Solving Fluid Questions: 2 Spheres & U-Tube | 65 Characters

[icg]

1. A thin spherical shell with a mass of 3.82 kg and a diameter of 0.200 m is filled with helium (density = 0.180 kg/m3). It is then released from rest on the bottom of a pool of water that is 3.73 m deep. Neglecting frictional effects, determine the value of that acceleration.

Can anyone help me with this question? I found the volume of the sphere v = m/density, and the area of the sphere, but got stuck on how to actually find the acceleration, would you have to use Force=Pressure/Area somewhere?


2. A U-tube of circular diameter 5.60 mm initally contain just water. If 4.00 milliliters(cm^3) of oil is added to the left hand side of the tube the level of the oil is 6.8 mm higher than the level of the water in the right hand side of the tube. Determine the height of the oil.

Im confused on what they mean by the circular diameter and do you need that to solve the question. I tried using the formula for volume of a cylinder, solving for height, but I don't think that helped at all. Can anyone give me some pointers?

Theres no examples like this in my notes, or in my text, and the assingment is due in 2 hours. Thanks

 

[glid02]

For the first question you should draw a freebody diagram and from there you can get the net force acting on the sphere: buoyant force - weight.

For the second question I think the circular diameter is best described by a donut, from the inside to the outside is 5.6 mm. The total weight of the oil is equal to the weight of the water it displaces, so
h(weight of oil)=(h-6.8)(weight of water). g is the same for both so basically you just have to use their respective densities.

Hope that helps a little.

 

[m2003]

I would recommend breaking down the problem into smaller parts and using relevant equations to solve for the unknown variables. For the first question, you can use the equation F=ma and consider the forces acting on the spherical shell to find the acceleration. For the second question, you can use the equation for pressure (P = ρgh) and the given information to solve for the height of the oil. It may also be helpful to draw a diagram to visualize the problem. Remember to include units in your calculations and double check your work. Good luck!