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3 days ago

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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?

1 answer:

Sav [2.8K]3 days ago

5 0

Answer:

A) $v_b=0.8\ m.s^{-1}$ denotes the resultant velocity of cart B post-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, kinetic energy remains conserved in this situation because both colliding bodies have identical mass.

G) Yes, momentum is conserved in every 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 car A, $v_a=0\ m.s^{-1}$

A)

The question mentions the cars experience an elastic collision:

By applying momentum conservation principles:

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

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

$v_b=0.8\ m.s^{-1}$ denotes the resulting velocity of 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, kinetic energy is conserved in this case due to both masses being identical in the collision.

G)

Indeed, momentum is consistently conserved in elastic collisions.

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