How Far Did the Cannonball Roll?

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In summary, during the siege of Constantinople in 1453, the Turks used a cannon capable of launching a 5.40 x 10^2 kg stone cannonball. A soldier accidentally dropped the cannonball while trying to load it into the cannon. The cannonball rolled down a hill at a 30.0° angle with the horizontal. If 5.30 x 10^4 J of work was done by gravity on the cannonball, the distance it rolled can be calculated using the formula for linear and rotational kinetic energy, with the moment of inertia of the ball being a key factor. The specific formula for the moment of inertia would need to be determined based on the specific class or context of the problem.
  • #1
duckywucky
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Homework Statement



In 1453, during the siege of Constantinople, the Turks used a cannon capable of launching a stone cannonball with a mass of 5.40 x 10^2 kg. Suppose a soldier dropped a cannonball with this mass while trying to load it into the cannon. The cannonball rolled down a hill that made an angle of 30.0° with the horizontal. If 5.30 x 10^4 J of work was done by gravity on the cannonball as it rolled down a hill, how far did it roll?

Homework Equations





The Attempt at a Solution



I know that you're looking for the distance traveled, obviously, but how do i get to that?!
KE = 1/2 mv^2?
 
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  • #2
duckywucky said:

Homework Statement



In 1453, during the siege of Constantinople, the Turks used a cannon capable of launching a stone cannonball with a mass of 5.40 x 10^2 kg. Suppose a soldier dropped a cannonball with this mass while trying to load it into the cannon. The cannonball rolled down a hill that made an angle of 30.0° with the horizontal. If 5.30 x 10^4 J of work was done by gravity on the cannonball as it rolled down a hill, how far did it roll?

Homework Equations





The Attempt at a Solution



I know that you're looking for the distance traveled, obviously, but how do i get to that?!
KE = 1/2 mv^2?

The cannonball has two forms of KE. Linear KE (your formula that you listed), and rotational KE , which is influenced by the moment of inertia of the ball...
 
  • #3
So what formula would i use for the inertia of the ball?
 
  • #4
duckywucky said:
So what formula would i use for the inertia of the ball?

You tell us! It's your class.
 

1. How do you measure the distance a ball rolled?

In order to measure the distance a ball rolled, you will need a measuring tool such as a ruler, tape measure, or meter stick. Place the measuring tool at the starting point of the ball and note the measurement. Then, roll the ball and measure the distance it traveled from the starting point to the ending point.

2. What factors can affect the distance a ball rolls?

There are several factors that can affect the distance a ball rolls, including the initial force applied to the ball, the surface it is rolling on, and any obstacles or friction encountered along the way. The shape and weight of the ball can also play a role.

3. How does the angle of the surface affect the distance a ball rolls?

The angle of the surface can affect the distance a ball rolls. A steeper angle will result in a shorter distance as the ball will encounter more resistance and friction. A flatter angle will allow the ball to roll further as there is less resistance.

4. Is there a mathematical formula for calculating the distance a ball rolls?

Yes, the distance a ball rolls can be calculated using the formula d = ½ x g x t^2, where d is the distance, g is the acceleration due to gravity (9.8 m/s^2), and t is the time the ball is in motion. However, this formula may not account for all factors that can affect the distance a ball rolls.

5. Can the distance a ball rolls be affected by air resistance?

Yes, air resistance can affect the distance a ball rolls. The denser the air, the greater the resistance, which can slow down the ball and decrease the distance it travels. This is why balls may roll further on a smooth surface with less air resistance compared to a rough surface with more air resistance.

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