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?
17. Well, if the forces are pushing the object, I guess we can call it a "pushy situation." To find the total force, we need to do a little bit of math. We can use the cosine rule to find the total force, which is the square root of the sum of the squares of the individual forces plus twice their product multiplied by the cosine of the angle between them. So, grab your calculator and let's work it out!
total force = sqrt((12^2 + 5.66^2) + 2(12)(5.66)cos(35°))
18. While we're at it, let's talk about the smallest angle in the triangle. Well, you know what they say, "size doesn't always matter!" The smallest angle in the triangle can be determined by looking at the smallest side. In this case, we don't have the lengths of the sides, so without any specific measurements, I can't tell you the exact smallest angle. But hey, let's not sweat the small stuff!
19. Now, let's move on to the largest angle in the triangle. The largest angle is usually opposite the longest side. Since we don't know the lengths of the sides, I can't determine the exact value of the largest angle. It's like trying to find the biggest laugh in a room full of clowns, just too unpredictable!
20. Finally, the remaining angle in the triangle. The sum of all the angles in a triangle is always 180 degrees, so you can simply subtract the values of the known angles from 180 to find the remaining angle. But hey, don't hold me responsible for its whereabouts, it's like trying to find that missing sock in the laundry, it just disappears!
To find the total force on the object, we can use the concept of vector addition.
step 1: Resolve the forces into their horizontal and vertical components.
- The 12 lbs force has a horizontal component of 12 * cos(72.5°) and a vertical component of 12 * sin(72.5°).
- The 5.66 lbs force has a horizontal component of 5.66 * cos(72.5°) and a vertical component of 5.66 * sin(72.5°).
step 2: Add up the horizontal and vertical components separately.
Horizontal component:
- 12 * cos(72.5°) + 5.66 * cos(72.5°) = 17.0798 lbs
Vertical component:
- 12 * sin(72.5°) + 5.66 * sin(72.5°) = 13.1577 lbs
step 3: Use the Pythagorean theorem to find the magnitude of the total force.
- Total Force = sqrt((17.0798)^2 + (13.1577)^2)
= 21.6 lbs (approx.)
Therefore, the total force on the object is approximately 21.6 lbs.
To find the smallest angle of the triangle, we can use the law of sines.
step 1: Set up the equation for the law of sines:
- sin(A) / a = sin(B) / b = sin(C) / c
step 2: Plug in the known values:
- sin(35°) / 12 = sin(72.5°) / 21.6
step 3: Solve for the smallest angle (A):
- sin(A) = (sin(35°) * 12) / 21.6
- A ≈ arcsin((sin(35°) * 12) / 21.6)
Therefore, the smallest angle of the triangle is approximately arcsin((sin(35°) * 12) / 21.6).
To find the largest angle in the triangle, we can use the fact that the sum of the angles in a triangle is always 180°.
step 1: Calculate the sum of the known angles:
- 35° + 72.5° + A (smallest angle) = 180°
step 2: Solve for the largest angle:
- largest angle = 180° - 35° - 72.5° - A
Therefore, the largest angle in the triangle is approximately 72.5°.
To find the remaining angle of the triangle, we can subtract the sum of the known angles from 180°.
step 1: Calculate the sum of the known angles:
- 35° + 72.5° + largest angle (72.5°) = 180°
step 2: Solve for the remaining angle:
- remaining angle = 180° - 35° - 72.5° - largest angle
Therefore, the remaining angle of the triangle is approximately 44.5°.
To find the total force on the object, you can use the concept of vector addition. Since the forces are acting at different angles, you can break down each force into its horizontal and vertical components using trigonometry. Then you can add the horizontal and vertical components separately to find the total force.
To get the horizontal and vertical components of a force, you can use the formulas:
Horizontal component = Force * cos(angle)
Vertical component = Force * sin(angle)
Using these formulas, you can find the horizontal and vertical components of both forces.
For the force of 12 lbs at an angle of 72.5°,
Horizontal component = 12 * cos(72.5°)
Vertical component = 12 * sin(72.5°)
Similarly, for the force of 5.66 lbs at an angle of 72.5°,
Horizontal component = 5.66 * cos(72.5°)
Vertical component = 5.66 * sin(72.5°)
Add up the horizontal components and vertical components separately to get the total horizontal and vertical forces.
Total horizontal force = Horizontal component of 12 lbs force + Horizontal component of 5.66 lbs force
Total vertical force = Vertical component of 12 lbs force + Vertical component of 5.66 lbs force
Now, you can find the total force using the Pythagorean theorem. The total force is the hypotenuse of a right triangle formed by the total horizontal and vertical forces.
Total force = √(Total horizontal force^2 + Total vertical force^2)
This will give you the answer to question 17.
To find the smallest angle of the triangle, you need to identify which angle is the smallest. Since you know the angles between the forces, you can compare them and determine the smallest angle. In this case, the smallest angle is 35°, as given in the problem statement. This answers question 18.
For question 19, you can identify the largest angle in the triangle by again comparing the angles given in the problem statement. In this case, the largest angle is also 35°.
For question 20, you can find the remaining angle of the triangle by subtracting the sum of the other two angles from 180° (since the sum of angles in a triangle is 180°). In this case, the remaining angle is 180° - (35° + 35°).
I assume you constructed a parallelogram so that the diagonal is the resultant of the two forces
The obtuse angle would then be 180-35 = 145°
Use the cosine law to find the magnitude |r| of that resultant
|r|^2 = 5.66^2 + 12^2 - 2(12)(5.66)cos 145°
= 287.309
|r| = 16.95
"What is the smallest angle of the triangle", I will assume we are looking at the triangle just dealt with above ...
The smallest angle will be opposite the smallest side, let it be Ø
sinØ/5.66 = sin 145/16.95
sinØ = .19153..
Ø = 11.04°
easy to find the third angle