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A ball has m=10 kg and v=10 m/s. It has the same momentum as which of the following?

Select one:
a. A ball with m = 100 kg and v = 1 m/s.
b. A ball with m = 5 kg and v = 20 m/s.
c. A ball with m = 2 kg and v = 50 m/s
d. all of these

Respuesta :

jacob193

Answer:

Choice d. All three balls listed in choice a, b, and c have a momentum of [tex]100\; \rm kg \cdot m \cdot s^{-1}[/tex] each, same as that of the [tex]10\; \rm kg[/tex] ball moving at [tex]10\; \rm m \cdot s^{-1}[/tex]. Assumption: all four balls are moving in the same direction.

Explanation:

The momentum [tex]p[/tex] of an object is equal to the product of its mass [tex]m[/tex] and its velocity [tex]v[/tex].

Momentum of a [tex]10\; \rm kg[/tex] ball moving at [tex]10\; \rm m \cdot s^{-1}[/tex]:

[tex]p = m \cdot v = 10\; \rm kg \times 10\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m \cdot s^{-1}[/tex].

Similarly:

  • Momentum of the ball in choice a: [tex]100 \; \rm kg \times 1\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m\cdot s^{-1}[/tex].
  • Momentum of the ball in choice b: [tex]5 \; \rm kg \times 20\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m\cdot s^{-1}[/tex].
  • Momentum of the ball in choice c: [tex]2 \; \rm kg \times 50\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m\cdot s^{-1}[/tex].

Hence the conclusion that these balls have the same momentum.

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