Mechanical energy of cannon ball

In summary, the cannonball has two potential energies. The first is when it is in the cannon, and the second is when it is at the top. The conservation of mechanical energy tells us that the total mechanical energy does not change from the moment the cannonball is shot out until it has reached the top.
  • #1
physics phan
5
0
ok,

heres the prob:

A 21.0 kg cannon ball is fired from a cannon with a muzzle speed of 1100 m/s at an angle of 37.3° with the horizontal. A second ball is fired at an angle of 90.0°. Use the law of conservation of mechanical energy to find

(b) the total mechanical energy at the maximum height for each ball. Let y = 0 at the cannon.


in (a), i had to find the height for each ball, which i did using ( mv^2/2 ) - mgh = 0

i found the first ball to be 2.27e4 m/s (using 1100sin37.3)
and the second ball to be 6.17e4

now i can find the mech energy

do you use ( mv^2/2 ) + mgh = Mech E

(i simplified changed in PE and changed in KE in the above equation)

and then add the two Mech Energies?
 
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  • #2
You will get the right answer in (a) by using (( mv^2/2 ) - mgh = 0), if v is your vertical initial speed.

But how did you reason to get this formula?
 
  • #3
I used the vertical velocity

in a part 1, i did 1100sin37.3 for v, and in part 2, it was a 90 degree angle

i got this formula because that's what we've been using in class... although i just posted the simplified version of it... the part where we started plugging in numbers
 
  • #4
OK, let's go to part (b).
What does "conservation" mean?
I, at least, mean that when some quantity is conserved (in time, for example), it doesn't change it's value (in time) (Agreed?)
Therefore, a cannonball's mechanical energy does not change its value from the moment (when it is shot out from the cannon) to its "final" moment (when it has reached the top).
Was this helpful?
 
  • #5
arildno said:
OK, let's go to part (b).
What does "conservation" mean?
I, at least, mean that when some quantity is conserved (in time, for example), it doesn't change it's value (in time) (Agreed?)
Therefore, a cannonball's mechanical energy does not change its value from the moment (when it is shot out from the cannon) to its "final" moment (when it has reached the top).
Was this helpful?

I understand what you are saying but I am not quite sure what to do still...

i am confused why they told us why the cannon is at y=0... unless that is just to tell us to add two positives

also, i am not sure how to find mech energy... we went over it in class for just a couple minutes and have no clue how to derive a proper formula for this problem
 
  • #6
Ok, here's some more:
I assume your teacher has told you that mechanical energy consists of two parts:
1. Kinetic energy
2. Potential energy
When you meet the phrase "total mechanical energy" that just means "kinetic energy + potential energy"

Why y=0?
How does this equation enable you to calculate the potential energy at the initial level, i.e. where the cannon is?
 
  • #7
i got it

it was 1/2 mv^2

sheeeesh x 1000


why didn't you tell me it was that easy

cmon oslo boy


keep it real dawg, aight
 

1. What is mechanical energy?

Mechanical energy is the sum of potential energy and kinetic energy in a system. It is the energy associated with the movement and position of an object.

2. How is the mechanical energy of a cannon ball calculated?

The mechanical energy of a cannon ball can be calculated using the equation E = mgh + 1/2mv^2, where m is the mass of the cannon ball, g is the acceleration due to gravity, h is the height of the cannon ball, and v is the velocity of the cannon ball.

3. What factors affect the mechanical energy of a cannon ball?

The mechanical energy of a cannon ball is affected by its mass, height, and velocity. The type of material the cannon ball is made of and any external forces acting on it can also affect its mechanical energy.

4. How does the mechanical energy of a cannon ball change during flight?

As the cannon ball is fired from the cannon, it initially has high potential energy due to its position at the top of the cannon. As it travels through the air, its potential energy decreases while its kinetic energy (energy of motion) increases. The total mechanical energy remains constant unless acted upon by external forces like air resistance or gravity.

5. What is the relationship between mechanical energy and the distance a cannon ball can travel?

The distance a cannon ball can travel is directly related to its mechanical energy. The greater the mechanical energy, the farther the cannon ball will travel before coming to a stop. This is because the higher the mechanical energy, the greater the initial velocity of the cannon ball, allowing it to travel a longer distance before slowing down due to air resistance and gravity.

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