Two forces are pushing on an object, one at 12 lbs of Force and one at 5.66 lbs of Force. The angle between them is 35° (each is 72.5 from horizontal, such that the forces make a v with the object in the center).


17. What is the total Force on the object?


18. What is the smallest angle of the triangle?


19. What is the largest angle in the triangle?


20. What is the remaining angle of the triangle?

To find the total force on the object, we can use vector addition. We need to break down the forces into their horizontal and vertical components.

Given:
Force 1 (F1) = 12 lbs of force
Force 2 (F2) = 5.66 lbs of force
Angle between the forces (θ) = 35°

First, let's find the horizontal and vertical components of each force using trigonometry.

Horizontal component of Force 1 (F1x) = F1 * cos(72.5°)
Vertical component of Force 1 (F1y) = F1 * sin(72.5°)

Horizontal component of Force 2 (F2x) = F2 * cos(72.5°)
Vertical component of Force 2 (F2y) = F2 * sin(72.5°)

Now, calculate the sum of the horizontal components and vertical components separately:

Total horizontal force (Ftotalx) = F1x + F2x
Total vertical force (Ftotaly) = F1y + F2y

Finally, use the Pythagorean theorem to find the magnitude of the total force (Ftotal):

Ftotal = √(Ftotalx^2 + Ftotaly^2)

Now let's solve each question step by step:

17. What is the total force on the object?

- Calculate F1x: F1x = 12 lbs * cos(72.5°)
- Calculate F1y: F1y = 12 lbs * sin(72.5°)
- Calculate F2x: F2x = 5.66 lbs * cos(72.5°)
- Calculate F2y: F2y = 5.66 lbs * sin(72.5°)
- Calculate Ftotalx: Ftotalx = F1x + F2x
- Calculate Ftotaly: Ftotaly = F1y + F2y
- Calculate Ftotal: Ftotal = sqrt(Ftotalx^2 + Ftotaly^2)

18. What is the smallest angle of the triangle?

Since we have a triangle, the smallest angle is formed between the two smallest sides. In this case, the smallest angle is formed between the two forces with magnitudes 5.66 lbs and 5.66 lbs.

19. What is the largest angle in the triangle?

Similarly, the largest angle is formed between the two longest sides. In this case, the largest angle is formed between the two forces with magnitudes 12 lbs and 12 lbs.

20. What is the remaining angle of the triangle?

To find the remaining angle of the triangle, subtract the sum of the smallest and largest angles from 180°.