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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 changes by a factor of 2 when its speed is doubled, regardless of its original speed.

Step by step solution

01

Understand the concept of momentum

Momentum is a vector quantity that is defined as the product of an object's mass and its velocity. It is mathematically represented as \( p=mv \). Here, 'p' is the momentum, 'm' is the mass and 'v' is the velocity.
02

Apply the change in velocity to the momentum

The object's speed (which can be considered as the magnitude of the velocity when direction is not a factor) is being doubled. Therefore, in the momentum equation \( p=mv \), only 'v' is changing while 'm' remains constant. If the original velocity 'v' is being doubled, the equation becomes \( p = m*2v \), which is twice the original momentum. This demonstrates that the factor by which the object's momentum changes if you double its speed is '2', irrespective of its original speed.

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