3. In a closed system where non-conservative forces (such as friction) are prese

Question

3. In a closed system where non-conservative forces (such as friction) are present, energy is still conserved but in
addition to the potential and kinetic, the energy converted to heat (in the case of friction) must be considered
as well. Consider a 20 [kg] box sliding down an incline plane. If the block starts from rest at a height of 8 [m] and has
a speed of 5 [m/s] after sliding 10 [m] down the incline (call the height at this point 0 [m]) and assuming
that friction is the only non-conservative force, calculate the work done by friction on the box after sliding
down the incline.

Explanation / Answer

In a CLOSED system energy is conserved. ie it can move from one type of energy or work to another; the TOTAL system energy remains constant, and available to be transfered to any other form of energy within that CLOSED system. Therefore by definition a system in which energy is conserved is called a CLOSED system.

Another {more descriptive} name for "resistive forces" is "nonconservative forces".

A nonconservative force {resistive force} produces work within a system that is NOT returned to the system's TOTAL energy for further transfer or use. It is effectively a LEAK in the TOTAL ENERGY of the system and makes that system a so called "OPEN system". In an OPEN system total energy is NOT conserved.

Since the first incline is frictionless, there is no energy loss in coming down. Hence KE at the foot of the incline = PE at the start. This gives the velocity at the foot of the first incline as
1/2 m*v^2 = m*g*h.
The frictional force on the horizontal surface = Uk*m*g
The work done in overcoming the fricional force =Uk*m*g*L

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