Question

If we assume that 60 % of the kinetic energy delivered by a 1.80-kg hammer with a speed of 7.80 m/s is transformed into heat that flows into the nail and does not flow out, what is the temperature increase of an 8.00-g aluminum nail after it is struck ten times?

Answer 1

Answer:

45.6°C

Explanation:

Kinetic energy = $\frac{1}{2}mv^2$

Use m= 1.80kg and v=7.80m/s (mass and speed of hammer).

K = 0,5*1.80kg*(7.80m/s)^2 = K=54.8J

Heat is 60% of Kinetic energy. Q = 0.6*54.8J = 32.9J

As it is stuck 10 times the total heat is 10*32.9J = Total Heat = 329J

Use the equation $Q = mC_v \Delta T$ to find change of temperature:

$\Delta T = \frac{Q}{mC_v}$

Q = 329J; m = 8.00g of aluminium; C_v = 0.900J/g°C (For aluminium)

$\Delta T = \frac{329J}{8.00g*0.900J/g°C}$

Calculating gives Change of Temperature = 45.6°C