15. An iron plate is held against an iron wheel so that a sliding frictional for

Question

15. An iron plate is held against an iron wheel so that a sliding frictional force of 50 N acts between the two pieces of metal. The relative speed at which the two surfaces slide over each other is 40 m/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 kg each, and each receives 50% of the internal energy. If the system is run as described for 10 s and each object is then allowed to reach a uniform internal temperature, what is the resultant temperature increase?

Explanation / Answer

Internal energy simply means the kinetic and potential energy of the individual atoms or molecules in an object. If you heat something, its internal energy increases.

If you rub something, you are doing mechanical work and providing energy; the energy gets turned to heat which increases the temperature of the object being rubbed - so its internal energy increases.

a) P = Fv = 50 * 40 = 2000 W

(This means each second 2016J of mechanical work are done (e.g. by a motor powering the system).
If we assume all the energy is turned to heat and increases the temperature of the iron plate and wheel, then the internal energy of the iron plate and wheel increase by 2016J each second.)
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b) In 10s the amount of work done = 2000 x 10 = 20000J. This is the heat produced in 10s.
Half(50%) of this (10000J) goes to the plate and the other half to the wheel. If T is the temperature rise of each object, then taking the specific heat capacity of iron as 450 J/(kg.degC)

Q = mcT
10,000 = 5 x 450 x T
T = 4.44 degC

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