If you ever slapped someone or got slapped yourself, you probably remember the burning sensation. Imagine you had the unfortunate occasion of being slapped by an angry person, which caused the temperature of the affected area of your face to rise by 2.4°C (ouch!). Assuming the slapping hand has a mass of 0.6 kg and about 0.150 kg of the tissue on the face and the hand is affected by the incident, estimate the velocity of the hand just before impact. Take the specific heat of the tissue to be 3.8 kJ/kg·K.

v= 2.14m/s

Explanation: according to the law of conservation of energy, the heat energy on the tissue equals the kinetic energy of the hand.

Heat energy = m'cΔθ

Kinetic energy = 1/2mv²

m' = mass of the tissue = 0.150kg, c= specific heat capacity of tissue = 3.8j/kg/k, Δθ = 2.4°c, m = mass of hand = 0.6kg, v = velocity of hand.

m'cΔθ = 1/2mv²

By substituting the parameters, we have that

0.150 * 3.8 * 2.4 = 1/2 * 0.6 * v²

0.150 * 3.8 * 2.4 * 2 = 0.6 * v²

2.736 = 0.6 * v²

v² = 2.736/ 0.6

v² = 2.14 m/s

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