Briefly describe the relative quantities of kinetic, gravitational potential and mechanical energy as a stone is thrown in the air vertically upward and falls to the person's hand at the same height that it left.
KE = (1/2)*m*v^2
PE = m*g*h
ME=KE+PE
initially from rest:
Everything is 0
As it leaves from rest, and reaches maximum height, PE increases (because from the formula, h increases)
When it reaches max height, for a moment, the stone will stop in the hair for a short time before coming down, and when this happen, velocity is 0 which means KE decreases
From conservation of energy, ME will be the same
So in short:
As the stone rises in height, the kinetic energy decreases and the potential energy increases. The mechanical energy will be the same.
as it leaves the hand, ME = (1/2)mv^2 and mgh = 0
When a stone is thrown vertically upward and falls back to the person's hand at the same height, the relative quantities of kinetic energy, gravitational potential energy, and mechanical energy change during different stages of its motion.
1. Throwing upward: Initially, the stone has kinetic energy due to its initial velocity. As it moves upward, its kinetic energy decreases because its speed decreases. At the same time, the stone gains gravitational potential energy as it moves against the force of gravity. Its mechanical energy (the sum of kinetic and potential energy) remains constant, neglecting any energy losses due to air resistance.
2. Maximum Height: At the highest point of its trajectory, the stone momentarily comes to a stop. At this point, its kinetic energy is zero, and all of its initial kinetic energy has been converted into gravitational potential energy. The stone has the maximum amount of potential energy and zero kinetic energy.
3. Falling back: As the stone falls back down, it gains kinetic energy due to the accelerating force of gravity. Its gravitational potential energy decreases as it descends, converting into kinetic energy. At any given height, the sum of the stone's kinetic and potential energies is equal to its mechanical energy, which remains constant throughout its motion.
4. Returning to the hand: When the stone reaches the person's hand at the same height it left, its kinetic energy is maximum, and its potential energy is zero. At this point, the stone has regained all of its initial kinetic energy, and the sum of its kinetic and potential energies is equal to its mechanical energy.
In summary, the relative quantities of kinetic, gravitational potential, and mechanical energy change during the stone's motion. Initially, the stone has kinetic energy, which is gradually converted into gravitational potential energy as it moves upward. At the highest point, all the kinetic energy has been converted into potential energy. On the way down, the potential energy is gradually converted back into kinetic energy until the stone reaches the person's hand, and its kinetic energy is maximum while potential energy is zero. The mechanical energy of the stone remains constant throughout the entire motion.
When a stone is thrown vertically upward and then falls back down to the same height, we can examine the relative quantities of kinetic energy (KE), gravitational potential energy (PE), and mechanical energy (ME) at different points of its trajectory.
1. Initial Point: At the moment the stone is thrown upwards, it has a certain amount of kinetic energy due to its motion. The stone's gravitational potential energy is relatively low since it is close to the ground. The mechanical energy is the sum of the kinetic and potential energy at this point.
2. Highest Point: As the stone reaches its highest point in the air, its velocity decreases to zero. Therefore, the kinetic energy becomes zero. The stone has the maximum amount of gravitational potential energy at this point, since it has gained elevation against gravity. The mechanical energy is solely in the form of potential energy.
3. Return Point: As the stone descends towards the person's hand, its kinetic energy starts increasing again, while its potential energy decreases. At the point where the stone reaches the same height it was thrown, it has zero potential energy, and its kinetic energy is at its maximum. The mechanical energy is again the sum of the kinetic and potential energy, with all the energy being in the form of kinetic energy.
In summary:
- At the start, the stone has higher kinetic energy and lower potential energy.
- At the highest point, the stone has zero kinetic energy and maximum potential energy.
- At the return point, the stone has maximum kinetic energy and zero potential energy.
- The mechanical energy remains constant throughout the trajectory, equal to the sum of kinetic and potential energy.
Remember that the conservation of mechanical energy states that the total mechanical energy of an object remains constant, as long as no external forces act on it.