Exploding Spaceship: Calculating Velocity and Energy

[rishabh_k]

Homework Statement

a 2710000kg spherical spaceship in deep space explodes into two pieces, one 3.61 times the mass of the other. (a) suppose the ship is initially at rest, and after the explosion the smaller piece is moving at 70.9m/s. Find the velocity of the larger piece. Find the energy supplied by the explosion.
(b) Suppose the ship is initially moving at the constant velocity 48.9m/s.After the explosion, the smaller piece is moving 70.9m/s in the same direction as the initial velocity. Find the velocity of the larger piece.
(c) Suppose the ship is initially moving at constant velocity 48.9m/s. After the explosion, the smaller piece is moving -70.9m/s.Find the velocity of the larger piece.

Homework Equations

The Attempt at a Solution

 

[LowlyPion]

Homework Statement

a 2710000kg spherical spaceship in deep space explodes into two pieces, one 3.61 times the mass of the other. (a) suppose the ship is initially at rest, and after the explosion the smaller piece is moving at 70.9m/s. Find the velocity of the larger piece. Find the energy supplied by the explosion.
(b) Suppose the ship is initially moving at the constant velocity 48.9m/s.After the explosion, the smaller piece is moving 70.9m/s in the same direction as the initial velocity. Find the velocity of the larger piece.
(c) Suppose the ship is initially moving at constant velocity 48.9m/s. After the explosion, the smaller piece is moving -70.9m/s.Find the velocity of the larger piece.

Surprise me and show me you knew all along that linear momentum was conserved.

 

[nlightner]

I would approach this problem by first understanding the concept of momentum conservation. According to the law of conservation of momentum, the total momentum of a system before and after an event remains constant. In this case, the explosion of the spaceship can be considered as an event, and the total momentum of the system (spaceship and its pieces) before and after the explosion should be equal.

(a) Using the law of conservation of momentum, we can write the equation:

m1v1 + m2v2 = (m1 + m2)v

Where m1 and m2 are the masses of the two pieces, v1 and v2 are the initial velocities of the two pieces, and v is the final velocity of the combined system.

We are given that the mass of the larger piece is 3.61 times the mass of the smaller piece, so we can write:

m1 = 3.61m2

Substituting this in the equation and solving for v, we get:

v = (m1v1 + m2v2) / (m1 + m2)

= (3.61m2 * 0 + m2 * 70.9) / (3.61m2 + m2)

= 70.9 / 4.61

= 15.38 m/s

Therefore, the velocity of the larger piece is 15.38 m/s.

To find the energy supplied by the explosion, we can use the equation:

E = 1/2 * m * v^2

Where E is the kinetic energy, m is the mass, and v is the velocity.

Substituting the values, we get:

E = 1/2 * (3.61m2) * (15.38)^2

= 209.4 * m2 Joules

(b) In this case, the initial velocity of the larger piece is given to be 48.9 m/s, and the smaller piece is moving in the same direction with a velocity of 70.9 m/s. Using the same equation as in part (a), we get:

v = (m1v1 + m2v2) / (m1 + m2)

= (3.61m2 * 48.9 + m2 * 70.9) / (3.61m2 + m2)

= 48.9 m/s