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AP®PhysicsCollege BoardPhysics 1: Algebra-BasedStudy GuidesUnit 4: Linear MomentumLinear Momentum & ImpulseImpulse Equation

Impulse Equation (College Board AP® Physics 1: Algebra-Based)

Study Guide

Katie M

Written by: Katie M

Reviewed by: Caroline Carroll

Impulse equation

  • The change in an object’s motion due to an external force acting on it for a time is described by impulse

  • Impulse is defined as the product of the average force exerted and the time interval during which it acts

J with rightwards arrow on top space equals space F with rightwards arrow on top subscript a v g end subscript increment t

  • Where:

    • J with rightwards arrow on top = impulse, measured in straight N times straight s

    • F with rightwards arrow on top subscript a v g end subscript = average force exerted, measured in straight N

    • increment t = time interval over which the force acts, measured in straight s

  • Impulse is a vector quantity, so it has magnitude and direction

  • Impulse has the same direction as the net force exerted on the system

  • Therefore, when the average force exerted over a time interval is zero open parentheses F with rightwards arrow on top subscript a v g end subscript space equals space 0 close parentheses, no impulse is exerted on the system

Applications of impulse

  • The concept of impulse is often used to prevent injury

  • For example, vehicles contain many safety features, such as crumple zones, seat belts, and airbags,

  • These features are designed to minimize the force open parentheses F with rightwards arrow on top subscript a v g end subscript close parentheses exerted on a passenger during a collision by

    • increasing the collision time open parentheses increment t close parentheses, as the impulse is constant

    • increasing the distance open parentheses d close parentheses over which kinetic energy open parentheses increment K close parentheses is dissipated (according to the Work-Energy Theorem)

Car safety features, including seat belts, airbags, and crumple zones. The seat belt and airbag increase the time over which the passenger experiences the impact force while the crumple zone absorbs energy which also reduces the impact force.
The seat belt, airbag and crumple zones help reduce the risk of injury on a passenger by increasing the collision time

Worked Example

How does a crash mat protect a gymnast from injury as they land on the ground during a gymnastics routine?

A      It reduces the kinetic energy loss of the gymnast

B      It reduces the momentum change of the gymnast

C      It shortens the stopping time of the gymnast and increases the force applied during the landing

D      It lengthens the stopping time of the gymnast and reduces the force applied during the landing

The correct answer is D

Answer:

Step 1: Analyze the scenario

  • During a landing, a force is exerted on the gymnast by the ground

  • The risk of injury can be reduced by minimizing the force exerted on the gymnast

  • When the gymnast lands on a crash mat, as opposed to the hard ground, the material compresses and lengthens the stopping time

  • This compression absorbs some of the kinetic energy and reduces the force exerted on the gymnast

Step 2: Eliminate the incorrect options

  • The change in kinetic energy is equivalent to the work done in deforming the mat, and this reduces the force by extending the distance over which energy is dissipated (since increment K space equals space W space equals space F d)

  • However, the kinetic energy loss of the gymnast depends on their speed before and after landing and is not reduced by the use of a crash mat

    • This eliminates option A

  • The change in momentum of the gymnast also depends on their speed before and after landing and is not reduced by the use of a crash mat

    • This eliminates option B

Step 3: Deduce the correct option

  • The crash mat increases the time taken for the gymnast to come to a stop

  • This decreases the acceleration (since a with rightwards arrow on top space equals space fraction numerator increment v with rightwards arrow on top over denominator increment t end fraction)

  • This reduces the force exerted on the gymnast (since J with rightwards arrow on top space equals space F with rightwards arrow on top increment t and impulse is constant)

    • Therefore, option D is correct

Examiner Tips and Tricks

Avoid making the common mistake in which students consider impulse and force as equivalent. You must realize that impulse describes the length of time a force is exerted on an object.

We can see this just by looking at the unit of impulse, newton seconds or straight N times straight s. This is why J with rightwards arrow on top space equals space F with rightwards arrow on top increment t.

Furthermore, if we look at the base unit of impulse, we can see it is actually equivalent to momentum, or more specifically (as we will discover in the next study guide), change in momentum

Force: 1 space straight N space equals space 1 space kg times straight m divided by straight s squared

Impulse: 1 space straight N times straight s space equals space 1 space kg times straight m divided by straight s squared space cross times space straight s space equals space 1 space kg times straight m divided by straight s space

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    Author
    Reviewer
    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.