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