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Chapter 33: Problem 21

By what factor does an object's momentum change if you double its speed when its original speed is (a) \(25 \mathrm{m} / \mathrm{s}\) and (b) \(100 \mathrm{Mm} / \mathrm{s} ?\)

Short Answer

Expert verified
The object's momentum is doubled when its speed is doubled, regardless of the original speed values.

Step by step solution

01

Understanding Momentum

Momentum is calculated by the equation \(P = m * v\). In this case, only the speed (velocity) changes, while the mass remains the same, which means any change factors in speed directly apply to the momentum.
02

Apply the change factor to the original speeds

We are asked to determine the factor change in momentum when we double the speeds. So if we double the initial speed, we end up with \(v' = 2 * v\).
03

Calculate the factor change in momentum

Since the object's mass remains constant, the change in momentum \(\Delta P = P' - P = m*v' - m*v = m*(2v) - m*v = m*v\). Therefore, the change factor in momentum when speed is doubled is 2, regardless of the original speed.

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