A 500 kg cannon rests on wheels that are free to roll. The cannon fires a 2 kg cannon ball horizontally with an average force of 400 N. What is the acceleration of the cannon ball? What is the recoil acceleration of the cannon
400 = 2*a(cb)
where a(cb) is acceleration of the cannon ball
400 = 500*a(c)
where a(c) is acceleration of the cannon
To determine the acceleration of the cannonball, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. The formula for Newton's second law is:
F = m * a
Where:
F is the force applied to the object (in this case, the cannonball),
m is the mass of the object (2 kg for the cannonball), and
a is the acceleration of the object.
Rearranging the formula to solve for acceleration (a), we get:
a = F / m
Now, we can substitute the given values into the equation:
a = 400 N / 2 kg
a = 200 m/s²
Therefore, the acceleration of the cannonball is 200 m/s².
To determine the recoil acceleration of the cannon, we can apply Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. In this case, the cannonball exerts a force on the cannon, resulting in a reaction force that causes recoil.
Since we know the mass of the cannon (500 kg) and the force exerted by the cannonball (400 N), we can use the formula of Newton's second law again:
F = m * a
Where:
F is the force exerted by the cannonball (400 N),
m is the mass of the cannon (500 kg), and
a is the recoil acceleration of the cannon.
Rearranging the formula to solve for acceleration (a), we get:
a = F / m
Substituting the given values into the equation:
a = 400 N / 500 kg
a = 0.8 m/s²
Therefore, the recoil acceleration of the cannon is 0.8 m/s².