A nail driven into a board increases in temperature. If we assume that 88.6 % of the kinetic energy delivered by a 2.3-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 in K of an 272 g aluminum nail after it is struck ten times? Assuming the specific heat capacity of aluminium is 0.9 JK-1g-1

1/2 mv^2 = mc changeT

or in this case: 10 * .886 * 1/2 mv^2 = mc changeT
First m is hammer, second is nail

do i need to convert kg to g?

To calculate the temperature increase of the aluminum nail after being struck ten times, we need to determine the amount of heat transferred to the nail during each strike, and then sum up the total heat transferred.

1. Calculate the initial kinetic energy of the hammer:
KE = (1/2) * m * v^2
KE = (1/2) * 2.3 kg * (7.80 m/s)^2
KE = 44.97 J

2. Calculate the amount of heat transferred to the nail during each strike:
Q = 0.886 * KE
Q = 0.886 * 44.97 J
Q = 39.84 J

3. Calculate the total heat transferred to the nail after ten strikes:
Q_total = 10 * Q
Q_total = 10 * 39.84 J
Q_total = 398.4 J

4. Calculate the temperature increase of the nail using the specific heat capacity:
ΔT = Q_total / (m * c)
ΔT = 398.4 J / (0.272 kg * 0.9 J/Kg·K)
ΔT = 1624.17 K

Therefore, the temperature increase of the 272 g aluminum nail after being struck ten times is approximately 1624.17 K.

To solve this problem, we need to calculate the heat generated by each strike of the hammer and then find the total heat generated by all ten strikes. Finally, we can use the specific heat capacity to calculate the temperature increase.

1. Calculate the kinetic energy delivered by the hammer:
The kinetic energy (KE) is given by the equation KE = 0.5 * mass * velocity^2. Plugging in the values, we have:
KE = 0.5 * 2.3 kg * (7.80 m/s)^2

2. Calculate the heat generated by each strike:
Since 88.6% of the kinetic energy is transformed into heat, we can multiply the calculated KE by 0.886 to get the heat generated by each strike.

3. Calculate the total heat generated by all ten strikes:
Multiply the heat generated by each strike by 10 (number of strikes) to find the total heat generated.

4. Calculate the temperature increase:
To calculate the temperature increase, we can use the formula: ΔT = Q / (m * c), where ΔT is the temperature increase, Q is the total heat generated, m is the mass of the nail, and c is the specific heat capacity of aluminum.

Plug in the values to calculate the temperature increase:
ΔT = Q / (0.272 kg * 0.9 J/(kg·K))

By following these steps and plugging in the values, you can calculate the temperature increase in Kelvin (K) for the aluminum nail after it is struck ten times.