Question

Two carts of equal mass are on a horizontal, frictionless air track. Initially cart A is moving toward stationary cart B with a speed of va. The carts undergo an inelastic collision, and after the collision the total kinetic energy of the two carts is one-half their initial total kinetic energy before the collision. What is the speed of each cart after the collision?

Answer 1

Answer:

v_{f} = v / 2

Explanation:

In this problem we will define a system formed by the two cars, in this case the forces during the collision are internal and the momentum is conserved.

Initial instant. Before the collision

        p₀ = m v

final instant. After the inelastic collision

        $p_{f}$ = (m + m) v_{f}

the moment is preserved

        p₀ = p_{f}

        m v = 2m v_{f}

        v_{f} = v / 2

since the cars have an inelastic collision the speed of the two vehicles is the same

Answer 2

The speed of both the carts (A and B) when undergo inelastic collision is one-half of initial velocity.

What is  momentum?

Momentum of a object is the force of speed of it in motion. Momentum of a moving body is the product of mass times velocity.

When the two objects collides, then the initial collision of the two body is equal to the final collision of two bodies by the law of conservation of momentum.

Two carts of equal mass are on a horizontal, frictionless air track. Initially, cart A is moving toward stationary cart B with a speed of va. The momentum of the cart before the collision is,

$P_i=mv$

The carts undergo an inelastic collision, and after the collision the total kinetic energy of the two carts is one-half their initial total kinetic energy before the collision.

Thus, the momentum after the collision is,

$P_f=(m_a+m_b)(v_f)$

Both card has same mass. Thus,

$P_f=(m+m)(v_f)\\P_f=2mv_f$

As, the momentum before the collision is equal to the momentum after the collision. Thus,

$P_f=P_i\\2mv_f=2mv\\v_f=\dfrac{v}{2}$

Hence, the speed of both the carts (A and B) when undergo inelastic collision is one-half of initial velocity.

Learn more about the conservation of momentum here;

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