Камень массой 200 г подкинули от уровня Земли вертикально вверх со скоростью 6 м/с. Пользуясь законом сохранения энергии, найдите максимальную высоту, на которую поднимется камень, а также кинетическую энергию камня на середине высоты полёта. Сделайте поясняющий рисунок с обозначением всех необходимых величин.
- Use the conservation of energy law to solve this problem. According to this law, the energy of a system remains constant, meaning that the initial energy of the stone must be equal to its energy at maximum height.
- Start by finding the potential energy of the stone at the beginning of its ascent. This can be calculated using the formula P = mgh, where m is the mass of the stone (200 g), g is the acceleration due to gravity (9.8 m/s²), and h is the initial height of the stone (in this case, the height of the Earth's surface).
- The stone also has kinetic energy at the start of its ascent, which can be calculated using the formula K = 0.5mv², where v is the initial velocity of the stone (6 m/s).
- At maximum height, the stone has no kinetic energy (since it stops moving) and all of its energy is in the form of potential energy. Therefore, we can set the potential energy at maximum height equal to the initial potential energy.
- To find the maximum height, set the potential energies at the beginning and end of the stone's ascent equal to each other and solve for h. This gives you the equation P = mgh = K = 0.5mv². Substitute in the values we know and solve for h. You should get a maximum height of approximately 2.45 meters.
- Finally, to find the kinetic energy at the midpoint of the stone's flight, you can use the formula K = 0.5mv² again, this time plugging in the midpoint velocity (which is half of the initial velocity) for v. This should give you a kinetic energy of approximately 0.45 joules.
Remember, the conservation of energy law applies to all types of energy, not just potential and kinetic. So even if the stone's height changes during its flight, the total energy of the system remains the same!
