Question

An iron nail is driven into a block of ice by a single blow of a hammer. The hammerhead has a mass of 0.5 kg and an initial speed of 3.2 m/s. Nail and hammer are at rest after the blow. How much ice melts? Assume the temperature of both the ice and the nail is 0◦C before and after. The heat of fusion of ice is 80 cal/g. Answer in units of g.

Answer 1

Answer:

The ice melts mass is:

$m_g=7.6x10^{-3} g$

Explanation:

Kinetic Energy  

$K_E = 1/2*m*v^2$

$K_E = 1/2*0.5kg*(3.2m/s)^2$

$K_E=2.56 kg*m^2/s^2$

Heat gained by ice= mass(g) x 80 cal

( 1 cal = 4.184 *10^7er or g cm^2/ sec^2)

Assuming no loss in heat,  in the motion so both continue with temperature 0~C

To find so the mass (gm) of ice melted

$m_g= 1/2 *(0.5*1000)*(3.2m/s)^2* 100*100 / (80*4.184*10^7)$

$m_g=7.6x10^{-3} g$