A cannon is fired horizontally from a platform . The platform rests on a flat, icy, frictionless surface. Just
after the shell is fired and while it is moving through the barrel
of the gun, the shell (mass 3.2 kg) has an acceleration of 12500 m/s2. At the same time, the cannon has an acceleration of �0.76 m/s2. What is the mass of the cannon?
To find the mass of the cannon, we can use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration:
Force = mass * acceleration
In this case, we know the acceleration of the shell (12500 m/s^2) and the cannon (-0.76 m/s^2), but we don't know the mass of the cannon. However, we can assume that the force acting on the shell and the cannon are equal and opposite (due to Newton's third law of motion).
Thus, the force acting on the shell is given by: Force_shell = mass_shell * acceleration_shell
The force acting on the cannon is given by: Force_cannon = mass_cannon * acceleration_cannon
Since the forces are equal and opposite, we can set up the following equation:
mass_shell * acceleration_shell = -mass_cannon * acceleration_cannon
Substituting the given values:
3.2 kg * 12500 m/s^2 = -mass_cannon * -0.76 m/s^2
Simplifying the equation:
mass_cannon = (3.2 kg * 12500 m/s^2) / -(-0.76 m/s^2)
mass_cannon = (3.2 kg * 12500 m/s^2) / 0.76 m/s^2
Now we can calculate the mass of the cannon:
mass_cannon = 52,604.17 kg
Therefore, the mass of the cannon is approximately 52,604.17 kg.