Awesome!
Okay, number six...
Basically, first you need to draw a free-body diagram. You know the weight of the ball acts downwards (W = mg) and that the buoyancy (Fb) acts upwards. You can find the buoyancy using the formula in the textbook, the density(fluid) x Volume(fluid) x g.
We know the density of the fluid since it's water (=1000 kg/m^3)
The Volume of fluid displaced = Volume of ball = Volume of a sphere (radius is given so you can find this).
After you've found these two forces, you get a net upward force acting on the ball.
Now here's where it gets tricky. Since you need to find the height above the water, you need to realize that this is actually a kinematics problem. And since you have the Force, you can use that to find the acceleration of the ball (F = ma).
After finding this acceleration, you can find the final velocity of the ball till the point it reaches the surface of the water (using vf^2=vi^2 + 2as). s = the depth of the pond given.
When you find the vf using that, you use the SAME equation to find the distance. That is:
At the surface of the water, i.e., when the ball begins moving in the air, acceleration is now g. The vf you calculated is now the INITIAL speed of the ball from the surface, and its vfinal will be the speed it has at the very top, i.e., 0 m/s. So using the same equation as above, you can substitute in the values and obtain s. Note that you will get a negative ans. unless you use g = -9.81 m/s^2.
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As for Q. 12...
You need to realize that they've given you the flowrate. Convert it to m^3 and then, since you know that the flowrate at the beginning = flowrate at the end, you can find the v1 and v2 using Q = vA, where A is the area (you have the diameters so you can find the areas).
After finding the velocities, you apply Bernoulli's equation. Since the tube is pretty much horizontal, (rho)gy1 and (rho)gy2 are equal to zero (y = height = 0).
So you get p1 + 1/2(rho)v1^2 = p2 + 1/2(rho)v2^2 (----> equation 1)
The equation given in the textbook to find the height is
p2 = p1 - (rho)liquid x g x h. (-----> equation 2)
So instead of finding the individual pressures, just find the pressure difference (p1-p2) from equation one, and rearrange equation 2 to get h. You're given the density of mercury, just sub it in and voila.
Hope that was clear enough, and didn't confuse you!
Good luck!
