Question

Two carts are involved in an elastic collision. Cart A with mass 0.550 kg is moving towards Cart B with mass 0.550 kg, which is initially at rest. Cart A stops after the collision and Cart B begins to move.A)If cart A has an initial velocity of 0.8 m/s , what is the velocity of Cart B after the collision?B)What is the initial kinetic energy of Cart A?C)What is the initial kinetic energy of Cart B?D)What is the final kinetic energy of Cart A?E)What is the final kinetic energy of Cart B?F)Is the kinetic energy conserved for elastic collisions?G)Is the momentum conserved for elastic collisions?

Answer 1

Answer:

A) $v_b=0.8\ m.s^{-1}$ is the final velocity of the cart B after collision.

B) $KE_A=0.176\ J$

C) $KE_B=0\ J$

D) $ke_a=0\ J$

E) $ke_B=0.176\ J$

F) Yes, here the kinetic energy is conserved because the mass of both the bodies involved in the collision is same.

G) Yes, momentum is always conserved for an elastic collision.

Explanation:

Given:

• mass of car A, $m_a=0.55\ kg$

• mass of car B, $m_b=0.55\ kg$

• initial velocity of car A, $u_a=0.8\ m.s^{-1}$

• final velocity of the car A, $v_a=0\ m.s^{-1}$

A)

As given in the question that the cars undergo an elastic collision:

According to the conservation of momentum:

$m_a.u_a+m_b.u_b=m_a.v_a+m_b.v_b$

$0.55\times 0.8+0.55\times 0=0.55\times 0+0.55\times v_b$

$v_b=0.8\ m.s^{-1}$ is the final velocity of the cart B after collision.

B)

Initial kinetic energy of cart A:

$KE_A=\frac{1}{2} m_a.u_a^2$

$KE_A=0.5\times 0.55\times 0.8^2$

$KE_A=0.176\ J$

C)

Initial kinetic energy of cart A:

$KE_B=\frac{1}{2} \times m_b.u_b^2$

$KE_B=0.5\times 0.55\times 0^2$

$KE_B=0\ J$

D)

The final kinetic energy of cart A:

$ke_A=\frac{1}{2} m_a.v_a^2$

$ke_a=0.5\times 0.55\times 0^2$

$ke_a=0\ J$

E)

The final kinetic energy of cart B:

$ke_B=\frac{1}{2} m_b.v_b^2$

$ke_B=0.5\times 0.55\times 0.8^2$

$ke_B=0.176\ J$

F)

Yes, here the kinetic energy is conserved because the mass of both the bodies involved in the collision is same.

G)

Yes, momentum is always conserved for an elastic collision.