Multiple Choice
An object receives an impulse. Which of the following statements is true?
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11. Momentum & Impulse
Intro to Impulse
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In the context of linear motion, how does the impulse delivered to an object relate to its change in momentum?
A
Impulse is always less than the change in momentum.
B
Impulse is always greater than the change in momentum.
C
Impulse is equal to the change in momentum, so .
D
Impulse and change in momentum are unrelated quantities.
Verified step by step guidance1
Recall the definition of impulse, which is the product of the average force applied to an object and the time interval over which it acts. Mathematically, impulse \(J\) is given by \(J = \bar{F} \Delta t\).
Understand that momentum \(p\) of an object is defined as the product of its mass \(m\) and velocity \(v\), so \(p = mv\).
Recognize that the change in momentum \(\Delta p\) is the difference between the final and initial momentum of the object, expressed as \(\Delta p = p_{final} - p_{initial}\).
Apply the impulse-momentum theorem, which states that the impulse delivered to an object is equal to the change in its momentum. This can be written as \(J = \Delta p\).
Conclude that impulse and change in momentum are directly related and always equal in magnitude, meaning the correct relationship is \(J = \Delta p\).
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