Question

what is the kinetic energy of the road with the stone find the attached files​

Answer 1

Answer:

The kinetic energy of the stone will not be equal at the same point on the way up or the way down, due to the presence of friction from the air. To show this, it is enough to compare the speed of the stone just after it leaves your hand (on the way up) with the speed just before it lands back in your hand (on the way down).

First consider the case without air resistance. You launch the stone with speed u directly upwards. The initial energy you give the stone is

KE=12mu2.

The stone goes up until it reaches its maximum height, where all of its initial kinetic energy is converted into potential energy. Then the stone comes back down, and by the time it reaches your hand again all of this potential energy has been converted back to kinetic energy. Let's call the final speed of the stone v. The final and initial energies must be the same. Since all the initial kinetic energy has been converted back to kinetic energy, the initial and final kinetic energies are the same, or in maths:

12mu2=12mv2

.

Now add air resistance to the picture. As the stone moves through the air, some of its kinetic energy is used up and converted into heat energy, raising the temperature of the stone and the air slightly. The initial and final energies of the entire system (stone and air) still have to be the same, so we now have

Initial energy12mu2==Final energy12mv2+(heat energy from friction).

Rearranging this equation, you get

Final kinetic energy=12mv2=12mu2−(heat energy from friction),

which is smaller than the initial kinetic energy. A similar argument shows that the kinetic energy is less on the way down than the way up for any point on the trajectory.