pounds * cosθ
3600 pounds * (cosθ + 1) = 3600 pounds
3600 pounds * sinθ = 0
Solving the equations:
cosθ = 2700 pounds / (3600 pounds + 1100 pounds) ≈ 0.643
sinθ = 0
Now, we can find the angle θ using the inverse cosine function:
θ ≈ arccos(0.643) ≈ 50.9 degrees
Therefore, the angle between the forces is approximately 50.9 degrees.
make your sketch, you should end up with a triangle with sides given
(the 3600 is the diagonal of the corresponding parallelogram)
using the cosine law, find the angle opposite the 3600, it should be a large
obtuse angle. Once you have that, use your parallelogram properties to find
the angle between the two forces.