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
Both the terms immigration ("moving into a population") and emigration ("moving out of a population") come from the Latin word m
Alexxx [7]

Answer:

im means into

e means out of

Explanation:

Using the definitions of immigration and emigration as points of reference, the following explanation applies.

Both terms are derived from migration which means moving from one place to another.

By further explanation:

The "im" in the definition of immigration means "into" while the "e" in the definition of emigration means "out of"

7 0
2 years ago
A golf ball is hit with an initial velocity of 20m/s at an angle of 30° to the horizontal. calculate;
svp [43]

Answer:

tcucugxojfjgfojcigxuogoudyifodtufukdutfuocyjxuogu

3 0
2 years ago
How much meters is a mile
elena-s [515]

Roughly 1609 meters in one mile

6 0
3 years ago
One of your summer lunar space camp activities is to launch a 1090 kg rocket from the surface of the Moon. You are a serious spa
Ludmilka [50]

Answer:

ΔP.E = 6.48 x 10⁸ J

Explanation:

First we need to calculate the acceleration due to gravity on the surface of moon:

g = GM/R²

where,

g = acceleration due to gravity on the surface of moon = ?

G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²

M = Mass of moon = 7.36 x 10²² kg

R = Radius of Moon = 1740 km = 1.74 x 10⁶ m

Therefore,

g = (6.67 x 10⁻¹¹ N.m²/kg²)(7.36 x 10²² kg)/(1.74 x 10⁶ m)²

g = 2.82 m/s²

now the change in gravitational potential energy of rocket is calculated by:

ΔP.E = mgΔh

where,

ΔP.E = Change in Gravitational Potential Energy = ?

m = mass of rocket = 1090 kg

Δh = altitude = 211 km = 2.11 x 10⁵ m

Therefore,

ΔP.E = (1090 kg)(2.82 m/s²)(2.11 x 10⁵ m)

<u>ΔP.E = 6.48 x 10⁸ J</u>

7 0
3 years ago
An interstellar space probe is launched from Earth. After a brief period of acceleration it moves with a constant velocity, 70.0
sleet_krkn [62]

Answer:

22.26 years

, 15.585 light years  , 11.13 light years

Explanation:

a)

t' = t/(\sqrt{1-(v/(c*v)/c)}

= 15.9/\sqrt{(1-0.7*0.7)}

= 22.26 years

b)

0.7*c*22.26 years

=15.585 light years  

c)

0.7*c*15.9

=11.13 light years

3 0
3 years ago
Other questions:
  • How much force is needed to keep a 25 N rock moving with constant speed across the level, frictionless ice?
    12·1 answer
  • A real object with height of 3.20 cm is placed to the left of a converging lens whose focal length is 90cm. The image is on the
    13·1 answer
  • A student pushes on a 20.0 kg box with a force of 50 N at an angle of 30° below the horizontal. The box accelerates at a rate of
    8·2 answers
  • In which of the following situations would be the government had been most likely to become involved in union protests?
    6·1 answer
  • company uses a ramp to slide boxes of parts to a shippingarea. Each box weighs about 10 kilograms. When sliding downthe ramp, th
    14·1 answer
  • If the Sun were to mysteriously turn into a black hole (don't worry . . . it won't!) and retain its current mass, what would hap
    15·1 answer
  • Two particles with masses m and 3m are moving toward each other along the x axis with the same initial speeds Vi. Particle m is
    11·1 answer
  • A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s average speed in miles per hour?
    5·1 answer
  • Im not going to lie, this is a physics Q right here<br> plz guys im being serious i need help
    11·1 answer
  • Is the system in the image moving? Explain. If it is moving, find its acceleration.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!