A 5.00g lead bullet is fired into a wooden fence post. The initial speed of the bullet is 250m/s, and when it comes to rest, half its kinetic energy goes into heating bullet. How much does the bullet's temperature increase?
The heat capacity of lead is C = .127.10^3J/kg*K (I googled it)
So the heat capacity of the bullet is Cm=.635 J/K
The kinetic energy of your bullet is KE = 1/2*5.10^-3 250^2 J
Therefore the increase in temp will be 1/2KE/(Cm) = 123 degrees
To determine the increase in temperature of the bullet, we can use the equation:
ΔT = ΔQ / (m * C)
Where:
ΔT is the change in temperature of the bullet,
ΔQ is the heat energy absorbed by the bullet,
m is the mass of the bullet, and
C is the specific heat capacity of the bullet material.
First, let's calculate the heat energy absorbed by the bullet. Since half of the bullet's kinetic energy goes into heating, we can use the equation:
ΔQ = 0.5 * KE
Where:
ΔQ is the heat energy absorbed by the bullet, and
KE is the initial kinetic energy of the bullet.
The initial kinetic energy of the bullet can be calculated using the equation:
KE = 0.5 * m * v^2
Where:
m is the mass of the bullet, and
v is the initial velocity of the bullet.
Let's calculate the initial kinetic energy of the bullet:
KE = 0.5 * 5.00 g * (250 m/s)^2
Note: To perform the calculations, we need to convert the mass of the bullet from grams to kilograms:
5.00 g = 0.005 kg
KE = 0.5 * 0.005 kg * (250 m/s)^2
Now, let's calculate the heat energy absorbed by the bullet:
ΔQ = 0.5 * KE
ΔQ = 0.5 * (0.5 * 0.005 kg * (250 m/s)^2)
Next, we need to find the specific heat capacity of lead. The specific heat capacity (C) of lead is approximately 128 J/(kg·K).
Now, let's calculate the change in temperature of the bullet:
ΔT = ΔQ / (m * C)
ΔT = (0.5 * (0.5 * 0.005 kg * (250 m/s)^2)) / (0.005 kg * 128 J/(kg·K))
By performing the necessary calculations, we can find the change in temperature of the bullet.
To find the increase in temperature of the bullet, we can use the principle of conservation of energy. The kinetic energy of the bullet is converted into heat energy, so we need to calculate the change in kinetic energy and then convert it to heat.
First, let's find the initial kinetic energy of the bullet:
Initial Kinetic Energy = (1/2) * mass * speed^2
Mass = 5.00 g = 0.005 kg
Speed = 250 m/s
Initial Kinetic Energy = (1/2) * 0.005 kg * (250 m/s)^2
Next, let's find the final kinetic energy of the bullet. Since the bullet comes to rest, its final kinetic energy will be zero.
Final Kinetic Energy = 0
Now, the change in kinetic energy is given by:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Change in Kinetic Energy = 0 - [(1/2) * 0.005 kg * (250 m/s)^2]
Next, we need to convert this change in kinetic energy to heat energy. We know that half of the kinetic energy is converted into heat energy.
Heat Energy = (1/2) * Change in Kinetic Energy
Heat Energy = (1/2) * [0 - (1/2) * 0.005 kg * (250 m/s)^2]
Finally, to find the increase in temperature, we need to use the specific heat capacity of lead (C) and the mass of the bullet (m).
Increase in Temperature = Heat Energy / (m * C)
The specific heat capacity of lead is approximately 128 J/(kg⋅°C).
Increase in Temperature = [(1/2) * [0 - (1/2) * 0.005 kg * (250 m/s)^2]] / (0.005 kg * 128 J/(kg⋅°C))
By simplifying the expression, you can calculate the increase in temperature of the bullet.