As part of a forensic test, a 5.0g lead bullet is fired into a fence post. the initial speed of the bullet is 250 m/s. when it comes to res, it is determined that half its kinetic energy had gone into heating the bullet. how much does the bullet's temperature change as a result of being fired into the post?
1/2 *(1/2 m v^20=m*specificheatlead*Deltatemp
1/4 v^2/specificheatlead =Deltatemp
122K
To determine the change in temperature of the bullet, we can start by calculating the initial kinetic energy (KE) of the bullet. The formula to calculate kinetic energy is:
KE = (1/2)mv^2
Where m is the mass of the bullet and v is its initial velocity.
Given:
Mass of the bullet (m) = 5.0 g = 0.005 kg
Initial velocity (v) = 250 m/s
Using the formula, we can calculate the initial kinetic energy (KE_initial) as follows:
KE_initial = (1/2) * m * v^2
= (1/2) * 0.005 kg * (250 m/s)^2
Now, since half of this kinetic energy is converted into heat, we can calculate the heat energy (Q) absorbed by the bullet using the formula:
Q = (1/2) * KE_initial
We can then use the specific heat capacity of lead (c) to calculate the change in temperature (ΔT) of the bullet. The specific heat capacity is the amount of heat energy required to raise the temperature of a given amount of substance by 1 degree Celsius.
The formula to calculate the change in temperature is:
ΔT = Q / (m * c)
Given:
Specific heat capacity (c) of lead = 130 J/kg°C
Now, we can calculate the change in temperature as follows:
Step 1:
Calculate the initial kinetic energy (KE_initial):
KE_initial = (1/2) * 0.005 kg * (250 m/s)^2
Step 2:
Calculate the heat energy absorbed (Q):
Q = (1/2) * KE_initial
Step 3:
Calculate the change in temperature (ΔT):
ΔT = Q / (m * c)
Using the given values and the formulas, you can now calculate the change in temperature of the bullet.