Charge on pendulum due to electric field

wendo

1. The problem statement, all variables and given/known data
A small m=1.70×10-3 kg plastic ball is suspended by a l=20.0 cm long string in a uniform electric field, as shown below. If the ball is in equilibrium when the string makes a θ=13.1° angle with the vertical, what is the net charge on the ball? Take E=1.04×103i N/C.



2. Relevant equations
Restoring force= mgsin theta??
E=F/q



3. The attempt at a solution
I'm really lost on how to start this question, I first thought that since the pendulum is in equilibrium, it means that the horizontal forces would be equal, so these forces being the restoring force and the electric force exerted by the electric field...
And then use the force to solve for q in q=F/E... but that wasn't right.

Then I thought well since it's in equlibrium, maybe the potential energy of the pendulum is somehow suppose to play a role in it, but once I find the potential energy, how can i relate that to the equation to force and electric field to finally get the charge on the ball?

hage567

You must sum up the forces in each direction (breaking them up into their components if necessary). So what are ALL the forces acting on the ball? (don't forget about gravity) Draw a diagram. You can use Newton's second law for this problem.

What exactly do you mean by "restoring force"? Do you mean the tension in the string?

wendo

hmm, okay so if I break down the forces to all the components, it seems to me that the vertical forces would cancel out and only the horizontal forces remain, but I'm not 100% sure. (my reasoning is that because its in equlibrium then all the forces in opposite directions would cancel out, however i feel like that this is not really suppose to be the case.

Can you explain to me how F=ma would be applied to this? I can see if I get Fnet then I can use this and apply it to the equation E=F/q to find the charge, but how can acceleration relate to electric field??

Doc Al

The problem states that the ball is in equilibrium, so the net force must be zero: that means both horizontal and vertical components. To use this, first identify all the forces that act on the ball. (I count 3 forces.)

This reduces to the equilibrium condition when the acceleration is zero, as it is here: Fnet = 0. (So you don't really need F = ma.)

Use the equilibrium condition (Fnet = 0) to solve for the force due to the electric field, then you can solve for the electric charge using E = F/q.

Acceleration is zero, since the ball is in equilibrium. (So acceleration plays no role here.)

wendo

I got it!!! THANK YOU for your help!!!!

weirdgirl

I have a similar question, and I'm getting confused on the tension part of the forces. Would the 3 forces be the horiz/vert of the tension force, then the electric field force? So you get Tcos(theta) + mg-Tsin(theta) + Eq = 0 ...then solve for q? I'm pretty sure this is wrong...any guidance?

Doc Al

No. Tension is one force, but it has horizontal and vertical components. Gravity and the electric force are the other two.
Write separate equations for the net horizontal force and the net vertical force. Then you can solve for q.

weirdgirl

I used tan(theta) for both of the tension components, then used (mg) and (E) to find q and got the right answer...is that the right way?

Doc Al

One of the tension components will be Tsinθ and the other will be Tcosθ. When you combine the two equations, you'll end up with tanθ. The only way to be sure that you're doing things correctly is for you to show every step that you did.

physics323

I have a problem with a similar diagram and question, here it is: A 100-g mass is suspended by a string. there is a strictly horizontal electric field present in this region having strength of E = 200 N/C. If the magnitude of the charge on the ball is 5.8 microCoulombs, then determine the tension T, in the string if the system is at equilibrium. The diagram given is the same as the one previously posted except it has a point, labeled A, to the left of the dotted line and a distance from point A to the mass is given as 1.5 meters. However, at the end of the question it says to ignore point A on the diagram. Also, my diagram does not show the direction of E, like this one does. I thought you simply use the equation force of electric field equals E times q, using T as the force. However, I don't think this seems correct. Any thoughts?

Doc Al

It will be in the same direction as shown in the diagram in this thread.
The electric force on the mass will equal F = Eq, but that's not equal to the tension. That's only one of the forces acting on the mass.
Read through this thread for clues. Hint: The mass in in equilibrium, so what must be the net force on it? What forces act on it?

physics323

Okay that helps alot I think I have it then. I have three forces working on the mass, the electric field, gravity, and the string. Since it's in equilibrium, the force of the electric field is equal to the x component of the tension, and the force of gravity is equal to the y component of the tension. From there I can just use the Pythagorean Theorem and solve, correct? One last thing though, when solving for the force of gravity should I just use 9.8 or 9.8 times the mass of the ball being suspended?

Doc Al

Sounds good.
The acceleration due to gravity is g = 9.8 m/s^2. To find the force of gravity, multiply by the mass: Weight = mg.

physics323

Okay that's what I did! I think I got it then, thank you so much!