How Much Energy Is Released in a Three-Part Explosion?

[PhysicsBeginner]

Hi everyone, I've been trying to do this question here but I'm stuck on the last part:
A 23.0 kg body is moving with a speed of 25.0 m/s in the direction of the positive x-axis when, owing to an internal explosion, it breaks into three parts. One part, which has a mass of 5.50 kg, moves away from the point of explosion with a speed of 65.0 m/s in the direction of the positive y axis. A second fragment, with unknown mass, moves with a speed of 125 m/s, at an angle of 15.0 degrees below the positive xaxis. The third fragment is observed to move in the direction of the negative x axis.

How much energy was released in the explosion?

I have found all the unknown masses and velocities and i am using the kinetic energy of a system equations which are the sum of the kinetic energy associated with the motion of the center of mass and the kinetic energy associated with the motion of the particles of the system. But I'm getting the wrong answer.

Can someone help me out?

 

[Doc Al]

Show your work and we'll take a look.

If you've correctly found the KEs of each piece after the collision, just add them up and subtract the initial KE. That will be the energy released.

 

[M98Ranger]

To calculate the energy released in the explosion, we need to use the principle of conservation of momentum and conservation of energy. The total momentum of the system before the explosion is equal to the total momentum after the explosion. This means that the initial momentum in the x-direction is equal to the final momentum in the x-direction, and the initial momentum in the y-direction is equal to the final momentum in the y-direction.

Using this principle, we can set up two equations: one for the x-direction and one for the y-direction. In the x-direction, we have:

(23.0 kg)(25.0 m/s) = (5.50 kg)(-125 m/s) + (m)(cos(15.0°))(125 m/s)

And in the y-direction, we have:

0 = (5.50 kg)(65.0 m/s) + (m)(sin(15.0°))(125 m/s)

Solving these equations simultaneously, we can find the mass of the third fragment to be 4.45 kg.

Now, to calculate the energy released, we can use the equation for kinetic energy: KE = 1/2mv^2. We can calculate the kinetic energy of each fragment and add them together to find the total energy released.

For the first fragment, we have:

KE1 = 1/2(5.50 kg)(65.0 m/s)^2 = 11,218.75 J

For the second fragment, we have:

KE2 = 1/2(4.45 kg)(125 m/s)^2 = 34,984.38 J

And for the third fragment, we have:

KE3 = 1/2(4.45 kg)(125 m/s)^2 = 34,984.38 J

Adding these values together, we get a total energy released of 81,187.51 J.

I hope this helps you in finding the correct answer. If you are still having trouble, you may want to double check your calculations and make sure you are using the correct units. Good luck!