Question

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

Answer 1

Answer:

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

Explanation:

The momentum $p$ of an object is equal to the product of its mass $m$ and its velocity $v$.

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

$p = m \cdot v = 10\; \rm kg \times 10\; \rm m \cdot s^{-1} = 100\; \rm kg \cdot m \cdot s^{-1}$.

Similarly:

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

Hence the conclusion that these balls have the same momentum.