7. A warship with a mass of 1.5x106 kg, fired a 75 kg shell from a gun with a 3.0 m long barrel in 0.05 seconds.
a. What was the acceleration of the shell?
To calculate the acceleration of the shell, we need to use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
In this case, we know the mass of the shell is 75 kg, so we need to find the force acting on the shell.
The force can be found using the equation:
Force = Mass * Acceleration
However, we don't have the force directly given. Instead, we can use the concept of impulse, which is the change in momentum of an object. The impulse experienced by the shell is equal to the force applied to it multiplied by the time it took to apply the force:
Impulse = Force * Time
We know the impulse because the shell was fired from the gun, so we can rearrange the equation and solve for force:
Force = Impulse / Time
Substituting the values we have:
Impulse = Mass * Change in Velocity
We know the mass of the shell is 75 kg and the change in velocity can be found using the formula:
Change in Velocity = Final Velocity - Initial Velocity
Since the shell was initially at rest in the gun barrel, the initial velocity is 0 m/s. The final velocity of the shell can be found using the formula:
Final Velocity = Distance / Time
The distance traveled by the shell is given as the length of the gun barrel, 3.0 m, and the time taken is given as 0.05 seconds.
Final Velocity = 3.0 m / 0.05 s
Once we have the final velocity, we can calculate the change in velocity and substitute it back into the impulse equation to find the force.
Finally, we can use the resulting force and the mass of the shell to calculate the acceleration by rearranging the equation:
Force = Mass * Acceleration
Acceleration = Force / Mass
Using these steps, you will be able to calculate the acceleration of the shell.