Work and Energy - Work done by the weight force and potential energy

Problem Statement:

A body of mass m = 4 kg is initially at rest at point A situated at a height hA = 10 m with respect to the surface of the Earth.

  1. Calculate the work of the weight force when the body descends from point A to point B situated at a height hB = 2 m.
  2. Compare this work with the variation of potential energy that the body experiences when it moves between points A and B.
  3. Calculate the velocity of the body when it reaches point B.

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Solution:

We have represented the physical situation described in the problem in the following figure.

The work of a force is given by:

The displacement vector dr for a straight path between points A and B is given by:

The force, in this case the weight, written using its vector components is:

We substitute both vectors in the work definition:

And after substituting the givens of the problem statement we obtain:


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The weight is a conservative force; therefore it is associated with a potential (gravitational) energy, which is given by the following expression:

The variation of potential energy that the mass experiences when it moves from point A to point B will then be:

And after substituting the givens we obtain:

Therefore, the following relationship is fulfilled between the work and the potential energy variation:

The above relationship is valid for all conservative forces.


To calculate the velocity of the mass at point B we will use the following relationship:

In the problem we have used g = 10 m/s2

Do not forget to include the units in the results of the problems.

 

 

 

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