Question

if the gravitational p.e of abody at a distance r from the centre of earth is u, the weight of the body at that poi nt is: please solving answer

Answer 1

When two or more bodies interact with each other, some work has to be done in assembling them together in their respective places.

Total work done in assembling bodies together, in their respective places, is called gravitational potential energy of the system.

Potential energy of a system of two masses is defined as the amount of work done in bringing these two masses from infinity to their respective places.

In the right side figure, as the bag moves upwards, kinetic energy decreases, and gravitational energy increases. At the highest point (B) Kinetic energy is zero, and Gravitational potential energy is highest.

As the bag did not get to, it start falling from point B downwards due to gravity. It starts falling slowly (kinetic energy is low) and then speeds up downwards. 

At point A, bag is at full speed and kinetic energy is highest, whiles gravitational energy is nearly lost. 

When the bag of gold coins hits the ground, kinetic energy is converted into heat and sound by the impact.

It is worth noting that the higher the gravitational energy of an object moving downwards, the lower the kinetic energy, and the lower the kinetic energy of an object moving upwards, the higher its gravitational energy.

Gravitational Potential Energy of a System

Change in gravitational potential energy of a system is defined as the -ve of the work done by the gravitational force as the configuration of the system is changed.


Uf - Ui = Wgr

Change in gravitational potential energy of two point masses m1 and m2 as their separation is changed from r1 to r2 is given by

U(r2) - U(r1) = Gm1m2 [1/r1 - 1/r2]

If, at infinite separation, gravitational potential energy is assumed to be zero, then the gravitational potential energy of the above two point mass system at separation r,


The below figure shows that the energy of the dart/gun system is initially present in the form of the elastic potential energy (PEs) and gravitational potential energy (PEg). The springs of the dart gun are compressed which accounts for the elastic potential energy.