Calculating Ball Diameter in a Beaker: Accounting for Tension and Buoyancy

[needhelpfast]

Ball in a Beaker - Diameter - Please Help!

Homework Statement

A thread attaches a 2.73-g Ping-Pong ball to the bottom of a beaker. When the beaker is filled with water so that the ball is totally submerged, the tension in the thread is 6.75 mN. Determine the diameter of the ball.

Homework Equations

r = [6(T + mg)/π × 10^3g]^1/3

The Attempt at a Solution

I am using the above equation but cannot get the right answer!

 

[ehild]

The equation is not correct. Try to derive the formula for the diameter yourself.

ehild

 

[Xerxes1986]

ehild is correct, you need to derive the equation yourself. I would recommend thinking about the force diagram first. Which forces are pulling the ping pong ball down? Which forces are pulling it up? They have to be equal and opposite to each other if the ball isn't accellerating.

 

[tak08810]

A thread attaches a 2.74-g Ping-Pong ball to the bottom of a beaker. When the beaker is filled with water so that the ball is totally submerged, the tension in the thread is 6.87 mN. Determine the diameter of the ball.

The force pushing the ping pong ball up is the buoyant force of the water. Thus if the force pulling it down is equal, the tension is equal to the buoyant force. According to Archimedes principal, the buoyant force on a object immersed in fluid is equal to the weigh of the fluid displaced by that object. So the weight of the fluid displaced is 6.87 mn. Thus, the mass is 0.00687 N / 9.87 N = 0.000701 kg. Then, d = m*v. D of water is 1000 kg * m^3. Solving for volume, we get the volume as 7.0102 * 10^-7 m^3. Then we solve for volume with (x/2)^3 * pi * 4/3 = 7.0102 * 10^-7 m^3. I get x to = 0.011022 m. But this is not the answer; what am I doing wrong?

 

[Redbelly98]

The force pushing the ping pong ball up is the buoyant force of the water. Thus if the force pulling it down is equal, the tension is equal to the buoyant force.

You are forgetting about another force that acts on the ball.

 

[tak08810]

You are forgetting about another force that acts on the ball.

Ah thank you! So tension + gravity is the force going down and the buoyant force opposes it.