a 4.0-kg cart rolling east on a level, frictionless track at 14 m/s collides with a stationary 3.0-kg cart. After the collision, the 4.0-kg cart is still rolling east, now at a speed of 2.0 m/s. Was this collision elastic or inelastic?

Question

a 4.0-kg cart rolling east on a level, frictionless track at 14 m/s collides with a stationary 3.0-kg cart. After the collision, the 4.0-kg cart is still rolling east, now at a speed of 2.0 m/s. Was this collision elastic or inelastic?

Answer 1

Use conservation of momentum, which MUST happen, to get the final velocity of the 3 kg cart, v.

4*14 = 4*2 + 3 v
v = 16 (east)
Now add up the initial and final kinetic energies to see if the collision is elastic.
Initial KE = (1/2)4*(14)^2 = 392 J
Final KE = (1/2)4*2^2 + (1/2)3*16^2 = 392 J

So, the collision is elastic.

Answer 2

To determine whether the collision between the two carts is elastic or inelastic, we need to examine whether kinetic energy is conserved before and after the collision.

In an elastic collision, the total kinetic energy of the system is conserved. This means that the sum of the kinetic energies of the two carts before the collision should be equal to the sum of their kinetic energies after the collision.

To calculate the kinetic energy before and after the collision, we can use the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Let's calculate the kinetic energy of each cart before the collision:

For the 4.0-kg cart rolling east at 14 m/s:
Kinetic Energy before collision = (1/2) * 4.0 kg * (14 m/s)^2 = 392 Joules

For the 3.0-kg stationary cart:
Kinetic Energy before collision = 0 Joules (since it is stationary)

Now, let's calculate the kinetic energy of each cart after the collision:

For the 4.0-kg cart rolling east at 2.0 m/s:
Kinetic Energy after collision = (1/2) * 4.0 kg * (2 m/s)^2 = 8 Joules

For the 3.0-kg cart:
Kinetic Energy after collision = 0 Joules (since it is at rest)

Now, let's add up the kinetic energies before and after the collision:

Before collision: 392 Joules + 0 Joules = 392 Joules
After collision: 8 Joules + 0 Joules = 8 Joules

Since the total kinetic energy is not conserved (392 Joules ≠ 8 Joules), we can conclude that the collision between the two carts is inelastic.

Note: In this case, some of the initial kinetic energy has been converted into other forms of energy during the collision, such as heat or sound.