Taking into account the potencial, kinetic and mechanical energy, the total mechanical energy is 278.005 J.
Potential energy refers to the position that a mass occupies in space and its magnitude is directly proportional to the height at which the object is, with respect to a reference position, to the mass of the object and to gravity:
Ep = m×g×h
On the other hand, kinetic energy manifests itself when bodies move and is associated with speed. The kinetic energy of a body depends on its mass and the square of its speed:
Ec = [tex]\frac{1}{2}[/tex]×m×v²
The mechanical energy of a body is the capacity it has to carry out mechanical work, that is, to produce a movement due to causes of mechanical origin, such as its position or its speed.
The mechanical energy of a body is the sum of its kinetic energy and its potential energy:
Em = Ep + Ec
Where
- Em is the mechanical energy (J).
- Ep the potential energy (J).
- Ec the kinetic energy (J).
Then:
Em= m×g×h + [tex]\frac{1}{2}[/tex]×m×v²
- Principle of conservation of mechanical energy
The Principle of conservation of mechanical energy indicates that, in the absence of friction and without the intervention of any external work, the sum of the kinetic and potential energies remains constant, that is, the mechanical energy of a body remains constant throughout the movement. if no friction force acts.
In this case, you know that:
- m= 3.5 kg
- g= 9.81 [tex]\frac{m}{s^{2} }[/tex]
- h= 3 m
- v= 10 [tex]\frac{m}{s}[/tex]
Complying with the Principle of Conservation of Mechanical Energy and replacing in the expression of mechanical energy:
Em= 3.5 kg×9.81 [tex]\frac{m}{s^{2} }[/tex]×3 m + [tex]\frac{1}{2}[/tex]×3.5 kg×(10 [tex]\frac{m}{s}[/tex])²
Solving:
Em=103.005 J + 175 J
Em= 278.005 J
Finally, the total mechanical energy is 278.005 J.
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