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In this case, the total mechanical energy is not conserved . Therefore, external forces are often referred to as non-conservative forces.
A quick review of internal forces
On the other hand, you also learned that if work is done on an object only by internal forces, the total mechanical energy possessed by the object cannot change. However, it can be transformed from potential energy to kineticenergy and vice versa.
In this case, the total mechanical energy is conserved . Therefore, internal forces are often referred to as conservative forces.
A quantitative relationship
The quantitative relationship between work and mechanical energy can be stated as follows:
MEf = MEi + We
where
This equation states that the final amount of mechanical energy possessed by an object is equal to the initial mechanical energy plus the work done on theobject by external forces.
Potential energy plus kinetic energy
The total mechanical energy at any point in time can be the sum of potential energy (gravitational or elastic potential energy) and kinetic energy due to motion.
Given that, we can rewrite the earlier equation as:
KEf + PEf = KEi + PEi + We
where
As mentioned, the work done by external forces can be either positive or negative work. Whether the work is positive or negative depends on the cosine ofthe angle between the direction of the force and the direction of the displacement of the object.
Consider the following scenario. The owners of an experimental rocket lift the rocket onto a platform above ground level and set it up for firing.
Later, when they fire the rocket, it goes straight up while the rocket engine is burning. When the rocketengine runs out of fuel and stops burning, the rocket coasts to its apex and stops climbing.Then it falls back to the surface of the earth in an unglamorous free fall.
Simplifying assumptions
We will make some simplifying assumptions:
Initial conditions
Here are the initial conditions for the rocket experiment:
Legs of the trip
We will analyze the rocket's round trip from the ground, into the air, and back to the ground in several legs as described below:
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