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You are lying in bed and want to shut your bedroom door. You have a bouncy "superball" and a blob of clay, both with the same mass. Which one would be more effective to throw at your door to close it?

a. The superball.
b. Neither will work.
c. The blob of clay.
d. Both the same.

Respuesta :

jacob193

Answer:

Choice A. The bouncy "superball" will exert approximately twice as much force than the blob of clay when tossed out at the same speed.

Explanation:

The momentum of an object is equal to the product of its mass and its velocity. The momentum of the system is conserved even if the collision is inelastic.

When the bouncy ball or the blob of clay hits the door, their momentum changes. Since momentum is conserved, the door would move in the opposite direction such that the total momentum stays at zero.

Let the mass of each object be [tex]m[/tex]. Suppose that both objects hit the door at a speed of [tex]v[/tex] in the same direction.

  • The bouncy ball will likely bounce back at about the same speed (in the opposite direction, away from the door.) The magnitude of the change in velocity will be at most [tex]2v[/tex]. The magnitude of the change in momentum will be at most [tex]2 \,m\cdot v[/tex].
  • However, when the blob of clay hits the door, its shape would change (and it would potentially stick to the door.) In other words, its velocity becomes almost [tex]0[/tex] after the collision. The magnitude of the change in its momentum will only be around [tex]m \cdot v[/tex], which is only about [tex]\dfrac{1}{2}[/tex] the momentum change due to the bouncy ball.

By Newton's Second Law, the net force on the door is proportion to the rate of change in its momentum. Assume that the two objects are in contact with the door for the same amount of time, the bouncy ball would exert about twice as much force on the door as the clay would. Hence it is "more effective" for closing the door.

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