Calculating Mass of Cannon Ball with Given Velocity Using Work-Energy Theorem

In summary, there is a problem involving a cannon exerting a force of 11200 N on a cannon ball in a 2.18 m barrel aimed at a 37.9 ◦ angle from the ground. The acceleration of gravity is 9.8 m/s^2 and the desired speed of the ball is 78.4 m/s. The solution can be found using the work energy theorem or by applying the equation v^2 = u^2 + 2as with F = ma to consider all forces acting on the ball.
  • #1
Joshua Lee
10
0

Homework Statement


You are in charge of a cannon that exerts a force 11200 N on a cannon ball while the ball is in the barrel of the cannon. The length of the cannon barrel is 2.18 m and the cannon is aimed at a 37.9 ◦ angle from the ground. The acceleration of gravity is 9.8 m/s 2 . If you want the ball to leave the cannon with speed v0 = 78.4 m/s, what mass cannon ball must you use? Answer in units of kg.

Homework Equations


KE=(1/2)mv^2
W=F*displacement*cos(theta)

The Attempt at a Solution


Used the kinetic energy equation to solve for mass
Then, used the second equation to find work.
I do not know how to get work to kinetic energy to plug into the mass solved equation.
 
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  • #2
This looks like a problem that assumes that you are familiar with a principle known as the "work energy theorem". This theorem relates the total work done on a particle to the change in the particle's kinetic energy. Have you covered this principle in class? If you are using a textbook, check the index to see if it is covered in the book.
 
  • #3
We have covered the theorem in class, but I don't see how that would apply. Would the change in energy be broken down into EF-E0 which would then be broken down into KE-K0?
I ended up solving the question using the v^2 equation in kinematics and F=ma. Does that tie into it all?
 
  • #4
You can work the problem using ##\sum \vec{F} = m \vec{a}##. If so, then you do not need to use any energy or work concepts. If you are going to use ##\sum \vec{F} = m \vec{a}##, then you should be sure that you think about all of the forces acting on the ball. (However, it could be that you would find that one of the forces is so much larger than the others that you can get an accurate enough answer by neglecting all but the largest force.)

From your list of "relevant equations" I assumed that you are trying to solve the problem using work and energy concepts. In this case, you only need the work energy theorem. You do not need to bring in ##\sum \vec{F} = m \vec{a}##. You don't need to break down the energy into different types of energy. The statement of the theorem only deals with work and kinetic energy.
 

1. How does the velocity of a cannon shot impact its distance?

The velocity of a cannon shot directly affects its distance. The higher the velocity, the farther the shot will travel. This is because velocity is a measure of an object's speed and direction, and a higher velocity means the object is moving faster and therefore covering more distance in a given time.

2. What factors influence the velocity of a cannon shot?

Several factors can impact the velocity of a cannon shot, including the weight and shape of the cannonball, the type and amount of gunpowder used, the angle of the cannon, and the conditions of the barrel, such as smoothness and cleanliness. Additionally, external factors such as wind and air resistance can also affect the velocity of a cannon shot.

3. Can the velocity of a cannon shot be calculated?

Yes, the velocity of a cannon shot can be calculated using the formula: V = √(2gh), where V is the velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the cannon from the ground. However, this calculation may not take into account all the factors that can influence the velocity of the shot, so it may not be entirely accurate.

4. How does the velocity of a cannon shot compare to other projectiles?

The velocity of a cannon shot is generally lower than other projectiles, such as bullets or rockets. This is because cannons were designed to fire heavy projectiles over long distances, rather than achieving high speeds. However, the velocity of a cannon shot can still reach significant speeds, depending on the factors mentioned above.

5. Why is it important to consider the velocity of a cannon shot in military strategy?

The velocity of a cannon shot is a critical factor in military strategy because it determines the range and impact of the shot. A higher velocity can result in a longer range and greater damage to the target. Military leaders must consider the velocity of their cannon shots when planning battles and tactics to maximize their effectiveness and achieve their objectives.

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