What Is the Cannon's Velocity Relative to the Ground?

In summary, a cannon firing a cannon ball at an angle above the horizontal will possess both y and x-axis velocities due to conservation of momentum. However, if the cannon is moving down into the ground, the y velocity with respect to the ground will stay zero. The velocity of the cannon with respect to the Earth should be the x velocity. Including the Earth in the system will conserve total momentum, but this is not important due to the Earth's larger mass.
  • #1
lvslugger36
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Suppose there is a cannon that shoots a cannon ball at a certain angle above the horizontal (a projectile). Since momentum is conserved in both directions, the cannon should posses a velocity now in the y (or z-axis if you would like to call it) and in the x axis.

1) However, what does it mean for a cannon to be moving down into the ground?
2) Also, if a question was asked saying what is the velocity of the cannon relative to the ground, would I use use the x-velocity or the vector sum of the x and y (or z) velocities (ie get the resultant)?
 
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  • #2
There is a normal reaction force on the canon due to the ground. thus net external force in the y direction is not zero and thus momentum in the y direction is not conserved. The canon's y velocity with respect to the ground stays zero. This is one of the constraints on the system. This, however, requires that the ground does not buckle or break under the weight of the canon. The velocity of the canon with respect to the Earth should be the x velocity.

If you consider the Earth in the system as well, then the total momentum will be conserved but the effect of this is not important as the mass of the Earth is much larger than the canon or canon ball.
 

FAQ: What Is the Cannon's Velocity Relative to the Ground?

1. What is momentum in physics?

Momentum is a concept in physics that refers to the quantity of motion possessed by an object. It is calculated by multiplying an object's mass by its velocity.

2. How is momentum related to Newton's laws of motion?

Momentum is closely related to Newton's laws of motion, specifically the law of inertia and the law of action and reaction. Inertia, the tendency of an object to resist changes in its motion, is directly related to an object's momentum. Additionally, the law of action and reaction states that for every action, there is an equal and opposite reaction, which can also affect an object's momentum.

3. What are the units of momentum?

The units of momentum are kg*m/s (kilogram meters per second) in the SI system, or lb*ft/s (pound feet per second) in the imperial system.

4. How is momentum conserved in a closed system?

In a closed system, where there are no external forces acting on the system, the total momentum of the system remains constant. This is known as the law of conservation of momentum.

5. How can momentum be applied in real-life situations?

Momentum has many practical applications in everyday life, such as in sports (e.g. a baseball player swinging a bat), transportation (e.g. a car accelerating), and collisions (e.g. a car crash). It can also be used in engineering and design to calculate the forces and velocities involved in various movements and interactions.

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