On a playground slide, a child has potential energy that decreases by 1000 \rm J while her kinetic energy increases by 900 \rm J. What other form of energy is involved, and how much?
In this scenario, the other form of energy involved is likely the energy dissipated as heat due to friction. To find out how much energy is dissipated as heat, we need to use the principle of conservation of energy.
The principle of conservation of energy states that the total energy of a closed system remains constant. In this case, the energy decreases by 1000 J in potential energy and increases by 900 J in kinetic energy. Therefore, the difference of 1000 J - 900 J = 100 J must be dissipated as heat.
Hence, the amount of energy dissipated as heat is 100 J.
To answer this question, we can use the conservation of energy principle. According to this principle, the total amount of energy in a system remains constant, with energy being transferred or transformed between different forms.
In this case, we know that the child's potential energy decreases by 1000 J and her kinetic energy increases by 900 J. Since the total energy should remain constant, we can find the amount of energy involved in another form.
The initial total energy (Ei) is the sum of the potential energy (PEi) and the kinetic energy (KEi) of the child before going down the slide. The final total energy (Ef) is the sum of the potential energy (PEf) and the kinetic energy (KEf) of the child after sliding down.
Ei = PEi + KEi
Ef = PEf + KEf
According to the conservation of energy principle:
Ei = Ef
Since the potential energy decreases by 1000 J and the kinetic energy increases by 900 J, we can write the equations:
Ei - 1000 J = Ef
Ei = Ef + 900 J
Equating the two equations, we get:
Ef + 900 J = Ef - 1000 J
Simplifying the equation, we find:
1900 J = -1000 J
Since the equation is inconsistent, it means that there is a form of energy involved that we haven't accounted for yet. The difference of 1900 J represents the energy involved in this other form.
Therefore, there is another form of energy involved, and its amount is 1900 J.