Work through kinetic energy

After applying the brake, the car skids to a stop

In our studies of energy we saw that the work of a force is nothing more than a way of measuring the amount of energy transferred or transformed from one system to another. This article will try to explain the matter in a simple way, performing the calculations of the work through the variation of the kinetic energy of a system.

Let’s calculate the work of a force in the following situation: a car of mass 6 000 kg, whose speed is 15 m/s, that is, 54 km/h, receives a force exerted on its brake, with an average intensity of 16 000 N This force has the same direction and opposite direction as the car’s displacement and causes it to stop after a distance of approximately 60 m.

Based on this information given above, we will first determine the value of the final and initial kinetic energies of the automobile. According to the mass and the initial and final velocities, we have:

The value of the work of the resultant force acting on an object during an interval of time is equal to the change in the kinetic energy of the object during the elapsed time interval. Therefore, we have:

Based on the information above, let us calculate the value of the change in kinetic energy (ΔEc) suffered by the car. 

The value found is nothing more than the work value of the resulting force:

In the result above we have a negative sign, this means that the car loses kinetic energy, transforming it into thermal energy in the tire and on the ground due to the contact forces. This result is valid for any situation and not just for the example presented.

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