Question

A 6.0-kg red cart moving at 36.0 cm/s collides with a 2.0-kg blue cart moving at 12.0 cm/s. After the collision, the red cart is moving at 24.0 cm/s and the blue cart is moving at 48.0 cm/s. (All velocities are rightward.)

Answer 1

When two objects collide, their momentum is conserved before and after the collision. In this inelastic collision between the red and blue carts, the final velocities of the two carts are calculated using the principle of conservation of momentum.

Step-by-step explanation:

When two objects collide, their momentum is conserved before and after the collision. In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, only momentum is conserved, while kinetic energy is not preserved.

In this scenario, the red and blue carts experience an inelastic collision since they stick together after the collision.

Before the collision:

Red cart mass (m1) = 6.0 kg, velocity (v1i) = 36.0 cm/s

Blue cart mass (m2) = 2.0 kg, velocity (v2i) = 12.0 cm/s

After the collision:

Final velocity of the red cart (v1f) = 24.0 cm/s

Final velocity of the blue cart (v2f) = 48.0 cm/s

Using the principle of conservation of momentum:

(m1 * v1i) + (m2 * v2i) = (m1 * v1f) + (m2 * v2f)

Plugging in the given values:

(6.0 kg * 36.0 cm/s) + (2.0 kg * 12.0 cm/s) = (6.0 kg * 24.0 cm/s) + (2.0 kg * 48.0 cm/s)

Simplifying the equation:

216.0 kg⋅cm/s + 24.0 kg⋅cm/s = 144.0 kg⋅cm/s + 96.0 kg⋅cm/s

240.0 kg⋅cm/s = 240.0 kg⋅cm/s

The equation is balanced, meaning momentum is conserved. The final velocities of the red and blue carts are correct according to the conservation of momentum principle.