a lead bullet at 100C strikes a steel plate and melts. what was its maximum speed? the specific heat of lead is 0.13 kJ/kg C
To determine the maximum speed of the lead bullet, we need to calculate the amount of heat energy transferred from the bullet to the steel plate. We can then use this energy to find the bullet's maximum speed using the principle of conservation of mechanical energy.
Let's break down the problem step-by-step:
Step 1: Calculate the heat energy transferred
The heat energy transferred can be calculated using the formula:
Q = m * c * ΔT
Where:
Q = heat energy transferred (in joules)
m = mass of the bullet (in kilograms)
c = specific heat capacity of lead (in kJ/kg°C)
ΔT = change in temperature (in °C)
In this case, we know:
m = mass of the bullet = unknown
c = specific heat capacity of lead = 0.13 kJ/kg°C
ΔT = change in temperature = (final temperature - initial temperature)
Since the bullet melts after striking the steel plate, we can assume its final temperature is the melting point of lead, which is 327.5°C. Additionally, we know the initial temperature of the bullet is 100°C.
ΔT = (327.5 - 100) = 227.5°C
Now we can calculate the heat energy transferred (Q).
Step 2: Calculate the bullet's maximum kinetic energy
By assuming all the heat energy transferred is used to melt the bullet, we can calculate the bullet's maximum kinetic energy using the equation:
Kinetic energy = Q
Step 3: Relate kinetic energy to velocity
The kinetic energy (KE) of an object can be related to its velocity (v) using the equation:
KE = (1/2) * m * v^2
Where:
KE = kinetic energy (in joules)
m = mass of the bullet (in kilograms)
v = velocity of the bullet (in meters per second)
Now, we substitute the calculated kinetic energy (Q) into this equation to solve for the velocity of the bullet (v).
Kinetic energy = (1/2) * m * v^2
Step 4: Calculate the maximum speed
Once we have the velocity (v), we can find the maximum speed of the bullet since velocity is a vector quantity that includes direction. The magnitude of the velocity vector is the speed.
Therefore, the maximum speed of the lead bullet can be calculated by taking the magnitude of the velocity vector.
It's important to note that we have assumed no other external forces (such as air resistance or friction) acting on the bullet during its motion. These assumptions may affect the accuracy of the calculated results.
By following these steps, we can find the maximum speed of the lead bullet when it melts upon striking the steel plate.