Someone help me please.
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Answer:
The two forces are;
1) Force 1 with magnitude of approximately 183.013 N, acting 30° to the left of the resultant force
2) Force 2 with magnitude of approximately 129.41 N acting at an inclination of 45° to the right of the resultant force
Explanation:
The given parameters are;
The (magnitude) of the resultant of two forces = 250 N
The angle of inclination of the two forces to the resultant = 30° and 45°
Let, F₁ and F₂ represent the two forces, we have;
F₁ is inclined 30° to the left of the resultant force and F₂ is inclined 45° to the right of the resultant force
The components of F₁ are = -F₁ × sin(30°)·i + F₁ × cos(30°)·j
The components of F₂ are = F₂ × sin(45°)·i + F₂ × cos(45°)·j
The sum of the forces = F₂ × sin(45°)·i + F₂ × cos(45°)·j + (-F₁ × sin(30°)·i + F₁ × cos(30°)·j) = 250·j
The resultant force, R = 250·j, which is in the y-direction, therefore, the component of the two forces in the x-direction cancel out
We have;
F₂ × sin(45°)·i = F₁ × sin(30°)·i
F₂ ·√2/2 = F₁/2
∴ F₁ = F₂ ·√2
∴ F₂ × cos(45°)·j + F₁ × cos(30°)·j = 250·j
Which gives;
F₂ × cos(45°)·j + F₂ ·√2 × cos(30°)·j = 250·j
F₂ × ((cos(45°) + √2 × cos(30°))·j = 250·j
F₂ × ((√2)/2 × (1 + √3))·j = 250·j
F₂ × ((√2)/2 × (1 + √3))·j = 250·j
F₂ = 250·j/(((√2)/2 × (1 + √3))·j) ≈ 129.41 N
F₂ ≈ 129.41 N
F₁ = √2 × F₂ = √2 × 129.41 N ≈ 183.013 N
F₁ ≈ 183.013 N
The two forces are;
A force with magnitude of approximately 183.013 N is inclined 30° to the left of the resultant force and a force with magnitude of approximately 129.41 N is inclined 45° to the right of the resultant force.
Answer: f = -12 cm
Explanation: <u>Combined</u> <u>lenses</u> is an array of simple lenses with a common axis. The combination is useful for correction of optical aberrations which cannot be corrected by simple lenses.
When two lenses are in contact and are thin, focal lengths are related as:
If there is a distance between the lenses, the focal length will be:
Since the lenses in the question above are thin and in contact, the focal length of one of them will be:
-12
The focal length of the other lens is -12 cm, with the negative sign meaning it's a converging lens.