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A 0.400 kg plastic ball and a 21.0 kg metal ball are rolling over horizontal ground with no friction. both balls are at rest when a force of equal magnitude is applied to them both over a distance of 1.30 m. after traveling the full distance and the force is removed from both balls, the momentum of the plastic ball is__

a. Zero
b. Greater than the momentum of the metal ball.
c. Equal to the momentum of the metal ball.
d. Less than the momentum of the metal ball.

1 Answer

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Final answer:

The momentum of the plastic ball is equal to the momentum of the metal ball after a force of equal magnitude is applied to both over the same distance and the force is removed, because both started from rest and no friction is involved. Option c is the correct answer.

Step-by-step explanation:

When a force of equal magnitude is applied to both a plastic ball and a metal ball over a distance of 1.30 m, and both balls start from rest, the work done on each ball is the same since Work (W) = Force (F) × Distance (d), and no friction is present. The work done on each object results in the same change in kinetic energy due to the work-energy principle.

Given that kinetic energy (KE) is converted into momentum (p) once the force is removed, and KE depends on mass (m) and velocity (v) as KE = ½mv², a higher velocity in the plastic ball (less massive) would counterbalance the greater mass of the metal ball to result in the same momentum, according to the equation p = mv.

Considering momentum is conserved and assuming the same efficiency in conversion from kinetic energy to momentum for both, the momentum of the plastic ball would be equal to the momentum of the metal ball when the force is removed, because they both started from rest and had the same force applied over the same distance.

Therefore, the correct option answer is c. Equal to the momentum of the metal ball

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