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 43.0N (about 10lb), and that you rub them together with an average speed of 33.0cm/s. Assume that the mass being warmed on each hand is 38.0g (the outer skin layer), that the specific heat of skin is 4.4kJ/(kg*K), and that all the energy generated goes into raising the temperature of your hands.

a) How long must you rub your hands together to produce a 2.5^oC increase in temperature?

Thank you for your help

Answer 1

a)

N = normal force between the hands = 43 N

= Coefficient of friction between the hands = 0.5

frictional force between the hands is given as

f = N = (0.5) (43) = 21.5 N

v = speed of hands = 33 cm/s = 0.33 m/s

power is given as

P = f v

m = mass being warmed = 38 g = 0.038 kg

c = specific heat of skin = 4400 J/(kg -K)

T = Change in temperature = 2.5 ^oC

t = time taken

Using conservation of energy

P t = m c T

fvt = m c T

(21.5) (0.33) t = (0.038) (4400) (2.5)

t = 58.915 sec