Projectile Mass & Energy: Solving for Speed in a Cannon Carrell

[joe215]

Homework Statement

If a projectile of mass m leaves the carrell of a cannon with a speed v, at what speed will a projectile of mass 2m leave the barrel.

I think i need to use conservation of energy but I am not sure how!

Thanks

 

[PhanthomJay]

Hint: Since the projectiles are fired over the same length of the carrell with the same force, and since work is force times the distance in the direction of the force, then the work done on the projectiles are the same in each case. Think about the work-energy theorem. Please show your attempt.

 

[nlightner]

for your question! You are correct, conservation of energy can be used to solve this problem. According to the principle of conservation of energy, the total energy of a system remains constant. In this case, the system includes the cannon, the projectile, and the surrounding environment.

To solve for the speed of the projectile of mass 2m, we can use the equation for conservation of energy:

Initial energy = final energy

The initial energy in this case is the kinetic energy of the projectile of mass m, which is given by:

KE = 1/2 * m * v^2

The final energy is the kinetic energy of the projectile of mass 2m, which we can represent as KE'.

Substituting these values into the conservation of energy equation, we get:

1/2 * m * v^2 = KE'

We can now solve for KE' by using the fact that the mass of the projectile is 2m, and the speed is unknown. So, we have:

KE' = 1/2 * (2m) * v'^2

where v' is the final speed of the projectile of mass 2m.

Substituting this into the conservation of energy equation, we get:

1/2 * m * v^2 = 1/2 * (2m) * v'^2

Simplifying this equation, we get:

v'^2 = v^2/2

Taking the square root of both sides, we get:

v' = v/√2

Therefore, the speed of the projectile of mass 2m will be v/√2, which is approximately 0.707 times the speed of the projectile of mass m.

I hope this explanation helps. Keep up the good work with your physics homework!