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
AnnZ [28]
2 years ago
11

Find the direction and magnitude of the net force exerted on the point charge q3 in the figure. Let q= +2.4 μC and d= 33cm.

Physics
2 answers:
kobusy [5.1K]2 years ago
8 0

With the use of electric force formula, the direction and magnitude of the net force exerted on the point charge q3 are 9.9 x 10^{11} N and 66 degrees

ELECTRIC FORCE (F)

F = \frac{KQq}{d^{2} }

Where K = 9 x 10^{9} Nm^{2}/C^{2}

The distance between q_{1} and q_{3} can be calculated by using Pythagoras theorem.

d = \sqrt{33^{2} + 33^{2}  }

d = 46.7 cm = 0.467 m

For force F_{1}, substitute all the parameters into the formula above

F_{1} = (9 x 10^{9} x 3 x 1)/0.467^{2}

F_{1} = 2.7 x 10^{10}/0.218

F_{1} = 1.24 x 10^{11} N

For force F_{4}, substitute all the parameters into the formula above

F_{4} = (9 x 10^{9} x 3 x 4)/0.33^{2}

F_{4} = 1.08 x 10^{11}/0.1089

F_{4} = 9.92 x 10^{11} N

For force F_{2}, substitute all the parameters into the formula above

F_{2} = (9 x 10^{9} x 3 x 2)/0.33^{2}

F_{2} = 5.4 x 10^{10}/0.1089

F_{2} = 4.96 x 10^{11} N

Summation of forces on Y component will be

F_{y} = F_{4} - F_{1} Sin 45

F_{y} = 9.92 x 10^{11} - 1.24 x 10^{11} Sin 45

F_{y} = 9.04 x 10^{11} N

Summation of forces on X component will be

F_{x} = F_{2} - F_{1} Cos 45

F_{x} = 4.96 x 10^{11} - 1.24 x 10^{11} Sin 45

F_{x} = 4.08 x 10^{11} N

Net Force = \sqrt{F_{x} ^{2} + F_{y} ^{2}  } }

Net force = \sqrt{(4.08*10^{11}) ^{2} + (9.04*10^{11}) ^{2}  }

Net force = 9.9 x 10^{11} N

The direction will be

Tan ∅ = F_{y}/F_{x}

Tan ∅ = 9.04 x 10^{11} / 4.08 x 10^{11}

Tan ∅ = 2.216

∅ = Tan^{-1}(2.216)

∅ = 65.7 degrees

Therefore, the direction and magnitude of the net force exerted on the point charge q3 are 9.9 x 10^{11} N and 66 degrees approximately.

Learn more about electric Force here: brainly.com/question/4053816

Colt1911 [192]2 years ago
5 0

The addition of vectors and Coulomb's law allows us to find the result for the force on the charge q₃ is:

  • The modulus is F = 5.71 N
  • The direction is: tes = -65º

Given parameters,

  • The value of the charges, q₁= +q, q₂= - 2 q, q₃= -3 q, q₄= -4q
  • The value of the charge q=+ 2.4 μC = 2.4 10⁻⁶ C
  • The side of the square is d = 33 cm = 0.33 m

To find.

  • The force on q3

<h3>Electric Force. </h3>

The electric force is given by Coulomb's law, which states that the force is proportional to the charges and inversely proportional to the square of the distance.

               F =k \frac{q_1q_2}{r_{12}^2}  

where F is the force, k Coulomb's constant, q the charges and r the distance between the charges.

<h3>Sum Vectors. </h3>

Force is a vector magnitude, so vector algebra must be used for vector addition, an easy and efficient way is to use an analytical method for addition:

  • We decompose each vector
  • We make the sum of the components
  • We construct the resulting vector.

In the attachment we have a diagram of the forces, the sum on each axis is:

x axis

          Fₓ= F₂- F₁ₓ

y axis

          F_y = -F_4 + F_{1y}  

Let's use trigonometry to find the component of force.

        cos 45 = \frac{F_1_x}{F_1}  

        cis 45 = \frac{F_1_y}{F_1}  

        F₁ₓ= F₁ cos 45

        F_1_y = F₁ sin 45

Let's look for the distance between the charges, for charges 2 and 3 charges 4 and 3 the distance of is equal to the side of the square

          r=r₂₃ = r₄₃ = d

The distance between charges 1 and 3 is the diagonal of the square that we can find with the Pythagorean theorem.

       R₁₃² = d² + d²

        R₁₃² = 2d²

We substitute in Coulomb's law.

        F₂₃ = k \frac{q_2q_3}{d^2}

        F₄₃ = k \frac{q_4q_3}{d^2}

         F₁₃ = k \frac{q_1q_3}{2d^2 }  

Let us substitute in the components of the force on each axis.

x axis

         Fₓ= F₂- F₁ₓ

         F_x = k \frac{q_2q_3}{d^2} - k \frac{q_1q_3}{2d^2} cos 45  \\F_x = k \frac{q_3}{d^2} ( q_2 - \frac{q_1 cos 45}{2})

y axis

          F_y = - F_4 + F_1_y  \\F_y = k \frac{q_4q_3}{d^2} - k \frac{q_1q_3}{2d^2} sin 45 \\F_y = k \frac{q_3}{d^2} ( -q_4 + \frac{q_1sin 45}{2})

We substitute in value of each charge.

x axis

           F_x = k \frac{3q}{d}  \ q( 2 - \frac{1 \ cos 45}{2} ) \\F_x = 3k (\frac{q}{d})^2  1.6464

y axis

         F_y = k \frac{3q}{d^2} ( -4 + \frac{1 \ sin45}{2} ) \\F_y = 3k  (\frac{q}{d})^2 ( -3.64645)

The resulting vector is

          F = F_x \hat i + f_y \hat j  

          F = 3k(\frac{q}{d} )^2 ( 1.6464 \hat i - 3.64645 \hat j )3k q² /d² ( 1.6464 i^ - 3.64645 j^ )

We calculate.

        F = 3 9 10⁹ ( 2.4 10-6/0.33)² ( 1.6464 i^ - 3.64645 j^ )

         F = 1.428( 1.6464 i⁻ 3.64645 j^

We build the resulting vector, for the module we use the Pythagorean theorem.

          F = \sqrt{F_x^2 + F_y^2}\\F = 1.428 \ \sqrt{1.6464^2+ 3.64645^2}

          F = 5.71N

Let's use trigonometry for the angle.

        tan \theta = \frac{F_y}{F_x}  

        \theta = tan^{-1}  (\frac{-3.64645}{1.6464} )  

        θ = -65º

This angle is half clockwise from the positive side of the x-axis.

in conclusion using vector addition and Coulomb's law we can find the result for the force on the charge q3 is:

  • The direction is: tes = -65º
  • The modulus is F = 5.71 N

Learn more about the electric force here: brainly.com/question/26153267

You might be interested in
Which of these activities increases the amount of carbon in the atmosphere? A. animals eating plants B. burning of fossil fuels
tester [92]

Answer:

B. Burning of fossil fuels

8 0
3 years ago
In levelling, the following staff readings were observed involving an inverted staff, A = 2.915 and B = -2.028. What is the rise
salantis [7]

Answer:

The rise from A to B is 0.887

Solution:

As per the question:

The following reading of an inverted staff is given as:

A = 2.915

B = -2.028

Here, for inverted staff, the greater reading shows greater elevation and lesser reading shows lower elevation.

Thus

The rise from A to B is given as:

A - B = 2.915 - 2.028 = 0.887

8 0
3 years ago
An athlete is running a 5-km race at an average speed of 8 km/h. She has to stop to tie her shoe. After tying her shoe, she cont
Ray Of Light [21]
The total time she took to complete the race increased
5 0
3 years ago
A sled with no initial velocity accelerates at a rate of 3.2 m/s2 down a hill. How long does it take the sled to go 15 m to the
grin007 [14]
S = ut + 1/2 at^2
a = 3.2 m/s^2
s = 15m
Find t
15 = 1/2(3.2)t^2
15 = 3.2t^2/2
30 = 3.2t^2
30/ 3.2 = 9.38
Square root of 9.38 = 3.06
It takes 3.06 seconds
3 0
3 years ago
Which phrase best describes wave motion
White raven [17]

Answer:

I would describe wave motion as “propagating oscillations” as a general phrase.

For something like water waves, I would say “water waves are oscillations of the surface of a body of water that propagate in a given direction.”

For electromagnetic waves I would say “An electromagnetic wave is an oscillating disturbance of the electric and magnetic fields that propagates through space.”

Explanation:

PLZ MARK BRAINLIEST

4 0
3 years ago
Read 2 more answers
Other questions:
  • 99% of all the matter that can be observed in the universe exists as
    6·1 answer
  • In 1781 with a reflecting telescope, Sir William Herschel discovered the planet WHAT
    14·2 answers
  • Increasing the amount of current that flows through a wire ______ the strength of an electromagnet
    12·2 answers
  • Ohm’s law describes the relationship between which quantities?
    14·2 answers
  • Examples of angular motion<br>​
    13·2 answers
  • (a) What is the angular speed ω about the polar axis of a point on Earth's surface at a latitude of 55° N? (Earth rotates about
    12·1 answer
  • The pressure, volume, and temperature of a mole of an ideal gas are related by the equation PV = 8.31T, where P is measured in k
    9·1 answer
  • What are the <br>difference between clinical and laboratory thermometer?<br><br><br>​
    7·1 answer
  • Which of the following is NOT an argument for showing that the Earth must be round: a. during an eclipse of the Moon, the shadow
    13·1 answer
  • A drill has a density of 11.342 g/cm3. Its mass is 1500 g. What is the volume of the drill? Round to TWO decimal places.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!