1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivahew [28]
3 years ago
7

I NEED HELP PLEASE, THANKS! :)

Physics
1 answer:
mrs_skeptik [129]3 years ago
7 0

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}}

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}}

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}

(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}

(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}

(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}

(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.}\\

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 $\large \boxed{\mathbf{9:1}}$}

You might be interested in
Correct the following statement:
ankoles [38]

Answer:

It's the 3rd option

Explanation:

Wind is caused by the differences in air pressure on Earth's surface.

4 0
3 years ago
A transformer has two sets of coils, the primary with N1 = 160 turns and the secondary with N2 = 1400 turns. The input rms volta
vovikov84 [41]

To solve the problem it is necessary to apply the concepts related to the voltage in a coil, through the percentage relationship that exists between the voltage and the number of turns it has.

So things our data are given by

N_1 = 160

N_2 = 1400

\Delta V_{1rms} = 62V

PART A) Since it is a system in equilibrium the relationship between the two transformers would be given by

\frac{N_1}{N_2} = \frac{\Delta V_{1rms}}{\Delta V_{2rms}}

So the voltage for transformer 2 would be given by,

\Delta V_{2rms} = \frac{N_2}{N_1} \Delta V_{1rms}

PART B) To express the number value we proceed to replace with the previously given values, that is to say

\Delta V_{2rms} = \frac{N_1}{N_2} \Delta V_{1rms}

\Delta V_{2rms} = \frac{1400}{160} 62V

\Delta V_{2rms} = 1446.66V

7 0
3 years ago
A particle is moving with (SHM) of period 8.0s and amplitude5.0m
nadezda [96]

Answer:

velocity(x)=15\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)

Max speed = \frac{15\, \pi}{4} \,\, \frac{m}{s}

Max acceleration = \frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}

Explanation:

Given the description of period and amplitude, the SHM could be described by:

f(x)=5\,sin(\frac{\pi}{4}x)

and its angular velocity can be calculated doing the derivative:

f(x)=5\, \,sin(\frac{\pi}{4}x)\\f'(x)=5\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)

And therefore, the tangential velocity is calculated by multiplying this expression times the radius of the movement (3 m):

velocity(x)=15\,\frac{\pi}{4}\,cos(\frac{\pi}{4}x)  and is given in m/s.

Then the maximum speed is obtained when the cosine function becomes "1", and that gives:

Max speed = \frac{15\, \pi}{4} \,\, \frac{m}{s}

The acceleration is found from the derivative of the velocity expression, and therefore given by:

acceleraton(x)=-15\,\frac{\pi^2}{16}\,sin(\frac{\pi}{4}x)

and the maximum of the function will be obtained when the sine expression becomes "-1", which will render:

Max acceleration = \frac{15\,\pi^2}{16} \,\,\frac{m}{s^2}

6 0
3 years ago
The time constant for RC circuit with the values of R1 and C1 is 5ms. What will be the time constant for a new RC circuit with t
lions [1.4K]

Answer:

d. 25 ms

Explanation:

  • In a RC circuit we call time constant to the product of the resistance times the capacitance, which represents the time when the charge reaches to the 63% of the final value, as follows:

       \tau_{1} = R_{1} *C_{1}  = 5 ms (1)

  • If we have a new circuit with new values for R and C, the time constant will be defined in the same way, as follows:

       \tau_{2} =10* R_{1} *0.5*C_{1}  = 5*(R_{1}* C_{1}) = 5* \tau_{1} = 5* 5 ms = 25 ms (2)

6 0
2 years ago
Which term is defined as the change in the direction of light when it goes from one medium into a different medium?
Vaselesa [24]
Refraction is the term  

8 0
2 years ago
Other questions:
  • Find the wavelength λ of the 80.0-khz wave emitted by the bat. express your answer in millimeters.
    14·1 answer
  • How much energy must be added to a bowl of 125 popcorn kernels in order for them to reach a popping temperature of 175°C? Assume
    14·1 answer
  • Can someone please explain the quantum theory in simple terms
    13·1 answer
  • Which of the following is an example of technology influencing science?
    11·1 answer
  • A physical pendulum in the form of a planar object moves in simple harmonic motion with a frequency of 0.460 Hz. The pendulum ha
    8·1 answer
  • A force of 3600 N is exerted on a piston that has an area of 0.030 m2. What force is exerted on a second piston that has an area
    11·2 answers
  • How far (in meters) will you travel in 3 minutes running at a rate of 6 m/s?
    11·1 answer
  • What is the net force acting on a .15 kg hockey puck accelerating at a rate of 12 m/s2
    12·2 answers
  • maize is a monocotyledonous seed and pea is a dicotyledonous seed why? give short and the suitable answer I will mark you as a b
    5·1 answer
  • James went to the doctor for a check-up and found his weight to be 1,000 N. How much mass does James have?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!