Question

A 1.11 kg hammer strikes a 26 g silver nail into a wood board. The nail is horizontally aligned and at the moment of impact with the nail, the hammer had a speed of 8.6 m/s. Assume both the hammer and the nail come to a stop and that all of the thermal energy generated goes into heating the nail. Determine how much the temperature of the nail will increase after one hit and how many hits it will take to increase its temperature 91°C.
ΔT after one hit =  
Minimum number of hits needed to increase the temperature by at least 91°C =   hits

Answer 1

here,

mass of hammer , m1 = 1.11 kg

mass of Nail , m2 = 26 g = 0.026 kg

initial speed of hammer , u = 8.6 m/s

let the change in temperature of nail in one hit be dT

using conservation of energy

0.5 * m1 * u^2 = m2 * specific heat of silver * dT

0.5 * 1.11 * 8.6^2 = 0.026 * 24 * dT

dT = 6.58 degree

the increase in temperature of nail in each hit is 6.58 degree

the Minimum number of hits needed to increase the temperature by at least 91 C , N = 91 / dT

N = 91 /6.58 = 14 hits