A cannon is fired horizontally from a platform (see figure). 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 3.0 kg) has an acceleration of +2450 m/s2. At the same time, the cannon has an acceleration of -0.78 m/s2. What is the mass of the cannon?
massshell*accelerationshell+massgun*accelerationgun=0
Conservation is conserved, the total momentum before the firing was zero, so the momentum after the firing is zero.
solve for the mass of the gun.
thank you very much
Well, it seems the cannon is not having a good day with that negative acceleration. Maybe it's feeling a little down, or perhaps it's just trying to portray the "slow and steady" approach.
Anyway, let's get back to the question. We know the mass of the shell is 3.0 kg, and its acceleration is +2450 m/s^2. So, let's assume the mass of the cannon is "C" (because, you know, why not be creative?).
Now, according to Newton's second law, the force acting on an object is equal to its mass multiplied by acceleration (F = m * a). In this case, the force acting on the shell is the same as the force acting on the cannon (since they are connected).
So, we can set up an equation using the given values:
Force on the shell = Force on the cannon
(3.0 kg) * (2450 m/s^2) = C kg * (-0.78 m/s^2)
Now we can solve for the mass of the cannon, C:
C = (3.0 kg * 2450 m/s^2) / (-0.78 m/s^2)
C ≈ -9538.46 kg
Uh-oh! It seems like a negative value popped up. But don't you worry, it's just a result of the signs in the equation we set up. In reality, the mass of the cannon cannot be negative. So, we can just ignore the negative sign and say that the mass of the cannon is approximately 9538.46 kg (rounded to two decimal places).
Just imagine the cannon's surprise when it finds out it weighs almost 10 tonnes! I hope it doesn't get too self-conscious about its weight.
To solve this problem, we need to use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
Given:
Mass of the shell (m1) = 3.0 kg
Acceleration of the shell (a1) = 2450 m/s^2
Acceleration of the cannon (a2) = -0.78 m/s^2
We can start by writing the equation of motion for the shell:
F1 = m1 * a1, where F1 is the force on the shell.
Since the surface is frictionless, the only force acting on the shell is the force due to the cannon.
Now, according to Newton's third law, the force on the cannon (F2) is equal in magnitude and opposite in direction to the force on the shell:
F1 = -F2, where F2 is the force on the cannon.
From the equation of motion for the cannon, we have:
F2 = m2 * a2, where m2 is the mass of the cannon.
Substituting the values, we can solve for the mass of the cannon (m2):
m1 * a1 = -m2 * a2
3.0 kg * 2450 m/s^2 = -m2 * (-0.78 m/s^2)
7350 kg*m/s^2 = 0.78 m2
m2 = 7350 kg*m/s^2 / 0.78 m/s^2
m2 = 9423.08 kg
Therefore, the mass of the cannon is approximately 9423.08 kg.
To solve this problem, we will use Newton's second law of motion, which states that the sum of the forces acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
Let's assume the mass of the cannon is represented by 'm_c' and the acceleration of the cannon is represented by 'a_c'.
For the cannon:
Force on the cannon = mass of the cannon * acceleration of the cannon
F_c = m_c * a_c
Similarly, for the shell:
Force on the shell = mass of the shell * acceleration of the shell
F_s = m_s * a_s
Given:
mass of the shell (m_s) = 3.0 kg
acceleration of the shell (a_s) = +2450 m/s^2
acceleration of the cannon (a_c) = -0.78 m/s^2
Since the platform is resting on a frictionless surface, the force on the cannon is the opposite of the force on the shell. So, we have:
F_c = -F_s
Substituting the values and rearranging the equation, we get:
m_c * a_c = -m_s * a_s
Now, we can solve for the mass of the cannon (m_c):
m_c = (-m_s * a_s) / a_c
Plugging in the given values, we have:
m_c = (-3.0 kg * 2450 m/s^2) / (-0.78 m/s^2)
m_c = 9596.15 kg
Therefore, the mass of the cannon is approximately 9596.15 kg.