Electric Force Homework: Calculate Charge on Spheres

[simplicity12]

Homework Statement

Two identical small spheres of mass 2.0 g are fastened to the ends of an insulating thread of length 0.60m. The spheres are suspended by a hook in the ceiling from the centre of the thread. The spheres are given identical electric charges and hang in static equilibrium, with an angle of 30 degrees between the string halves. Calculate the magnitude of the charge on each sphere.

Homework Equations

F(g)= mg
F(e)= kq(1)q(2)/r^2

The Attempt at a Solution

I found the gravitational force acting on one of spheres by F(g)=mg, where the mass is 0.002 kg and the g is 9.80 N/m, and i got 0.0196 N.
Since the system is static equilbrium. The vertical component of the tensile force is equal to the force of gravity. Next i did the F(tensile horizontal)/Fg= tan15, and i got 5.25 X 10^-3 N. The next part is what confuses me... do i need to double the horizontal tensile force since i only considered one half of the string... or do i just leave it, and then using the equation F(e)= kq^2/r^2, to find the charge? The answer in the book says it's 1.2 X 10^-7 C. Can someone please clarify this for me?

 

[anathema]

Hello there,

Your approach to the problem is correct so far. You have correctly calculated the gravitational force acting on one of the spheres. Now, since we know that the system is in static equilibrium, we can set the horizontal component of the tension force equal to the force of gravity. This is because the spheres are hanging at an angle of 30 degrees, which means the vertical component of the tension force will cancel out with the force of gravity. Therefore, we only need to consider the horizontal component of the tension force.

To answer your question, you do not need to double the horizontal tension force. This is because the tension force acts in both halves of the string, and each half will have an equal and opposite horizontal component of the tension force. So, we can just use the horizontal component of the tension force in our calculations.

Now, using the equation F(e) = kq1q2/r^2, we can find the magnitude of the charge on each sphere. We know the distance between the two spheres (r) is equal to the length of the string (0.60m), and we can calculate the value of k using the known value of the electric constant. Plugging in the values, we get:

F(e) = (8.99 x 10^9)(q^2)/(0.60^2) = 0.00525 N

Solving for q, we get q = √(0.00525 x 0.60^2)/(8.99 x 10^9) = 1.2 x 10^-7 C

This is the magnitude of the charge on each sphere. I hope this helps clarify the solution for you. Keep up the good work!

 

[m2003]

I would like to clarify the correct approach to solving this problem. First, it is important to recognize that in static equilibrium, the net force acting on the spheres must be zero. This means that the force of gravity acting on each sphere must be balanced by the electric force between them.

To find the charge on each sphere, we can use the equation F(g) = F(e), where F(g) is the force of gravity and F(e) is the electric force. We know the mass and gravitational acceleration, so we can solve for F(g). Then, using the given distance between the spheres and the angle of 30 degrees, we can find the distance between the spheres and use it to solve for the electric force using the equation F(e) = kq1q2/r^2.

Since the spheres are identical and have the same charge, we can set q1 = q2 = q and solve for q. This will give us the magnitude of the charge on each sphere.

It is important to note that the horizontal component of the tensile force does not need to be doubled, as it is already balanced by the force of gravity. We only need to consider the vertical component of the tensile force in our calculations.

In summary, the correct approach to solving this problem is to set the forces of gravity and electricity equal to each other and solve for the charge on each sphere. I hope this helps clarify the solution for you.