Final answer:
To calculate the temperature increase of an aluminum nail hit by a hammer, convert the kinetic energy of the hammer to heat, and then use the specific heat of aluminum to find the change in temperature. The nail's temperature increase is found by calculating the heat transferred after ten strikes and dividing it by the product of the nail's mass and the specific heat capacity of aluminum.
Step-by-step explanation:
The question involves calculating the temperature increase of an aluminum nail after being struck by a hammer. This requires understanding the transfer of kinetic energy into heat and then using the specific heat capacity of aluminum to find the temperature change.
Step-by-Step Solution
Firstly, calculate the total kinetic energy (KE) delivered to the nail by using the formula KE = 1/2 * m * v^2, where m is the mass of the hammer, and v is its speed. Using the given values, m = 1.80 kg and v = 7.80 m/s, the KE = 1/2 * 1.80 kg * (7.80 m/s)^2 = 54.684 J.
Since it is given that 60% of this energy is transformed into heat, the heat (Q) transferred to the nail after one strike is Q = 0.60 * KE. Therefore, the heat transferred after ten strikes is 10 * Q.
Next, to find the temperature increase (ΔT), use the formula Q = m * c * ΔT, where m is the mass of the nail, c is the specific heat capacity of aluminum (c = 900 J/kg°C for aluminum), and ΔT is the temperature change. The heat transferred to the nail after ten strikes can be equated to the heat absorbed by the nail, allowing us to solve for ΔT.
By rearranging the formula to ΔT = Q / (m * c) and inserting the values for Q, m (0.008 kg for the 8.00 g nail), and c, we can compute the temperature increase of the nail.