What is the mass of the sphere?

[lollypop]

hello everybody:

A hollow, plastic sphere is held below the surface of a freshwater lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.700 M^3 and the tension in the cord is 930 N.

Calculate the buoyant force exerted by the water on the sphere. Take the density of water to be 1000 kg/m^3 and the free fall acceleration to be 9.80 m/s^2.
**for this I set up Bouyant = density *Volume*gravity = 6860 N

What is the mass of the sphere? Take the density of water to be 1000kg/m^3 and the free fall acceleration to be 9.80m/s^2 .
**here I used Buoyant = mg-T and solved for m, so answer for m= 605 kg

The cord breaks and the sphere rises to the surface. When the sphere comes to rest, what fraction of its volume will be submerged? Express your answer as a percentage.
** here is my problem , so far all I have is that the sphere is at rest so there is no external force acting on it, so F=B+T+(-mg) =0 right?? I don't know what else to use for this part. Any clues??

 

[Chen]

**for this I set up Bouyant = density *Volume*gravity = 6860 N

Correct.

**here I used Buoyant = mg-T and solved for m, so answer for m= 605 kg

Not so sure about that one. Shouldn't be it:
B = mg + T
Since both mg and T act in the same direction, downward? The cord isn't pushing the sphere up, it is pulling it down.

The cord breaks and the sphere rises to the surface. When the sphere comes to rest, what fraction of its volume will be submerged? Express your answer as a percentage.
** here is my problem , so far all I have is that the sphere is at rest so there is no external force acting on it, so F=B+T+(-mg) =0 right?? I don't know what else to use for this part. Any clues??

For the sphere to be at rest, mg must equal B. There is no tension anymore, since the cord was broken. You need to express B as a function of the volume of the sphere that is still submerged, and find it.

mg = B = \rho V' g
V' = \frac{m}{\rho }

 

[M98Ranger]

Hello!

To answer your question, we need to use the concept of buoyancy and Archimedes' principle. When the sphere is submerged in water, there are two forces acting on it: the weight of the sphere (mg) and the buoyant force (B) exerted by the water. These two forces are equal and opposite, so the net force on the sphere is zero, causing it to stay at rest.

When the cord breaks and the sphere rises to the surface, it will continue to experience the same two forces, but now the direction of the buoyant force will be upwards, while the weight of the sphere will still be downwards. This will cause the sphere to accelerate upwards until it reaches the surface and comes to rest again.

To find the fraction of the sphere's volume that will be submerged, we can use the equation B = density of fluid * volume of displaced fluid * gravity. Since the sphere has a volume of 0.700 m^3 and the density of water is 1000 kg/m^3, the volume of water displaced by the sphere will also be 0.700 m^3. Therefore, the buoyant force acting on the sphere will be 6860 N, as you correctly calculated earlier.

Now, to find the fraction of the sphere's volume that will be submerged, we can use the equation B = density of object * volume of object * gravity. This time, we will use the density of the sphere, which we can find by using the formula density = mass/volume. From the previous calculation, we know that the buoyant force is equal to the weight of the sphere (mg), so we can rearrange the formula to find the mass of the sphere: mass = B/g. Plugging in the values, we get a mass of 700 kg for the sphere.

Now, we can use the mass and volume of the sphere to find its density (density = mass/volume), which turns out to be 1000 kg/m^3. This is the same density as water, which means that the sphere will be completely submerged in water. Therefore, the fraction of the sphere's volume that will be submerged is 100%, or 100%.

I hope this helps! Let me know if you have any other questions.