Calculating Tension of a String Suspended Ball

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In summary, one small ball with a mass of 35 g and a charge of -0.1 µC is suspended from the ceiling by a string, hanging 5.0 cm above an insulating floor. A second small ball with a mass of 85 g and a charge of 0.2 µC is rolled directly beneath it. The question is whether the second ball will leave the floor. The answer is no, as the gravitational force pulling it down is greater than the electrostatic force pulling it up. The electrostatic force is calculated to be 0.022 N, while the gravitational force is 0.343 N. Therefore, the tension of the string must be at least 0.343 N to keep
  • #1
yjk91
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Homework Statement


A small ball with a mass of 35 g and a charge of -0.1 µC is suspended from the ceiling by a string. The ball hangs at a distance of 5.0 cm above an insulating floor. If a second small ball with a mass of 85 g and a charge of 0.2 µC is rolled directly beneath the first ball, will the second ball leave the floor?

ans: 0.415 N




The Attempt at a Solution



T of the ball
T = mg = 0.035kg * 9.8 = 0.343 N

F of two balls
F = k * q1* q2 / (l)^2
= 0.021576 N

i am not sure what to do any hints?
 
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  • #2
ans: 0.415 N

0.415N? Isn't this a yes or no question?

So gravity pulls the second ball down with 0.343N of force, whereas the other ball pulls it up with 0.022N. Do you think the ball will go up?

By the way, I think you made a mistake in calculating the electrostatic force. It should be higher, although not high enough to change the answer.
 
  • #3
the answer is no opps
there is a second part of the question about what the tension of the string is and I'm not sure how to get it
 

What is the formula for calculating tension of a string suspended ball?

The formula for calculating tension of a string suspended ball is T = mg + ma, where T is the tension, m is the mass of the ball, g is the acceleration due to gravity, and a is the acceleration of the ball.

How do you determine the mass of the ball in order to calculate tension?

The mass of the ball can be determined by using a scale or balance to measure its weight in kilograms. This value can then be used in the tension formula.

What is the unit of measurement for tension?

The unit of measurement for tension is Newtons (N). This is a unit of force that is equivalent to 1 kilogram-meter per second squared (kg*m/s^2).

Can tension be negative?

Yes, tension can be negative. This occurs when the force pulling on the string is greater than the weight of the ball, causing the string to be slack and the tension to be in the opposite direction of the weight.

How does changing the length of the string affect the tension?

The tension in the string increases as the length of the string decreases. This is because a shorter string requires a greater force to keep the ball suspended at the same height.

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