Inelastic collision of a cannonball

[reminiscent]

Homework Statement

Homework Equations

Total initial momentum = total final momentum
Momentum = m*v
Kinetic energy = 1/2 * m * v²

The Attempt at a Solution

What I found so far:
m₁v_1i = (m₁+m₂)v_f
Total kinetic energy = 1/2 * (m₁ + m₂)v_f² - 1/2 * m₁ * v_1i²

I am confused on how friction comes into play here. I know that friction is a non-conservative force.

 

[ehild]

Homework Statement

Homework Equations

Total initial momentum = total final momentum
Momentum = m*v
Kinetic energy = 1/2 * m * v²

The Attempt at a Solution

What I found so far:
m₁v_1i = (m₁+m₂)v_f
Total kinetic energy = 1/2 * (m₁ + m₂)v_f² - 1/2 * m₁ * v_1i²

I am confused on how friction comes into play here. I know that friction is a non-conservative force.

You can take the whole process as two stages.
The cannonball hits the tank, and is embedded. What kind of collision is this? Is energy conserved?
After the collision, the tank and the ball inside, move on a rough pavement and come to rest at 50 cm distance. What kind of motion is that?

 

[SteamKing]

Homework Statement

Homework Equations

Total initial momentum = total final momentum
Momentum = m*v
Kinetic energy = 1/2 * m * v²

The Attempt at a Solution

What I found so far:
m₁v_1i = (m₁+m₂)v_f
Total kinetic energy = 1/2 * (m₁ + m₂)v_f² - 1/2 * m₁ * v_1i²

I am confused on how friction comes into play here. I know that friction is a non-conservative force.

The energy imparted to the tank by the projectile must be used to move the tank against the friction which exists between the tank and the pavement. In essence, part of the energy of the projectile must be converted to work in order to overcome friction.

 

[reminiscent]

So since this is an elastic collision, momentum is conserved but KE is not. I would have to substitute what I found first into Kf, then that would equal to mu*(total mass)*g*d, correct? I just solve for v initial for the cannon ball. I got 377 m/s.

 

[ehild]

So since this is an elastic inelastic collision, momentum is conserved but KE is not. I would have to substitute what I found first into Kf, then that would equal to mu*(total mass)*g*d, correct? I just solve for v initial for the cannon ball. I got 377 m/s.

The result is correct.