# What is the gravitational potential energy?

What is the gravitational potential energy?

- Everyone knows that a large object placed high up represents a potentially dangerous situation for the person passing under it. This object can however be well wedged, and therefore does not necessarily represent a danger. This danger exists if the medium exerting the force that opposes gravity is unreliable. In physics, to quantify the energy of this mass in height, one speaks of gravitational potential energy .

We can associate a potential energy to each conservative force and gravity is no exception to the rule. The gravitational potential energy is usually denoted E_pE

p

E, start subscript, p, end subscript. This is the work that an object can provide due to its position in a gravitational field.

Take a mass objectmmmlifted to a heighthhh, as shown below. The object is lifted vertically via a pulley and rope system. The force exerted to lift the box and the force of gravity,F_gF

g

F, start subscript, g, end subscript, are therefore parallel. Whethergggis the intensity of the acceleration of gravity, we can determine the work done by the force on the object by multiplying the intensity of the force of gravity,F_gF

g

F, start subscript, g, end subscript, by the distance traveled vertically by the object,hhh. This calculation assumes that the acceleration due to gravity is constant over the heighthhh.

\begin{aligned}E_p &= F_g\cdot h \\ &= m\cdot g \cdot h\end{aligned}

E

p

=F

g

⋅h

=m⋅g⋅h

Gravitational potential energy builds up in the object when it is lifted vertically.

Gravitational potential energy builds up in the object when it is lifted vertically.

Gravitational potential energy builds up in the object when it is lifted vertically.

If the force exerted to lift the object were removed, it would fall back to the ground and the potential energy of gravity would be converted into kinetic energy during the fall. You will find in the article on the conservation of energy some examples of problems solved thanks to the principle of transformation of the potential energy of gravity into other forms of energy.

The interesting thing about gravitational potential energy is that its reference level is arbitrary. In other words, one can freely choose any level on the vertical axis as the point whereh=0h=0h, equals, 0. In simple mechanical problems, the zero point is often taken to be the floor or the surface of a table, because that is the most practical. However, one could choose any point of reference, sometimes called a reference frame . The gravitational potential energy could even be negative if the object passed below the reference level, but this is not a problem. It suffices to take care to keep the same frame of reference throughout the calculation.More details on negative energy (requires knowledge of integral calculus).

Exercise 1a: What electrical energy must an elevator motor with an overall efficiency of 25% supply to lift a 75 kg person to a height of 50 m? It is assumed that a counterweight keeps the elevator car in perfect balance when it is empty.

elevator system

elevator system

elevator system

See the answer.

Exercise 1b (subsidiary question): What is the cost of the elevator trip knowing that the cost of electricity is0{,}10 \dfrac{€}{\text{kW}\cdot \text{h}}0 , 1 0

kW⋅h

€

0, comma, 10, start fraction, €, divided by, start text, k, W, end text, dot, start text, h, end text, end fraction?See the answer.

Exercise 2:Gravitational potential energy is one of the few forms of energy that can easily be stored in very large quantities. To store excess electrical energy from solar or wind generation, it is necessary to be able to store large amounts of energy, which can then be transferred to the electrical grid when demand is higher. For this, pumped storage installations are used (see the example shown below). These hydroelectric plants are also called STEP (pumped energy transfer stations). Water is pumped into an upper reservoir using the excess energy, which powers a motor driving a pump-turbine. When energy demand is higher, the process is reversed. The pump becomes a generator powered by the gravitational potential energy of the water stored in the upper reservoir. Water can be released very quickly and provide thepower needed to cover the peaks in electricity consumption of an entire city, or even of severa

What is the gravitational potential energy?