Force of Gravity & Coulomb's Law Force Question

In summary, the conversation discusses finding the magnitude of charge on two small spheres suspended from a common point. The solution involves using the force of gravity and the electric force, as well as drawing a force diagram and considering tangential forces. The final answer is 0.58 μC.
  • #1
Medeiros

Homework Statement


Two small spheres of 15 g each are suspended from a common point by threads of length 35 cm. Each thread makes an angle with the vertical of 20 degrees. Each sphere carries the same charge. Find the magnitude of this charge.
(The correct answer is: 0.58 μC)

Homework Equations


1) F= k|q1| |q2| / r2
2) SOH CAH TOA
3) F=ma

The Attempt at a Solution



I drew a picture of the 2 strings hanging from the same point and labelled the angles.
Knowing that F(g)=max on Y axis and = 0 on X axis,
I thought I could get the force of gravity on the two particles by

angle x g x mass
sin(20) x 9.81 x 0.015 = 0.05033...N
(I also did this another way by finding a vector from how much of the string on the Y axis as missing, and doing a ratio between that and the length of the string, which took a long time and turned out to be sin(20) anyway)
From there, I plugged that force in Eq.1:
q2 = Fr2 / k
so q = 0.56625 μC

Although it is close, I didn't round off anything to get that answer, and my answer still doesn't round off to the correct one.
I was just wondering if
1. Did I get the force the wrong way?
2. Is there an easier way to do it?
2. Is there another way to do this?

Thank you in advance
 
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  • #2
You seem to be saying mg*sinθ = kq2/r2. Is this correct?
Draw a force diagram. What is the magnitude of the tangential force tending to reduce the angle? What is the magnitude of the tangential force tending to increase the angle?
 
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  • #3
mjc123 said:
You seem to be saying mg*sinθ = kq2/r2. Is this correct?
Draw a force diagram. What is the magnitude of the tangential force tending to reduce the angle? What is the magnitude of the tangential force tending to increase the angle?
Yep that is correct.

I THINK I drew the tangential force vectors tending to reduce the angle in my first attempt and made it equal to the force increasing the angle (the electric force) which was the same as sin(20)*g*m

If that's not it, I'm not sure what it is then
 
  • #4
Is the electric force tangential?
 

Related to Force of Gravity & Coulomb's Law Force Question

What is the force of gravity?

The force of gravity is a natural phenomenon by which all objects with mass are brought towards each other. The strength of this force is determined by the masses of the objects and the distance between them. On Earth, the force of gravity is what keeps us grounded and is responsible for the motion of planets around the sun.

How is the force of gravity calculated?

The force of gravity can be calculated using Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This can be expressed as F = G (m1m2)/r^2, where F is the force of gravity, G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

What is Coulomb's law of force?

Coulomb's law of force is a fundamental principle in electrostatics that describes the force between two charged particles. It states that the force between two particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This can be expressed as F = k (q1q2)/r^2, where F is the force, k is the Coulomb constant, q1 and q2 are the charges of the particles, and r is the distance between them.

How does Coulomb's law of force relate to gravity?

Coulomb's law of force and Newton's law of universal gravitation are similar in their mathematical form, but they describe different types of forces. While gravity is a force between objects with mass, Coulomb's law deals with the force between objects with electric charge. Both laws follow the inverse-square law, where the force decreases as the distance between the objects increases.

What is the difference between gravitational force and Coulomb's law force?

The main difference between gravitational force and Coulomb's law force is the type of objects that are involved. Gravitational force acts between objects with mass, while Coulomb's law force acts between objects with electric charge. Additionally, gravitational force is always attractive, while Coulomb's law force can be either attractive or repulsive, depending on the charges of the objects.

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