Two cars (A and B) of mass 1.1 kg collide. Car A is initially moving at 18 m/s, and car B is initially moving in the opposite direction with a speed of 9 m/s. The two cars are moving along a straight line before and after the collision. (Enter the magnitudes.)

Question

Two cars (A and B) of mass 1.1 kg collide. Car A is initially moving at 18 m/s, and car B is initially moving in the opposite direction with a speed of 9 m/s. The two cars are moving along a straight line before and after the collision. (Enter the magnitudes.)

If the two cars have a completely inelastic collision, calculate the change in momentum (in kg · m/s) of the two-car system.

Answer 1

This is nuts. There is no change of momentum, momentum is conserved, PERIOD.

Answer 2

To calculate the change in momentum of the two-car system during a completely inelastic collision, we need to consider the conservation of momentum.

The conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is defined as its mass multiplied by its velocity. Mathematically, momentum (p) can be expressed as:

p = m * v

Where:
p is the momentum,
m is the mass, and
v is the velocity.

Let's calculate the momentum of each car before the collision:

For Car A:
Mass (m1) = 1.1 kg
Initial velocity (v1i) = 18 m/s

Momentum of Car A before the collision (p1i) = m1 * v1i

For Car B:
Mass (m2) = 1.1 kg
Initial velocity (v2i) = -9 m/s (negative because it's moving in the opposite direction)

Momentum of Car B before the collision (p2i) = m2 * v2i

The total momentum before the collision (p_total_i) is the sum of the individual momenta:

p_total_i = p1i + p2i

Now, let's calculate the momentum of the two-car system after the collision:

Since it's a completely inelastic collision, the two cars stick together after the collision and move with a common final velocity.

Let's assume the final velocity of the combined cars is vf.

The mass of the combined cars (m_total) is the sum of the individual masses:

m_total = m1 + m2

The momentum of the combined cars after the collision (p_total_f) is the mass of the combined cars multiplied by the final velocity:

p_total_f = m_total * vf

According to the conservation of momentum, p_total_i = p_total_f:

p_total_i = p_total_f

Substituting the individual momenta and the mass of the combined cars:

p1i + p2i = m_total * vf

Now, let's calculate the change in momentum of the two-car system (Δp_total), which is the difference between the initial and final momentum:

Δp_total = p_total_f - p_total_i

To find the change in momentum (Δp_total), we need to calculate the individual momenta and the mass of the combined cars.

Let's solve for Δp_total: