How did they divide the equations ?

  • Thread starter aleksbooker
  • Start date
In summary, the conversation discussed how to "divide the equations" in a physics problem involving two point charges on threads. The equations involved the use of standard units, angles, and forces. The division of the equations allowed for the elimination of a variable and provided a useful tool in solving the problem.
  • #1
aleksbooker
22
0
How did they "divide the equations"?

Homework Statement



Two 5.0g point charges on 1.0m-long threads repel each other after being charged to +100nC.
What is angle theta? You can assume theta is a small angle.

8SSFQJJ.png


Homework Equations


[itex]K=9.0*10^9 Nm^2/C^2[/itex]
[itex]g=9.8m/s^2[/itex]
[itex]q=\frac{K|q_1||q_2|}{d^2}[/itex]

The Attempt at a Solution



I determined my unknowns and translated everything into standard units, and drew out the free-body diagram.

eQsK9SG.png


Translated everything into standard units.
5.0g = 5.0*10^(-3) kg
100nc = 100*10^(-9) C

[itex]\frac{1}{2}d=\sin{\theta}[/itex]
[itex]d=2\sin{\theta}[/itex]
[itex]T_x=T\sin{\theta}=F_{2on1}=\frac{Kq^2}{d^2}[/itex]
[itex]T_x=T\sin{\theta}=F_{2on1}=\frac{Kq^2}{(2\sin{\theta})^2}[/itex]
[itex]T_x=T\sin{\theta}=F_{2on1}=\frac{Kq^2}{4sin^2{\theta} }[/itex]
[itex]T_y=T\cos{\theta}=mg[/itex]

The "missing" step:
The solutions manual says that the next step from here is to "divide the two equations and solve for q". What I don't know is how they "divided the two equations" to get this:

[itex]\sin^2{\theta}\tan{\theta}=\frac{Kq^2}{4L^2mg}=4.59*10^{-4}[/itex]
 
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  • #2
Divide this equation:
aleksbooker said:
[itex]T\sin{\theta}=\frac{Kq^2}{4sin^2{\theta} }[/itex]
By this one:
[itex]T\cos{\theta}=mg[/itex]

Divide the left sides by each other and the right sides by each other.
 
  • #3
hi aleksbooker! :wink:
aleksbooker said:
[itex]T_x=T\sin{\theta}=F_{2on1}=\frac{Kq^2}{4sin^2{\theta} }[/itex]
[itex]T_y=T\cos{\theta}=mg[/itex]

What I don't know is how they "divided the two equations"

you divide Tsinθ by Tcosθ, to give you Ttanθ = … ? :smile:

(hmm … there seems to be an L2 missing :confused:)
 
  • #4
tiny-tim said:
(hmm … there seems to be an L2 missing :confused:)
Apparently, L is the length of the string, which is given as 1 m.
 
  • #5
Mind blown. Thanks @Doc Al. Okay, that works - I'm assuming it only makes to do something like this when you can use it to eliminate a variable (like T in this problem).
 
  • #6
Yea, L was the length of the string.
 
  • #7
aleksbooker said:
I'm assuming it only makes to do something like this when you can use it to eliminate a variable (like T in this problem).
Think of it as just another tool in your bag of tricks. A useful one.
 

Related to How did they divide the equations ?

1. How do scientists divide equations?

Scientists divide equations by using basic mathematical operations such as division, multiplication, addition, and subtraction. They also use variables and constants to represent unknown quantities in the equation.

2. What is the purpose of dividing equations in science?

The purpose of dividing equations in science is to simplify complex mathematical relationships and make them easier to analyze and solve. It also helps in determining the relationship between different variables in a system.

3. Can any equation be divided?

Yes, any equation can be divided as long as it follows the basic rules of mathematical operations. However, in some cases, dividing an equation may lead to an undefined or infinite solution.

4. How do scientists know when to divide an equation?

Scientists decide to divide an equation when they want to isolate a specific variable or when they want to manipulate the equation to make it easier to solve. This decision is based on the problem they are trying to solve and the information they are given.

5. Are there any special methods for dividing equations in science?

Yes, there are some special methods for dividing equations in science, such as the method of partial fractions and the method of long division. These methods are used to solve specific types of equations and are commonly used in higher-level mathematics and physics.

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