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?
Please help me out, thank you <3
make a sketch
complete the parallogram with the resultant as the diagonal
consider the triangle with sides 12 and 5.66 with the contained angle of 145°, with the longest side representing the resultant
let that longest side be x
by cosine law
x^2 = 12^2 + 5.66^2 - 2(12)(5.66)cos 145°
..
..
x = 16.95... (total force on object)
smallest angle is opposite the 5.66 side, call it Ø
sinØ/5.66 = sin145/x
sinØ = .1915...
Ø = 11.042°
largerst angle is 145°
third angle is 180- sum of the other two
= 23.96°
To solve these questions, we'll use vector addition and basic trigonometry. Here's how to find the answers step by step:
17. To find the total force on the object, we can use vector addition. Since forces are vectors, we can break them down into their horizontal and vertical components. The horizontal component of the first force (12 lbs) is 12 * cos(72.5°) and the vertical component is 12 * sin(72.5°). Similarly, the horizontal and vertical components of the second force (5.66 lbs) can be found using cos(72.5°) and sin(72.5°), respectively.
Now, add up the horizontal and vertical components separately to get the total horizontal and vertical forces. Finally, use the Pythagorean theorem to find the magnitude of the total force.
18. The smallest angle of the triangle can be found by noticing that the given angles are 72.5° from the horizontal, meaning they are complementary angles (add up to 90°). So, the smallest angle would be 90° - 35° = 55°.
19. The largest angle in the triangle can be found using the fact that the three angles of a triangle add up to 180°. Since we already know two angles (35° and 72.5°), subtracting their sum from 180° will give us the largest angle.
20. The remaining angle of the triangle can be found by subtracting the sum of the smallest and largest angles from 180°.
Now, let's calculate the answers.
17. The total force can be found by adding up the horizontal and vertical components of the two forces:
Horizontal component: (12 * cos(72.5°)) + (5.66 * cos(72.5°))
Vertical component: (12 * sin(72.5°)) + (5.66 * sin(72.5°))
Using these values, we can calculate the magnitude of the total force using the Pythagorean theorem:
Total force = sqrt((Horizontal component)^2 + (Vertical component)^2)
18. The smallest angle of the triangle is 55°.
19. To find the largest angle, subtract the sum of the given angles (35° + 72.5°) from 180°.
Largest angle = 180° - (35° + 72.5°)
20. Lastly, the remaining angle can be found by subtracting the sum of the smallest and largest angles from 180°.
Remaining angle = 180° - (Smallest angle + Largest angle)
Now, plug in the given values into the formulas and calculate the answers.