A 70g steel bullet moves at 200m/s just before imbedding itself into a thick anchored wood post. If 70% of the initial kinetic energy goes into heating the bullet (steel c = 460 J/kg-C)...how hot does the bullet become if it initially is at 26 degrees Celsius? What would be the bullet's temperature if it had been twice as massive (2 times 70g)?

Question

A 70g steel bullet moves at 200m/s just before imbedding itself into a thick anchored wood post. If 70% of the initial kinetic energy goes into heating the bullet (steel c = 460 J/kg-C)...how hot does the bullet become if it initially is at 26 degrees Celsius? What would be the bullet's temperature if it had been twice as massive (2 times 70g)?

Answer 1

To find the temperature the bullet reaches after the collision and the percentage of kinetic energy converted into heat, we can use the following steps:

Step 1: Calculate the initial kinetic energy of the bullet.
The formula for kinetic energy is:
Kinetic energy (KE) = (1/2) * mass * velocity^2

Given:
Mass of the bullet (m) = 70g
Velocity of the bullet (v) = 200m/s

Converting the mass from grams to kilograms:
m = 70g = 0.07kg

Calculating the kinetic energy:
KE = (1/2) * m * v^2

Step 2: Calculate the energy converted into heat.
Given that 70% of the initial kinetic energy goes into heating the bullet, we can calculate it using the formula:
Heat energy (Q) = 70% * KE

Step 3: Calculate the temperature change of the bullet.
Using the formula for heat energy:
Q = mass * specific heat capacity * temperature change

Given:
Specific heat capacity of steel (c) = 460 J/kg-C
Initial temperature of the bullet (T_initial) = 26 degrees Celsius

Rearranging the formula to solve for the temperature change:
Temperature change (ΔT) = Q / (mass * c)

Substituting the known values into the equation:
ΔT = (0.7 * KE) / (m * c)

Step 4: Calculate the final temperature of the bullet.
Final temperature (T_final) = T_initial + ΔT

Now, let's calculate both the temperature the bullet reaches and its temperature if it had been twice as massive:

For the original bullet:
Step 1: Calculate the initial kinetic energy.
KE = (1/2) * 0.07 * 200^2

Step 2: Calculate the energy converted into heat.
Q = 0.7 * KE

Step 3: Calculate the temperature change.
ΔT = (0.7 * KE) / (0.07 * 460)

Step 4: Calculate the final temperature.
T_final = 26 + ΔT

For the bullet with twice the mass (140g):
Step 1: Calculate the initial kinetic energy.
KE = (1/2) * 0.14 * 200^2

Step 2: Calculate the energy converted into heat.
Q = 0.7 * KE

Step 3: Calculate the temperature change.
ΔT = (0.7 * KE) / (0.14 * 460)

Step 4: Calculate the final temperature.
T_final = 26 + ΔT

By following these steps and plugging in the respective values into the equations, you will be able to find the temperature the bullet reaches and its temperature if it had been twice as massive.