Question

What is the relationship between height and gpe

Answer 1

The relationship between height and gravitational potential energy is directly proportional, following the equation G.P.E. = mgh. GPE increases as the height of an object increases, and it is measured in Joules, reflecting the energy due to the object's position above a reference level.

Step-by-step explanation:

The relationship between height (h) and gravitational potential energy (GPE) is directly proportional. This means, as an object is raised to a higher elevation above the ground, its GPE increases. The formula for calculating GPE is G.P.E. = mgh, where m represents the mass of the object in kilograms, g is the acceleration due to gravity (approximately 10 m/s² on Earth's surface), and h is the height in meters. The unit of GPE is Joules, which quantifies the energy associated with the object's position in the gravitational field.

In physics, only the change in GPE (ΔGPE) is of significance, which is measured as the difference in energy when an object's height changes relative to a reference level. For instance, if a 0.500-kg mass from a cuckoo clock is lifted by 1.00 m, its GPE changes by mgh. The concept of GPE is vital in various applications, including understanding how energy is conserved within systems influenced by gravitational forces.

Answer 2

Let the force exerted by Earth on an object of mass 'm' at height 'h' where the gravitational acceleration is 'g' be 'F' and the potential energy of the object be 'E'.

We know,
F = mg
(for a body experiencing gravitational pull of magnitude 'g')

And, E = mgh
Replacing mg = F in E, we get:
E = F x h

That is the relation between potential energy for a body at height 'h' and the gravitational force it experiences at that height.