Answer:
1. Largest force: C; smallest force: B; 2. ratio = 9:1
Explanation:
The formula for the force exerted between two charges is
![F=K\dfrac{ q_{1}q_{2}}{r^{2}}](https://tex.z-dn.net/?f=F%3DK%5Cdfrac%7B%20q_%7B1%7Dq_%7B2%7D%7D%7Br%5E%7B2%7D%7D)
where K is the Coulomb constant.
q₁ and q₂ are also identical and constant, so Kq₁q₂ is also constant.
For simplicity, let's combine Kq₁q₂ into a single constant, k.
Then, we can write
![F=\dfrac{k}{r^{2}}](https://tex.z-dn.net/?f=F%3D%5Cdfrac%7Bk%7D%7Br%5E%7B2%7D%7D)
1. Net force on each particle
Let's
- Call the distance between adjacent charges d.
- Remember that like charges repel and unlike charges attract.
Define forces exerted to the right as positive and those to the left as negative.
(a) Force on A
![\begin{array}{rcl}F_{A} & = & F_{B} + F_{C} + F_{D}\\& = & -\dfrac{k}{d^{2}} - \dfrac{k}{(2d)^{2}} +\dfrac{k}{(3d)^{2}}\\& = & \dfrac{k}{d^{2}}\left(-1 - \dfrac{1}{4} + \dfrac{1}{9} \right)\\\\& = & \dfrac{k}{d^{2}}\left(\dfrac{-36 - 9 + 4}{36} \right)\\\\& = & \mathbf{-\dfrac{41}{36} \dfrac{k}{d^{2}}}\\\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DF_%7BA%7D%20%26%20%3D%20%26%20F_%7BB%7D%20%2B%20F_%7BC%7D%20%2B%20F_%7BD%7D%5C%5C%26%20%3D%20%26%20-%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%20%20-%20%5Cdfrac%7Bk%7D%7B%282d%29%5E%7B2%7D%7D%20%20%2B%5Cdfrac%7Bk%7D%7B%283d%29%5E%7B2%7D%7D%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5Cleft%28-1%20-%20%5Cdfrac%7B1%7D%7B4%7D%20%2B%20%5Cdfrac%7B1%7D%7B9%7D%20%5Cright%29%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5Cleft%28%5Cdfrac%7B-36%20-%209%20%2B%204%7D%7B36%7D%20%5Cright%29%5C%5C%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B-%5Cdfrac%7B41%7D%7B36%7D%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Cend%7Barray%7D)
(b) Force on B
![\begin{array}{rcl}F_{B} & = & F_{A} + F_{C} + F_{D}\\& = & \dfrac{k}{d^{2}} - \dfrac{k}{d^{2}} + \dfrac{k}{(2d)^{2}}\\& = & \dfrac{k}{d^{2}}\left(\dfrac{1}{4} \right)\\\\& = &\mathbf{\dfrac{1}{4} \dfrac{k}{d^{2}}}\\\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DF_%7BB%7D%20%26%20%3D%20%26%20F_%7BA%7D%20%2B%20F_%7BC%7D%20%2B%20F_%7BD%7D%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%20%20-%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%20%20%2B%20%5Cdfrac%7Bk%7D%7B%282d%29%5E%7B2%7D%7D%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5Cleft%28%5Cdfrac%7B1%7D%7B4%7D%20%5Cright%29%5C%5C%5C%5C%26%20%3D%20%26%5Cmathbf%7B%5Cdfrac%7B1%7D%7B4%7D%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Cend%7Barray%7D)
(C) Force on C
![\begin{array}{rcl}F_{C} & = & F_{A} + F_{B} + F_{D}\\& = & \dfrac{k}{(2d)^{2}} + \dfrac{k}{d^{2}} + \dfrac{k}{d^{2}}\\& = & \dfrac{k}{d^{2}}\left( \dfrac{1}{4} +1 + 1 \right)\\\\& = & \dfrac{k}{d^{2}}\left(\dfrac{1 + 4 + 4}{4} \right)\\\\& = & \mathbf{\dfrac{9}{4} \dfrac{k}{d^{2}}}\\\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DF_%7BC%7D%20%26%20%3D%20%26%20F_%7BA%7D%20%2B%20F_%7BB%7D%20%2B%20F_%7BD%7D%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7B%282d%29%5E%7B2%7D%7D%20%2B%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%20%20%2B%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5Cleft%28%20%5Cdfrac%7B1%7D%7B4%7D%20%2B1%20%2B%201%20%5Cright%29%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5Cleft%28%5Cdfrac%7B1%20%2B%204%20%2B%204%7D%7B4%7D%20%5Cright%29%5C%5C%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B%5Cdfrac%7B9%7D%7B4%7D%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Cend%7Barray%7D)
(d) Force on D
![\begin{array}{rcl}F_{D} & = & F_{A} + F_{B} + F_{C}\\& = & -\dfrac{k}{(3d)^{2}} - \dfrac{k}{(2d)^{2}} - \dfrac{k}{d^{2}}\\& = & \dfrac{k}{d^{2}}\left( -\dfrac{1}{9} - \dfrac{1}{4} -1 \right)\\\\& = & \dfrac{k}{d^{2}}\left(\dfrac{-4 - 9 -36}{36} \right)\\\\& = & \mathbf{-\dfrac{49}{36} \dfrac{k}{d^{2}}}\\\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DF_%7BD%7D%20%26%20%3D%20%26%20F_%7BA%7D%20%2B%20F_%7BB%7D%20%2B%20F_%7BC%7D%5C%5C%26%20%3D%20%26%20-%5Cdfrac%7Bk%7D%7B%283d%29%5E%7B2%7D%7D%20%20-%20%5Cdfrac%7Bk%7D%7B%282d%29%5E%7B2%7D%7D%20%20-%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5Cleft%28%20-%5Cdfrac%7B1%7D%7B9%7D%20-%20%5Cdfrac%7B1%7D%7B4%7D%20-1%20%5Cright%29%5C%5C%5C%5C%26%20%3D%20%26%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%5Cleft%28%5Cdfrac%7B-4%20-%209%20-36%7D%7B36%7D%20%5Cright%29%5C%5C%5C%5C%26%20%3D%20%26%20%5Cmathbf%7B-%5Cdfrac%7B49%7D%7B36%7D%20%5Cdfrac%7Bk%7D%7Bd%5E%7B2%7D%7D%7D%5C%5C%5C%5C%5Cend%7Barray%7D)
(e) Relative net forces
In comparing net forces, we are interested in their magnitude, not their direction (sign), so we use their absolute values.
![F_{A} : F_{B} : F_{C} : F_{D} = \dfrac{41}{36} : \dfrac{1}{4} : \dfrac{9}{4} : \dfrac{49}{36}\ = 41 : 9 : 81 : 49\\\\\text{C experiences the largest net force.}\\\text{B experiences the smallest net force.}\\](https://tex.z-dn.net/?f=F_%7BA%7D%20%3A%20F_%7BB%7D%20%3A%20F_%7BC%7D%20%3A%20F_%7BD%7D%20%20%3D%20%20%5Cdfrac%7B41%7D%7B36%7D%20%3A%20%5Cdfrac%7B1%7D%7B4%7D%20%3A%20%5Cdfrac%7B9%7D%7B4%7D%20%3A%20%5Cdfrac%7B49%7D%7B36%7D%5C%20%3D%2041%20%3A%209%20%3A%2081%20%3A%2049%5C%5C%5C%5C%5Ctext%7BC%20experiences%20the%20largest%20net%20force.%7D%5C%5C%5Ctext%7BB%20experiences%20the%20smallest%20net%20force.%7D%5C%5C)
2. Ratio of largest force to smallest
![\dfrac{ F_{C}}{ F_{B}} = \dfrac{81}{9} = \mathbf{9:1}\\\\\text{The ratio of the largest force to the smallest is $\large \boxed{\mathbf{9:1}}$}](https://tex.z-dn.net/?f=%5Cdfrac%7B%20F_%7BC%7D%7D%7B%20F_%7BB%7D%7D%20%3D%20%5Cdfrac%7B81%7D%7B9%7D%20%3D%20%5Cmathbf%7B9%3A1%7D%5C%5C%5C%5C%5Ctext%7BThe%20ratio%20of%20the%20largest%20force%20to%20the%20smallest%20is%20%24%5Clarge%20%5Cboxed%7B%5Cmathbf%7B9%3A1%7D%7D%24%7D)
The body shivers to produce energy and it uses the energy to keep it warm. The body would stop shivering when it has produced enough energy to keep it warm and the atmosphere around it has got warmer
82ohms
Explanation:
The equivalent resistance in the circuit is 82ohms
Given parameters:
R1 = 50ohms
R2 = 32ohms
Unknown:
Equivalent resistance = ?
Solution:
A resistor is an body in circuit that opposes the flow of electric current.
Resistors are usually connected in circuit and in series arrangement.
When resistors are connected in series, they have the same current passing through them.
Equivalent resistance is the sum of each of the connected resistors
Equivalent resistance = R1 + R2 = 50 + 32 = 82ohms
learn more:
Circuits brainly.com/question/2364338
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The student's shoulder supports the weight of the bag.
<h3>What is the free body diagram?</h3>
Free-body diagrams are utilized to display the relative direction and strength of all forces that are being applied to an item in a certain scenario. A unique illustration of the geometric diagrams that were covered in a previous lesson is the free-body diagram. We will make use of these graphics throughout the entire study of physics.
A university student is carrying a backpack. One strap is hanging the rucksack immobile from one shoulder.
The weight of the backpack is balanced by the shoulder of the student.
The free-body diagram is attached below.
More about the free body diagram link is given below.
brainly.com/question/24087893
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