Answer:
Explanation:
This is a First Law of thermodynamics problem. We have to remember that the total energy available to a system is constant throughout the whole problem and that energy cannot be created or destroyed. So we need to find the total energy available right at the start. Well it just so happens that we are told that the total energy is 1000J and that it is all potential energy when the sphere is at rest and is 25 m off the ground. If the object isn't moving, all the energy is potential until it starts moving and the energy begins to convert from potential to kinetic a little bit at a time. The thing that we don't know is the mass of the shpere. Begin with the fact that the PE = 1000 (I'm going to se 2 sig fig's since there's only 1 in 1000). If
PE = 1000 and PE = mgh, then
1000 = m(9.8)(25) so
m = 4.1 kg
We also need the height at which this sphere has a PE of 600. Again, if
PE = 600 and PE = mgh, then
600 = (4.1)(9.8)h so
h = 15 Filling in the total energy equation now, using the fact that the total energy available to the system is 1000J:
TE = PE + KE and
1000 = (4.1)(9.8)(15) + [tex]\frac{1}{2}(4.1)v^2[/tex] and we are looking for v.
1000 = 6.0 × 10² + 2.1v² so
[tex]v=\sqrt{\frac{1000-6.0*10^2}{2.1} }[/tex] and
[tex]v=\sqrt{\frac{4.0*10^2}{2.1} }[/tex] gives us
v = 14 m/s
