Question

В каком случае два тела разной массы, поднятые на разную высоту, будут иметь одинаковую энергию

Answer 1

Пусть m1>m2    сравнить h1 и h2

m1*g*h1=m2*g*h2
m1/m2=h2/h1

значит надо поднять тело на высоту h2>h1

h2=h1*m1/m2

Answer 2

 m1gh1=m2gh2, отсюда m1/m2=h2/h1, т. е. отношение масс должно быть обратно пропорционально высотам.Также можно доказать геометрически. Рисунок приложил

Answer 3

Case of Two Bodies with Different Masses and Equal Energy

When two bodies of different masses are raised to different heights, they will have equal potential energy when the heights and masses are such that the product of mass and gravitational potential energy is the same for both bodies. This occurs when the product of mass and gravitational potential energy is equal for both bodies.

Gravitational Potential Energy Formula: The gravitational potential energy (U) of an object of mass (m) at a height (h) above the reference point is given by the formula: U = mgh Where: - U = gravitational potential energy - m = mass of the object - g = acceleration due to gravity - h = height above the reference point

Condition for Equal Potential Energy: For two bodies with masses m1 and m2 raised to heights h1 and h2 respectively to have equal potential energy, the condition is: m1 * g * h1 = m2 * g * h2

This means that the product of mass and height for both bodies must be equal for them to have the same potential energy.