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Momentum and Impulse

Understand momentum as mass multiplied by velocity and impulse as change in momentum

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It Is All A Matter Of Impulse

It Is All A Matter Of Impulse

Credit: Charlie Cowins
Source: commons.wikimedia.org/wiki/File:Peng_Shuai_-_Flickr_-_chascow.jpg
License: CC BY-NC 3.0

As a tennis ball is struck by a racket, an extremely large force is applied to the ball over a very small amount of time. Assuming the average impact time is on the order of 1 millisecond, this would mean that the force exerted on a tennis ball during a 140-mph serve is approximately 140,000 N!

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  • The significant force on the ball can be explained by the concept of impulse. The impulse is an interaction between a system and its environment, where during this interaction the momentum of the system changes. How much the momentum changes by is dependent upon how long the system is acted on and by how much force is applied on the system. Therefore, the change in momentum \begin{align*}p_{(\text{final})} - p_{(\text{initial})}\end{align*} or the impulse \begin{align*}I\end{align*}, equals the force \begin{align*}F\end{align*} applied multiplied by how long it is applied, \begin{align*}t\end{align*}.

\begin{align*}\Delta p = p_{\text{final}} - p_{\text{initial}} = I=F \Delta t\end{align*}

Credit: Mike Babcock
Source: http://www.flickr.com/photos/13613374@N00/3098836311
License: CC BY-NC 3.0

Air bags help decrease harsh impact force on the human body [Figure2]

 

  • By understanding the physics behind impulses, thousands of lives are saved every year in automobile accidents. During an accident, a passenger in a car would experience the same change in momentum whether the air bags are installed or not. The air bags increase the time it takes for the change in momentum to occur. The cushioning extends the period of impact, decreasing the impact's force on the human body.

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Using the information provided above, answer the following questions.

  1. Consider two objects of equal mass and shape, object 1 and object 2. If both objects experience the same change in momentum but object 1 experience the change in half the time, which object would have a greater force applied to it?
  2. Why is there no mention of external forces in the description of impulse, i.e. gravitational, electrical, etc?
  3. Name other possible methods that could be used to increase the amount of time a person in a car accident would be brought to a stop.

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Image Attributions

  1. [1]^ Credit: Charlie Cowins; Source: commons.wikimedia.org/wiki/File:Peng_Shuai_-_Flickr_-_chascow.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Mike Babcock; Source: http://www.flickr.com/photos/13613374@N00/3098836311; License: CC BY-NC 3.0

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