It is possible to warm your hands on a cold day by rubbing them together. Assume

Question

It is possible to warm your hands on a cold day by rubbing them together. Assume that the coefficient of sliding friction between your hands is 0.5, that the normal force between the hands is 50.0N (about 11lb), and that you rub them together with an average speed of 39.0cm/s. Assume that the mass being warmed on each hand is 38.0g (the outer skin layer), that the specific heat of skin is 4.0kJ/(kg*K), and that all the energy generated goes into raising the temperature of your hands. How long must you rub your hands together to produce a 2.0oC increase in temperature?

Explanation / Answer

Given that ,

Normal force Fn = 50 N

Coefficient of sliding friction µs = 0.5

Speed of the hands v = 39 cm/s = 0.39 m/s

Mass of the material being warmed on each hand = 38 g = 0.38 kg

Specific heat of the skin C = 4 kJ/kg K = 4000 J/kg K

Change in the temperature T = 2.00 C

The work done by rubbing converts to heat

So the heat gained be Q = M * C * T = 2 * m * C * T

Work done W = Force * distance = F * S = µs * Fn * v * t

Where M = 2 * m because we are given mass warmed in one hand so we have to double the mass to get total mass warmed

We can write distance as product of speed v and time t

Now work done = heat gained

Fn * µs * v * t = 2 * m * C * T

Then time t = ( 2 * m * C * T )/ ( Fn * µs * v )

                    = ( 2 * 0.38 * 4000 * 2 )/( 50 * 0.5 * 0.39 )

                        = 6080 / 9.75

                     = 623.5 sec = 10 mins 23 sec

So the time required to raise the temperature is t =623.5 sec

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