Answer:
3 m/s
Explanation:
Initial = Final
Mass * Velocity = Mass *Velocity
8000kg * 12m/s = (8000kg+ 24000kg) * (Final Velocity)
(96000 kgm/s) / (32000kg) = (Final Velocity)
Final Velocity = 3 m/s
Answer:
![P = 1.090\,N](https://tex.z-dn.net/?f=P%20%3D%201.090%5C%2CN)
Explanation:
The constant speed means that ball is not experimenting acceleration. This elements is modelled by using the following equation of equilibrium:
![\Sigma F = P - W + F_{D}](https://tex.z-dn.net/?f=%5CSigma%20F%20%3D%20P%20-%20W%20%2B%20F_%7BD%7D)
![\Sigma F = P - \rho \cdot V \cdot g + c\cdot v = 0](https://tex.z-dn.net/?f=%5CSigma%20F%20%3D%20P%20-%20%5Crho%20%5Ccdot%20V%20%5Ccdot%20g%20%2B%20c%5Ccdot%20v%20%3D%200)
Now, the exerted force is:
![P = \rho \cdot V \cdot g - c\cdot v](https://tex.z-dn.net/?f=P%20%3D%20%5Crho%20%5Ccdot%20V%20%5Ccdot%20g%20-%20c%5Ccdot%20v)
The volume of a sphere is:
![V = \frac{4\cdot \pi}{3}\cdot R^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B4%5Ccdot%20%5Cpi%7D%7B3%7D%5Ccdot%20R%5E%7B3%7D)
![V = \frac{4\cdot \pi}{3}\cdot (0.014\,m)^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B4%5Ccdot%20%5Cpi%7D%7B3%7D%5Ccdot%20%280.014%5C%2Cm%29%5E%7B3%7D)
![V = 1.149\times 10^{-5}\,m^{3}](https://tex.z-dn.net/?f=V%20%3D%201.149%5Ctimes%2010%5E%7B-5%7D%5C%2Cm%5E%7B3%7D)
Lastly, the force is calculated:
![P = (8910\,\frac{kg}{m^{3}} )\cdot (1.149\cdot 10^{-5}\,m^{3})\cdot (9.81\,\frac{m}{s^{2}} )+(0.950\,\frac{kg}{s})\cdot (0.09\,\frac{m}{s} )](https://tex.z-dn.net/?f=P%20%3D%20%288910%5C%2C%5Cfrac%7Bkg%7D%7Bm%5E%7B3%7D%7D%20%29%5Ccdot%20%281.149%5Ccdot%2010%5E%7B-5%7D%5C%2Cm%5E%7B3%7D%29%5Ccdot%20%289.81%5C%2C%5Cfrac%7Bm%7D%7Bs%5E%7B2%7D%7D%20%29%2B%280.950%5C%2C%5Cfrac%7Bkg%7D%7Bs%7D%29%5Ccdot%20%280.09%5C%2C%5Cfrac%7Bm%7D%7Bs%7D%20%29)
![P = 1.090\,N](https://tex.z-dn.net/?f=P%20%3D%201.090%5C%2CN)
Scientists believe that on large scales the Universe is isotropic (the same in all directions). Thus, from our perspective, half of all spiral galaxies should spin clockwise, and half counter-clockwise.
The Total Mechanical Energy
As already mentioned, the mechanical energy of an object can be the result of its motion (i.e., kinetic energy) and/or the result of its stored energy of position (i.e., potential energy). The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy.