A nail driven into a board increases in temperature. If 60% of the kinetic energy delivered by a 1.8 kg hammer with a speed of 7.8 m/s is transformed into heat that flows into the nail and does not flow out, what is the increase in temperature of an 8 g aluminum (c = 900 J/(kg • C°)) nail after it is struck 10 times

To find the increase in temperature of the nail after it is struck 10 times, we need to calculate the amount of heat transferred to the nail.

The formula to calculate the heat transferred is given by:

Q = m * c * ΔT

Where:
Q is the heat transferred
m is the mass of the object (in kg)
c is the specific heat capacity of the material (in J/(kg • C°))
ΔT is the change in temperature (in C°)

First, let's calculate the heat transferred in each strike. We know that 60% of the kinetic energy delivered by the hammer is transformed into heat. So, we can calculate the kinetic energy of the hammer using the formula:

KE = (1/2) * m * v^2

Where:
m is the mass of the hammer (in kg)
v is the speed of the hammer (in m/s)

Given:
Mass of hammer (m) = 1.8 kg
Speed of hammer (v) = 7.8 m/s

Plugging in the values, we can calculate the kinetic energy of the hammer:

KE = (1/2) * 1.8 kg * (7.8 m/s)^2

Next, we need to calculate the heat transferred to the nail in each strike. Since 60% of the kinetic energy is transformed into heat, we can calculate it using:

Heat (Q) = 0.6 * KE

Now we have the heat transferred in one strike. We can multiply it by the number of strikes (10) to find the total heat transferred to the nail:

Total Heat (Q_total) = Q * 10

Now we have the total amount of heat transferred to the nail. To find the change in temperature (ΔT) of the nail, we rearrange the formula:

ΔT = Q_total / (m_nail * c_nail)

Where:
m_nail is the mass of the nail (in kg)
c_nail is the specific heat capacity of aluminum (in J/(kg • C°))
ΔT is the change in temperature (in C°)

Given:
Mass of nail (m_nail) = 8 g = 0.008 kg
Specific heat capacity of aluminum (c_nail) = 900 J/(kg • C°)

Plugging in the values, we can calculate the change in temperature:

ΔT = Q_total / (0.008 kg * 900 J/(kg • C°))

Now you can calculate ΔT by substituting the values into the equation and solving for ΔT. The answer will give you the increase in temperature of the aluminum nail after it is struck 10 times

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