2.9 Thermodynamics and Inelastic Collisions: Conservation of Momentum

Inelastic Collisions

• In a collision, two objects interact and exchange energy and momentum.
• In an elastic collision, the total kinetic energy of the colliding objects is conserved. This means that the kinetic energy before the collision is equal to the kinetic energy after the collision.
• In an inelastic collision, some of the kinetic energy is transformed into other forms of energy, such as thermal energy or sound energy. This means that the kinetic energy before the collision is not equal to the kinetic energy after the collision.
• In an elastic collision, the colliding objects will bounce off each other with the same speed and direction they had before the collision. In an inelastic collision, the colliding objects will stick together or deform and continue moving together as a single object after the collision.
• The type of collision that occurs depends on the properties of the colliding objects and the nature of the collision. For example, collisions between hard, non-deformable objects tend to be more elastic, while collisions between soft, deformable objects tend to be more inelastic.

To solve this problem, you would first need to classify the collision as either elastic or inelastic. To do this, you could use the fact that in an elastic collision, the total kinetic energy of the colliding objects is conserved. In this case, the initial kinetic energy of the 5 kg cart is 3^25 = 45 J, and the final kinetic energy of the 5 kg cart is 1^25 = 5 J, which are not equal. Therefore, this collision is inelastic.

Next, you could use the conservation of linear momentum to find the common final velocity of the carts after the collision. To do this, you would set the initial momentum of the 5 kg cart to the final momentum of the 2 kg cart, and solve for the final velocity of the 2 kg cart. This would give you a common final velocity of -1 m/s for the carts.

Then, you could use the initial and final velocities and masses of the carts to solve for the initial and final kinetic energies of the 5 kg cart and the change in kinetic energy during the collision. This would give you an initial kinetic energy of 45 J, a final kinetic energy of 5 J, and a change in kinetic energy of -40 J during the collision.

To solve this problem, you would first need to classify the collision as either elastic or inelastic. To do this, you could use the fact that in an elastic collision, the total kinetic energy of the colliding objects is conserved. In this case, the initial kinetic energy of the 20 kg ball is 5^220 = 500 J, and the final kinetic energy of the combined balls is (2^220)+(3^2*10) = 280 J, which are not equal. Therefore, this collision is inelastic.

Next, you could use the conservation of linear momentum to find the change in kinetic energy of the system during the collision. To do this, you would set the initial momentum of the 20 kg ball to the final momentum of the combined balls, and solve for the final kinetic energy of the combined balls. This would give you a change in kinetic energy of 220 J during the collision.