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
Alex787 [66]
3 years ago
8

Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge

q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?

Mathematics
1 answer:
salantis [7]3 years ago
5 0

Answer:

q = 0.105uC

Step-by-step explanation:

We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.

Considering the horizontal and vertical components.

First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:

E=kq/r²

Where r = 20cm

= 20/100

= 0.2m

K = 9.0×10^9

9.0×10^9 × q /0.2²

9.0×10^9/0.04

2.25×10^11 q

These are vector fields of course

Sum the horizontal components

Ecos0 + Ecos300 = E+0.5E

= 1.5E

Sum the vertical components

Esin0 + Esin300 = -E√3/2

Resultant = √3E at -30° or 330°

So the force on q at the lower right corner is q√3×E

The balls have two forces, horizontal = √3×E×q

and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg

mg×tanθ = q√3E.

..1

Then θ will be...

Since the hypotenuse = 80cm

80cm/100

= 0.8m

The distance from the centroid to the lower right vertex is 0.1/cos30 =

0.1/0.866

= 0.1155m

Hence,

0.8×sinθ = 0.1155

Sinθ = 0.1155/0.8

Sin θ = 0.144375

θ = arch sin 0.144375

θ = 8.3°

From equation 1

mg×tanθ = q√3E

g = 9.8m/s^2

m = 3.0g = 0.003kg

0.003×9.8×tan(8.3)

0.00428 = q√3E

0.00428 = q×1.7320×E

Where E=kq/r²

Where r = 0.2m

0.0428 = kq^2/r² × 1.7320

K = 9.0×10^9

0.0428/1.7320 = 9.0×10^9 × q² / 0.2²

0.02471×0.04 = 9.0×10^9 × q²

0.0009884 = 9.0×10^9 × q²

0.0009884/9.0×10^9 = q²

q² = 109822.223

q = √109822.223

q = 0.105uC

You might be interested in
Which quadrilateral has four right angles and four sides of equal length?
olasank [31]

Answer:

Square.

Step-by-step explanation:

A square is a rectangle, but a rectangle is not a square.

8 0
2 years ago
Read 2 more answers
In the expression, x^2 + 6x + 9, which is the coeffcient?
ikadub [295]

The coefficient is the number next to the letter.

Although the x squared term has a coefficient of 1, it is not listed in the answer choices. However, the coefficient of the middle term 6x is listed.

Answer: 6

3 0
2 years ago
A blueprint for a house shows the height of the house to be 3 3/8 inches. The actual house is 21 1/3 feet tall. What is the unit
Amanda [17]
6.32ft per inch (rounded to the hundredth place).

You can get this number by dividing the total number of feet by the total number of inches 
6 0
3 years ago
*NO LINKS HELP ASAP*
vitfil [10]

Answer:

28 i think.

Step-by-step explanation:

A week has 7 days so 7×2 is 14 and thats the same for the other week. Add those together and you'll get 28.

8 0
2 years ago
Which choice is the explicit formula for the following geometric sequence? 0.2, -0.06, 0.018, -0.0054, 0.00162
Crazy boy [7]

Answer:

aₙ = 0.2(-0.3)⁽ⁿ⁻¹⁾

Step-by-step explanation:

The geometric sequence with the first term a, a common ratio r has the nth term given as

Tₙ = arⁿ⁻¹

where Tₙ is the nth term

From the given sequence

a = 0.2

r = -0.06/0.2

= -0.3

Hence the nth term

= 0.2 * -0.3ⁿ⁻¹

The right option is E

8 0
3 years ago
Other questions:
  • If Kim has 10 apples and jack has 10 strawberries how many fruits do they have
    7·1 answer
  • Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for and exam. The data sets
    5·1 answer
  • A box contains 5 plain pencils and 5 pens. A second box contains 5 color pencils and 7 crayons. One item from each box is chosen
    5·2 answers
  • Chang knows one side of a triangle is 13 cm Which set of two sides is possible for the lengths of the other two sides of this
    8·1 answer
  • Average Earnings of Workers The average earnings of year-round full-time workers 25–34 years old with a bachelor’s degree or hig
    6·1 answer
  • Jill works 2.5 hours and earns $37.5. How many hours does she have to work to receive $240?​
    10·1 answer
  • B. Juan’s cell phone company charges $35 a month for phone service plus $0.50 for each text message. How many text messages does
    8·2 answers
  • Ike Phillips worked 6.7 hours at time-and-a-half pay and 3.4
    10·1 answer
  • What property of operations is used to show that 12x + 6y is equivalent to(2x + y)?
    11·1 answer
  • The table represents an exponential function
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!