Respuesta :
Answer:
[tex]\displaystyle W=-m.g.H[/tex]
Explanation:
Energy Transformation
Also called as energy conversion, is the process where energy changes from one form to another. There are three types of energy present in this problem. When the object is at rest at the top of the ramp, it has gravitatory potential energy, calculated as
[tex]U=m.g.H[/tex]
When the object slides down the frictionless ramp, it loses all of the potential energy since it's converted to kinetic energy, given by
[tex]\displaystyle K=\frac{m.v^2}{2}[/tex]
Thus
[tex]K=m.g.H[/tex]
Finally, when the object is in contact with a rough surface, all the energy is transformed into thermal energy. The work done by the friction force is equivalent to the change of kinetic energy, since all the velocity is lost during the process:
[tex]\displaystyle W=\Delta E=K_f-K=0-K=-\frac{m.v^2}{2}[/tex]
Since the kinetic energy is equal to the original potential energy:
[tex]\boxed{\displaystyle W=-m.g.H}[/tex]
The negative sign indicates the work was against the movement, i.e. the force and the displacement are 180° apart.
Note this result does not depend on the distance D needed to stop the block or the coefficient of kinetic friction.
The macroscopic work done on the block by friction during this process is -mgh
Kinetic energy:
All of the potential energy will be considered kinetic since it slides down the ramp, so the friction does negative work to slow the box to stop
We know that
Change in kinetic energy=total work done on the object
Here
dk=work done during friction+work done due to gravity
0= wfrict+wgravity
And,
wfrict=-wgravity=-mgh
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