Two spheres (m = 3 g) on long threads repel each other after being equally charged. what is the charge q?
Answers
The charge q is ±7.46 × 10⁻⁷C.
Electrostatic Force, Coulomb's Law:The electrostatic force is a type of force that only charged objects experience. The term electrostatic is made up of two parts: 'electro,' which refers to electricity, and static,' which means stationary. As a result, an electrostatic force exists between any two fixed charges.The electrostatic force is attractive when the two charges have opposite charges and repulsive when they have the same charge.Coulomb's Law is used to calculate the strength of the electrostatic force between two points and stationary objects. The electrostatic force between two points and stationary charges is directly proportionate to the product of both charges and inversely proportional to the square of the distance between the charges, according to Coulomb's Law.
Give:
The mass of each charge, m = 3.0 g = 3 × 10⁻³ kgThe length of each thread, l = 1.0 mThe two charges are equal, q₁ = q₂ = qTake a look at the charge on the left. The following forces are at work in response to this charge:
The tension of the thread, TThe gravitational force, W = mg where m is the mass and g = 9.8 m/s² is the acceleration due to gravity.The electrostatic force, F due to the charge of the right.(Refer to the diagram below)
Because the charge is in equilibrium, the charge's vertical and horizontal forces must be zero.
We have the following in the vertical direction:
[tex]\begin{aligned}T \cos 20^{\circ} &=W \\\Rightarrow T &=\frac{m g}{\cos 20^{\circ}} \\&=\frac{3.0 \times 10^{-3} \mathrm{~kg} \times 9.8 \mathrm{~m} / \mathrm{s}^2}{\cos 20^{\circ}} \\&=3.13 \times 10^{-2} \mathrm{~N}\end{aligned}[/tex]
Coulomb's Law states that the electrostatic force between two point charges, q₁, and q₂, separated by r is given by the equation:
[tex]\begin{aligned}F &=\frac{q_1 q_2}{4 \pi \epsilon_0 r^2} \\&=\frac{K q_1 q_2}{r^2}\end{aligned}[/tex]
Here,
The distance between the charges is r.The permittivity of free space is [tex]\epsilon_0[/tex].Coulomb's Constant is K = 9 × 10⁹ N.m²/C².Using trigonometric personalities, the distance between any two charges is:
[tex]\begin{aligned}r &=2 l \sin 20^{\circ} \\&=2 \times 1.0 \mathrm{~m} \times 0.342 \\&=0.684 \mathrm{~m}\end{aligned}[/tex]
We have the following in the vertical direction:
[tex]\begin{aligned}F_e &=T \sin 20^{\circ} \\\Rightarrow \frac{K q_1 q_2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow \frac{K q^2}{r^2} &=T \sin 20^{\circ} \\\Rightarrow q^2 &=\frac{r^2 T \sin 20^{\circ}}{K} \\&=\frac{(0.684 \mathrm{~m})^2 \times 3.13 \times 10^{-2} \mathrm{~N} \times \sin 20^{\circ}}{9 \times 10^9 \mathrm{~N} \cdot \mathrm{m}^2 / \mathrm{C}^2} \\&=55.65 \times 10^{-14} \mathrm{C}^2 \\\Rightarrow q &=\pm 7.46 \times 10^{-7} \mathrm{C}\end{aligned}[/tex]
Therefore, the charge q is ±7.46 × 10⁻⁷C.
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The correct question is given below:
Two 3.0g point charges on 1.0m - long threads repel each other after being equally charged, as shown in the figure. What is the charge q?
Related Questions
Find a number such that one-half of the number is three more than one-fourth of the number.
Answers
The number such that one-half of the number is three more than one-fourth of the number is 12.
It is given in the question that a number is such that one-half of the number is three more than one-fourth of the number.
We have to find the number.
Let the number be x.
According to the question, we can write,
x/2 = x/4 + 3
Solving the linear equation, we get,
x/2 - x/4 = 3
(2x - x)/4 = 3
x/4 = 3
x = 4*3
x = 12
Hence, the number such that one-half of the number is three more than one-fourth of the number is 12.
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What is the area of the base of this right circular cone in terms of л?
r = 4 m
h = 6 m
___ л m^2
Answers
Answer:
16π m²
Step-by-step explanation:
area of circle = πr²
area = π × (4 m)²
area = 16π m²
x = 10 g y = 10 kg y + x =
a)10.1 kg
b)100.1 g
c)10.1 kg
d)10.01 g
Answers
The correct option is d)10.01 kg; y + x = 10.01 kg.
What is referred as the unit conversion?When converting units, you are generally given one measure but instead asked to convert it to another.
For example, you may be given a volume in "gallons" but also asked to convert it to "fluid ounces." They will have given you (or you will be able to quickly find) the conversion units which are appropriate for the task. In order to complete the conversion, you will be required to multiply or divide by one of the following unit equivalences.For the given values in the question;
x = 10 g and y = 10 kg
As, both the values are of mass.
For adding both values, the unit must be same.
So, convert the value of x in kg from g.
1 kg = 1000 g
Thus, 1 g = 1/1000 kg
10 g = 10/1000 kg
10 g = 0.01 kg
Now add both;
x + y = 0.01 + 10
x + y = 10.01 kg
Thus, the value of x + y is found as 10.01 kg.
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The correct question is-
a)10.1 kg
b)100.1 g
c)10.1 kg
d)10.01 kg
A random sample of 100 diabetics undergoes genotyping and it was found that 23 of them have the gene. compute the z test statistic needed for this hypothesis test.
Answers
The z test statistic needed for this hypothesis test is 0.75 .
Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.
NOW,
sample proportion = p = x / n = 0.23
Test statistics
z = ( p - p0 ) / [tex]\sqrt{ p0*(1-p0)}[/tex] / n
= ( 0.23 - 0.20) / [tex]\sqrt{ (0.20*0.80) / 100}[/tex]
= 0.75
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(-2,-4) and (3,-9)?
Answers
What we answering with these 2 points ?
Where's the question?
Complete the table of values for f(x) = -3|x+1|-4 using the table of values for g(x) = |x|
Answers
f(x)>=-7
Functions:
Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.
If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x
Given :
f(x) = -3|x+1|-4
using the table of values for g(x) = |x|
Solution :
f(x) = -3|x+1|-4
f(x) = -3|g(x)+1|-4
f(x) = -3||x|+1|-4
which means |x| is always positive |x|>0
f(x) = -3||x|+1|-4
f(x) = -3x-3-4
f(x) = -3x-7
f(x)>=-7
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Is height discrete or continuous data? Give a reason for your answer.
please help
Answers
Answer: Continuous data
Step-by-step explanation:
Please help due soon.
Answers
Answer:
-3x>24
Step-by-step explanation:
-3x-10>14
now we add 10 to both sides, 10+14 is 24
so, the missing step is -3x>24
Five sections of fencing around a garden are 7 yards long, 8 3/4 yards long, 12 1/2 yards long, 15 1/3 yards long, and 7 3/4 yards long. What is the total length of the fencing?
Answers
Answer: 51.33
Step-by-step explanation:
7+8.75+12.5+15.33+7.75 = 51.33
The equation of line j is y+5=8(x+4). Perpendicular to line j is line k, which passes through the point (4, – 1). What is the equation of line k?
Answers
8x+y=31
perpendicular means the slopes are opposite reciprocals of each other. perpendicular to: y +5= 8(x +4) → m = 8 m⊥ = -8
Input the slope (m⊥ = -8) and the point (x₁, y₁) = (4, -1) into the Point-Slope formula: y - y₁ = m(x - x₁)
y - (-1) = -8(x -4)
y + 1 = -8 x + 32 simplified
8x+y =31
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The cheerleaders want to raise money to go to camp, so they decide to sell spirit ribbons. They will earn 50¢ for each ribbon that they sell. However, they have to purchase the ribbons first for a total cost of $75. Use the table below to figure their total profit from selling ribbons.
What is the total profit after selling 0 ribbons?
Answers
Using a linear function, we have that:
The rule is P(x) = 0.5x - 75.The total profit after selling 0 ribbons is of -$0.75.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For this problem, when x increases by 10, the profit increases by 5, hence the slope is:
m = 5/10 = 0.5.
Then:
P(x) = 0.5x + b.
When x = 10, P(x) = -70, hence:
-70 = 0.5(10) + b
b = -75.
Hence:
The rule is P(x) = 0.5x - 75.The total profit after selling 0 ribbons is of -$0.75.More can be learned about linear functions at https://brainly.com/question/24808124
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In the word grapefruit the ratio of vowels to consonants is 2:3 .find the ratios of vowels to consonats in the word pineapple and strawberry. give each ratio in its simplest form.
Answers
Answer:
48 because of the vowels it became 48 .
Step-by-step explanation:
I Quesliod. Make sure you start new workings. In the word grapefruit, the ratio of vowels to consonants is . Find the ratios of vowels to consonants in the words pineapple and strawberry. Give each ratio in its simplest form. grapefruit Vowels :Consonants Remember: vowels are a, e, i, o, u
f(x) = 12x + 10 is a function which can used to to calculate a person's daily paycheck.
Which would be a reasonable domain for this function?
A : all real numbers
B : 0
C : 0
D : 0
Answers
A : all real numbers
Answer:
A. All real numbers.
Step-by-step explanation:
select the correct answer. what is the slope of the line that goes through the points (-4,2) and (8,5)?
A. "-4"
B. "-1/4"
C. 1/4
D. 4
Answers
Answer: The slope of the line that goes through the points is = ¼
Step-by-step explanation:
Define Slope:
The slope is a numerical value that describes the steepness of a line and is usually determined by calculating the ratio of the vertical distance to the horizontal distance (rise over run) between two points.
The slope of the line that goes through the points (-4,2) and (8,5).
Let, X1=-4
Y1=2
X2=8
Y2=5
We can use m=(y2-y1) / (x2-x1)
replace with x1, y1 and x2, y2 values in this equation
We can write: m=[(5-2) / (8-(-4))]
Solve it: M= 3/12
M=1/4
So, the slope of the line that goes through the points is = ¼.
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Determine whether each of the following functions is a solution of laplace's equation uxx uyy = 0.
Answers
Both functions are the solution to the given Laplace solution.
Given Laplace's equation: [tex]u_{x x}+u_{y y}=0[/tex]
We must determine whether a given function is the solution to a given Laplace equation.If a function is a solution to a given Laplace's equation, it satisfies the solution.(1) [tex]u=e^{-x} \cos y-e^{-y} \cos x[/tex]
Differentiate with respect to x as follows:
[tex]u_x=-e^{-x} \cos y+e^{-y} \sin x\\u_{x x}=e^{-x} \cos y+e^{-y} \cos x[/tex]
Differentiate with respect to y as follows:
[tex]u_{x x}=e^{-x} \cos y+e^{-y} \cos x\\u_{y y}=-e^{-x} \cos y-e^{-y} \cos x[/tex]
Supplement the values in the given Laplace equation.
[tex]e^{-x} \cos y+e^{-y} \cos x-e^{-x} \cos y-e^{-y} \cos x=0[/tex]
The given function in this case is the solution to the given Laplace equation.
(2) [tex]u=\sin x \cosh y+\cos x \sinh y[/tex]
Differentiate with respect to x as follows:
[tex]u_x=\cos x \cosh y-\sin x \sinh y\\u_{x x}=-\sin x \cosh y-\cos x \sinh y[/tex]
Differentiate with respect to y as follows:
[tex]u_y=\sin x \sinh y+\cos x \cosh y\\u_{y y}=\sin x \cosh y+\cos x \sinh y[/tex]
Substitute the values to obtain:
[tex]-\sin x \cosh y-\cos x \sinh y+\sin x \cosh y+\cos x \sinh y=0[/tex]
The given function in this case is the solution to the given Laplace equation.
Therefore, both functions are the solution to the given Laplace solution.
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The correct question is given below:
Determine whether each of the following functions is a solution of Laplace's equation uxx + uyy = 0. (Select all that apply.) u = e^(−x) cos(y) − e^(−y) cos(x) u = sin(x) cosh(y) + cos(x) sinh(y)
In exercises 21 and 22, find the indicated angle measure. (See photo)
Answers
Answer:
42°, 101°
Step-by-step explanation:
These answers come from the angle subtraction postulate.
please help thank youuuu
Answers
Answer: 87/100
Step-by-step explanation:
#12: m∠GKH = ____
need the answer
Answers
Check out the attached photo
Filip is inviting 6 friends to a party. Each friend wants 5 cookies and each box has 8 cookies. How many boxes should Filip get?
Answers
6*5=30
30/8=3.75
round up for 4.
PLEASE HELP ASAP!
:))
Answers
Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.
Step-by-step explanation:
What does it mean converse in geometry?
The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."
So, in the figure below, if we can choose n║m, then ∠1≅∠2
Since n║m , by the corresponding Angles Postulate,
∠1≅∠2.
Therefore, by the definition of congruent angles,
m∠1=m∠2
Since ∠1 and ∠2 form a linear pair, they are supplementary, so
m∠1+m∠2=180°.
Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.
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Options are
A. (-3, -1)
B. (3,1)
C. (6,4)
D. (2,6)
Answers
Answer: D
Step-by-step explanation: 2,6
how could you use a compass to construct a segment that is twice the length of a given segment?
Answers
By taking the measure of the given line segment and making arc on one of the end points from one point of the line segment and joining those three points will be the line as twice as the given segment.
Following are the steps to construct a line segment that is twice the given segment :
Step 1 : Take the compass and measure the length of the given line segment let’s say AB
Step 2 : Now with that measure put one end of the compass on one of the points of a line segment, either point A or point B.
Step 3 : Now mark an arc on the right side of the point if the compass is on point B or mark the arc on the left side if the compass is on point A.
Step 4 : Mark that arc as point C and join the line AC or BC.
Hence AC or BC will be the new line segment which will as twice as the given line segment.
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Evaluate.
7- 24 ÷ 8 × 4 + 6
Answers
Answer:
-35
Step-by-step explanation:
Question =7-24÷8×4+6
=7-192÷4+6
=7-49+6
=-41+6
=-35
Therefore,right answer is (-35)
PLEASE MARK ME AS THE BRAINIEST.
Can someone help me please
Answers
Answer:
182.5
Step-by-step explanation:
182.5
steps
623420÷3416=
182.5
2
You can also use scientific notation for very small numbers. The
thickness of a dollar bill is about 0.0043 inches. Write this quantity in
scientific notation.
A. First move the decimal point to the right to get a number that is
greater than or equal to 1 but less than 10.
0.0043 The decimal point moves 3
places to the right.
Remove the extra zeros to get the first factor:
B. Since 0.0043 is less than 1, you moved the decimal point to the right,
so the exponent in the power of 10 will be negative.
-3
0.0043 = 4.3
X 10
Answers
the thickness in scientific notation is:
4.3* 10⁻³ inches
How to write the thickness in scientific notation?
Here we know that the thickness of a dollar bill is 0.0043 inches.
Now, scientific notation refers to the notation where we have a single digit at the left of the decimal point, and the order of the number is defined by a factor of a power of 10.
To write our number in scientific notation we need to count the number of zeros that we have before the first non-zero decimal, and we can see that it is equal to 3.
Then we can move all the digits 3 units to the left, and add a factor 10⁻³ to correct that, then we will get:
0.0043 = 4.3* 10⁻³
From this, we conclude that the thickness in scientific notation is:
4.3* 10⁻³ inches
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On the first day of class, a statistics professor asked her students to report their grade point averages (gpas) as part of a class survey. for those students who knew their gpas, the histogram was:______.
Answers
On the first day of class, a statistics professor asked her students to report their grade point averages (gpas) as part of a class survey. for those students who knew their gpas, the histogram was Left skewed.
The meaning of grade point averages?
You can determine your grade point average (GPA) by dividing the total number of high school credits you have earned by the total of all of your course grades. The majority of secondary and universities record grades on a 4.0 scale.What exactly does a 4.0 GPA mean?
High schools commonly report grade point averages (GPAs) on a 4.0 scale. A 4.0, or the highest grade, is awarded. You can get your total GPA by averaging your grades from all of your classes. This scale is regularly used in the majority of institutions and many secondary schools.Learn more about grade point averages
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Solve the compound inequality 6b < 36 or 2b + 12 > 6
A. b < 6 or b > 6
B. b < 6 or b > 3
C. b > 6 or b < −3
D. b < 6 or b > −3
Answers
Answer:
D.)
Step-by-step explanation:
Justin is evaluating the expression 12.53.8x, when x is 7.9.
12.5+3.847.9)
16.3(7.9)
128.77
What was Justin's error?
Justin should have multiplied 12.5 and 7.9 first.
Justin should have added 12.5 and 7.9 first.
Justin should have multiplied 3.8 and 7.9 first.
O Justin should have added 3.8 and 7.9 first.
Answers
Justin should have multiplied 3.8 and 7.9 first
How to evaluate an expression?He is trying to evaluate the expression 12.5 + 3.8x, when x = 7.9.
This was Justin solution to the expression
12.5 + 3.8(7.9)
16.3(7.9)
128.77
Now let's do our own arithmetic,
12.5 + 3.8x
we have to substitute the value of x in the equation.
12.5 + 3.8(7.9)
Using PEMDAS principle, we have to multiply before addition.
Therefore,
12.5 + 3.8(7.9)
12.5 + 30.02
42.52
Hence, Justin should have multiplied 3.8 and 7.9 first
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please help me with this problem
Answers
Answer:
The equivalent fraction of 6/9 is 4/6
Explanation:
9 divided by 6 = 1.5
6 x 1.5 = 9
Consider the expression 4a + (-3b), where bis a negative number and a < b. Is the sum positive or negative?
Answers
The sum will be negative.
The product of two negative numbers is always positive and if we add two numbers, the sign of the greater number is used in the result.
Here, we are given an expression 4a + (-3b)
Also we are told that a < b and b is a negative number
Mow, since b is a negative number, (-3b) will always be positive. This is because the product of two negative numbers, here -3 and b, will always be positive.
Now, a can be positive or negative. If a is positive, the sum will always be positive. However, if it is negative, the sum can be either positive or negative.
Here, in fact, since a < b, a will always be negative only
Let us take an example, say a = -3 and b = -2
Then the sum becomes 4(-3) + (-3)(-2)
= -12 + 6
= -6
If we observe closely since a and be are both negative and a < b, in absolute terms a will always be greater than b since for negative numbers higher the value, smaller is the number.
Thus, we can conclude that 4a > (-3b) for all values of a and b
and since 4a will always be negative, the sum will also be negative.
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