An iron plate is held against an iron wheel so that a...

An iron plate is held against an iron wheel so that a sliding frictional force of $50 \mathrm{~N}$ acts between the two pieces of metal. The relative speed at which the two surfaces slide over each other is $40 \mathrm{~m} / \mathrm{s}$. (a) Calculate the rate at which mechanical energy is converted to internal energy. (b) The plate and the wheel have masses of $5.0 \mathrm{~kg}$ each, and each receives $50 \%$ of the internal energy. If the system is run as described for $10 \mathrm{~s}$ and each object is then allowed to reach a uniform internal temperature, what is the resultant temperature increase?

An iron plate is held against an iron wheel so that a sliding frictional force of $50 \mathrm{~N}$ acts between the two pieces of metal. The relative speed at which the two surfaces slide over each other is $40 \mathrm{~m} / \mathrm{s}$. (a) Calculate the rate at which mechanical energy is converted to internal energy.
(b) The plate and the wheel have masses of $5.0 \mathrm{~kg}$ each, and each receives $50 \%$ of the internal energy. If the system is run as described for $10 \mathrm{~s}$ and each object is then allowed to reach a uniform internal temperature, what is the resultant temperature increase?

Key Concepts

Work-Energy Principle

This principle states that the work done by forces on a system leads to a change in the energy of that system. In this scenario, the mechanical work done by friction is directly related to the increase in internal energy and, ultimately, the increase in temperature.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of a unit mass of a substance by one degree. In this context, it is used to determine how much the temperature of the iron objects increases when the converted internal energy is absorbed.

Energy Distribution

Energy distribution involves how the internal energy, generated by friction, is shared between multiple objects. When energy is split evenly between the objects, each one's temperature increase is calculated based on the fraction of energy it receives, its mass, and its specific heat capacity.

Frictional Power

This concept involves calculating the rate at which work is done by friction. When two surfaces slide against each other, the frictional force multiplied by the relative velocity gives the power, or the rate of energy conversion from mechanical energy to internal (thermal) energy.

Energy Conversion

Energy conversion here refers to the transformation of mechanical energy into internal energy due to friction. The work done against friction is not lost but is converted into heat, raising the internal energy of the materials involved.

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