Impulse And Impulsive Force

2.7 Impulse and Impulsive Force
PHYSICS • Form 4 • Chapter 2: Force and Motion I

2.7 Impulse and Impulsive Force

In high-impact events like kicking a football, crashing a car, or landing from a jump, forces act over very short time intervals. This topic covers impulse (the change of momentum) and impulsive force (the rate of change of momentum), exploring how the time of impact alters the force experienced and how Newton's Third Law explains the action-reaction pairs involved.

Learning Objectives

  • Define impulse and state its formula as the change of momentum, \(J = mv - mu = Ft\).
  • Define impulsive force and state its formula as the rate of change of momentum, \(F = \dfrac{mv - mu}{t}\).
  • Explain the relationship between impact time and impulsive force when change of momentum is constant, \(F \propto \dfrac{1}{t}\).
  • State Newton's Third Law of Motion and identify action-reaction pairs in various situations.
  • Describe daily life applications that increase impulse or control impulsive force.
  • Solve numerical problems involving impulse and impulsive force with correct units and directional signs.

Factors Affecting Impulsive Force and Impulse Applications

Compare how extending or reducing contact time modifies impulsive force, and how follow-through enhances impulse.

Extending impact time reduces impulsive force

Soft surfaces, crumple zones and bending knees increase the impact time \(t\). Since \(F \propto \dfrac{1}{t}\), a larger \(t\) produces a smaller impulsive force \(F\).

Soft surface / crumple zone large \(t\) → small \(F\)

Reducing impact time increases impulsive force

A hard surface such as a pestle and mortar stops the moving object in a very short time. A small \(t\) produces a large impulsive force \(F\).

Hard surface / pestle & mortar small \(t\) → large \(F\)

Action-reaction pair at contact point

In every collision, the action force and reaction force are equal in magnitude and opposite in direction, acting on different bodies.

Action on ball → Reaction on foot Action on obstacle → Reaction on car Action on mortar → Reaction on pestle

Short Explanation

What is Impulse?

Impulse is a change of momentum. It is calculated using \(J = mv - mu = Ft\), where \(J\) is impulse in \(\mathrm{N\,s}\) or \(\mathrm{kg\,m\,s^{-1}}\), \(F\) is applied force in \(\mathrm{N}\), \(t\) is time of action in \(\mathrm{s}\), and \(mv - mu\) is the change of momentum.

What is Impulsive Force?

Impulsive force is the rate of change of momentum in a collision or impact in a short period of time. It is calculated using \(F = \dfrac{mv - mu}{t}\).

Relationship between impulsive force and impact time

\(F \propto \dfrac{1}{t}\)

When the change of momentum \(mv - mu\) is constant, a smaller impact time produces a larger impulsive force, and a larger impact time produces a smaller impulsive force.

Newton's Third Law of Motion

For every action there is a reaction of equal magnitude, but in the opposite direction. In collisions and impacts, forces always occur in pairs acting on different bodies.

Situation Effect on impact time Effect on impulsive force Purpose
Follow-through in football Extends contact time Increases impulse, not necessarily peak force Higher final velocity of ball
Bending legs upon landing Extends impact time Reduces impulsive force Prevents injury
Crumple zone in vehicles Extends impact time Reduces impulsive force Protects occupants
Mortar and pestle Reduces impact time Increases impulsive force Crush food effectively

Worked Example 1

A plasticine ball of mass \(0.058\ \mathrm{kg}\) moving at \(10\ \mathrm{m\,s^{-1}}\) sticks to a wall. Its impulse is \(J = 0.058(0) - 0.058(10) = -0.58\ \mathrm{N\,s}\). The negative sign shows the impulse acts opposite to the initial velocity.

Worked Example 2

A golf ball of mass \(45.93\ \mathrm{g} = 0.04593\ \mathrm{kg}\) is hit from rest to \(50\ \mathrm{m\,s^{-1}}\) in \(0.005\ \mathrm{s}\). The impulsive force is \(F = \dfrac{0.04593(50) - 0.04593(0)}{0.005} = 459.3\ \mathrm{N}\).

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

Why does a high jumper or long jumper bend their knees upon landing?

Check Answer
Answer: Bending the knees extends the time of impact upon landing, which reduces the magnitude of the impulsive force acting on the body and prevents injury.
2

State Newton's Third Law of Motion.

Check Answer
Answer: Newton's Third Law of Motion states that for every action there is a reaction of equal magnitude, but in the opposite direction.
3

A golf ball of mass \(0.045\ \mathrm{kg}\) is hit from rest to a speed of \(40\ \mathrm{m\,s^{-1}}\) in an impact time of \(0.005\ \mathrm{s}\). What is the impulsive force acting on the ball?

Check Answer
Answer: \(F = \dfrac{mv - mu}{t} = \dfrac{0.045(40) - 0.045(0)}{0.005} = \dfrac{1.8}{0.005} = 360\ \mathrm{N}\).

Common Mistakes

  • !Forgetting that velocity and impulse are vector quantities: students often forget to assign a negative sign to velocities when an object bounces backwards.
  • !Confusing impulse (\(J = Ft\), measured in \(\mathrm{N\,s}\) or \(\mathrm{kg\,m\,s^{-1}}\)) with impulsive force (\(F = \dfrac{mv - mu}{t}\), measured in \(\mathrm{N}\)).
  • !Failing to convert mass from grams (\(\mathrm{g}\)) to kilograms (\(\mathrm{kg}\)) before substituting into formulae.
  • !Misunderstanding action-reaction pairs by thinking they cancel each other out on the same object, rather than acting on two completely different objects.

Concept Misunderstandings

Misunderstanding

A follow-through kick increases the force exerted by the foot on the ball.

Correct Concept

Follow-through maintains contact between the foot and the ball for a longer time interval \(t\), which increases the total impulse \(Ft\) and final velocity, not necessarily the peak applied force.

Misunderstanding

Impulse and impulsive force are the same physical quantity.

Correct Concept

Impulse is the change of momentum \(mv - mu\), while impulsive force is the rate of change of momentum \(\dfrac{mv - mu}{t}\).

Misunderstanding

Extending impact time reduces the change of momentum.

Correct Concept

For a car brought to a complete stop from a fixed speed, the total change of momentum \(mv - mu\) is constant; extending impact time only reduces the average impulsive force \(F\).

Summary

  • Impulse \(J = mv - mu = Ft\), measured in \(\mathrm{N\,s}\).
  • Impulsive force \(F = \dfrac{mv - mu}{t}\), measured in \(\mathrm{N}\).
  • When change in momentum is constant, \(F \propto \dfrac{1}{t}\).
  • Increasing \(t\) decreases impulsive force, such as crumple zones and bending knees.
  • Decreasing \(t\) increases impulsive force, such as pestle and mortar.
  • Follow-through increases contact time \(t\) to maximize impulse and final velocity.
  • Newton's Third Law: every action force has an equal and opposite reaction force acting on separate bodies.

Short Activity

Objective: Identify impulse, impulsive force, impact time and Newton's Third Law.

A. Objective Quiz

1 What is the primary purpose of a car's crumple zone during a collision?

2 Which of the following describes Newton's Third Law of Motion?

B. Fill in the Blanks

3 Impulsive force is defined as the rate of change of in a collision or impact in a short period of time.

4 If the change of momentum is constant, the impulsive force is inversely proportional to the impact .

C. Matching / Drag and Drop

Drag each application or law to the correct physical effect or explanation. If using a phone, tap the answer first, then tap the matching box.

Application / Law
Follow-through in football
Crumple zone of a car
Mortar and pestle
Newton's Third Law of Motion
Physical Effect / Explanation
Lengthens contact time to produce a larger impulse and higher velocityCorrect ✓Try againEmpty
Extends impact time during collision to reduce impulsive forceCorrect ✓Try againEmpty
Shortens impact time to produce a large impulsive forceCorrect ✓Try againEmpty
Action and reaction forces are equal in magnitude and opposite in directionCorrect ✓Try againEmpty
 

Keywords

Impulse Impulsive Force Impact Time Follow-through Newton's Third Law of Motion Crumple Zone

Impulse And Impulsive Force

2.7 Impulse and Impulsive Force
PHYSICS • Form 4 • Chapter 2: Force and Motion I

2.7 Impulse and Impulsive Force

In high-impact events like kicking a football, crashing a car, or landing from a jump, forces act over very short time intervals. This topic covers impulse (the change of momentum) and impulsive force (the rate of change of momentum), exploring how the time of impact alters the force experienced and how Newton's Third Law explains the action-reaction pairs involved.

Learning Objectives

  • Define impulse and state its formula as the change of momentum, \(J = mv - mu = Ft\).
  • Define impulsive force and state its formula as the rate of change of momentum, \(F = \dfrac{mv - mu}{t}\).
  • Explain the relationship between impact time and impulsive force when change of momentum is constant, \(F \propto \dfrac{1}{t}\).
  • State Newton's Third Law of Motion and identify action-reaction pairs in various situations.
  • Describe daily life applications that increase impulse or control impulsive force.
  • Solve numerical problems involving impulse and impulsive force with correct units and directional signs.

Factors Affecting Impulsive Force and Impulse Applications

Compare how extending or reducing contact time modifies impulsive force, and how follow-through enhances impulse.

Extending impact time reduces impulsive force

Soft surfaces, crumple zones and bending knees increase the impact time \(t\). Since \(F \propto \dfrac{1}{t}\), a larger \(t\) produces a smaller impulsive force \(F\).

Soft surface / crumple zone large \(t\) → small \(F\)

Reducing impact time increases impulsive force

A hard surface such as a pestle and mortar stops the moving object in a very short time. A small \(t\) produces a large impulsive force \(F\).

Hard surface / pestle & mortar small \(t\) → large \(F\)

Action-reaction pair at contact point

In every collision, the action force and reaction force are equal in magnitude and opposite in direction, acting on different bodies.

Action on ball → Reaction on foot Action on obstacle → Reaction on car Action on mortar → Reaction on pestle

Short Explanation

What is Impulse?

Impulse is a change of momentum. It is calculated using \(J = mv - mu = Ft\), where \(J\) is impulse in \(\mathrm{N\,s}\) or \(\mathrm{kg\,m\,s^{-1}}\), \(F\) is applied force in \(\mathrm{N}\), \(t\) is time of action in \(\mathrm{s}\), and \(mv - mu\) is the change of momentum.

What is Impulsive Force?

Impulsive force is the rate of change of momentum in a collision or impact in a short period of time. It is calculated using \(F = \dfrac{mv - mu}{t}\).

Relationship between impulsive force and impact time

\(F \propto \dfrac{1}{t}\)

When the change of momentum \(mv - mu\) is constant, a smaller impact time produces a larger impulsive force, and a larger impact time produces a smaller impulsive force.

Newton's Third Law of Motion

For every action there is a reaction of equal magnitude, but in the opposite direction. In collisions and impacts, forces always occur in pairs acting on different bodies.

Situation Effect on impact time Effect on impulsive force Purpose
Follow-through in football Extends contact time Increases impulse, not necessarily peak force Higher final velocity of ball
Bending legs upon landing Extends impact time Reduces impulsive force Prevents injury
Crumple zone in vehicles Extends impact time Reduces impulsive force Protects occupants
Mortar and pestle Reduces impact time Increases impulsive force Crush food effectively

Worked Example 1

A plasticine ball of mass \(0.058\ \mathrm{kg}\) moving at \(10\ \mathrm{m\,s^{-1}}\) sticks to a wall. Its impulse is \(J = 0.058(0) - 0.058(10) = -0.58\ \mathrm{N\,s}\). The negative sign shows the impulse acts opposite to the initial velocity.

Worked Example 2

A golf ball of mass \(45.93\ \mathrm{g} = 0.04593\ \mathrm{kg}\) is hit from rest to \(50\ \mathrm{m\,s^{-1}}\) in \(0.005\ \mathrm{s}\). The impulsive force is \(F = \dfrac{0.04593(50) - 0.04593(0)}{0.005} = 459.3\ \mathrm{N}\).

Try to Answer First

Answer in your mind, then press “Check Answer”.

1

Why does a high jumper or long jumper bend their knees upon landing?

Check Answer
Answer: Bending the knees extends the time of impact upon landing, which reduces the magnitude of the impulsive force acting on the body and prevents injury.
2

State Newton's Third Law of Motion.

Check Answer
Answer: Newton's Third Law of Motion states that for every action there is a reaction of equal magnitude, but in the opposite direction.
3

A golf ball of mass \(0.045\ \mathrm{kg}\) is hit from rest to a speed of \(40\ \mathrm{m\,s^{-1}}\) in an impact time of \(0.005\ \mathrm{s}\). What is the impulsive force acting on the ball?

Check Answer
Answer: \(F = \dfrac{mv - mu}{t} = \dfrac{0.045(40) - 0.045(0)}{0.005} = \dfrac{1.8}{0.005} = 360\ \mathrm{N}\).

Common Mistakes

  • !Forgetting that velocity and impulse are vector quantities: students often forget to assign a negative sign to velocities when an object bounces backwards.
  • !Confusing impulse (\(J = Ft\), measured in \(\mathrm{N\,s}\) or \(\mathrm{kg\,m\,s^{-1}}\)) with impulsive force (\(F = \dfrac{mv - mu}{t}\), measured in \(\mathrm{N}\)).
  • !Failing to convert mass from grams (\(\mathrm{g}\)) to kilograms (\(\mathrm{kg}\)) before substituting into formulae.
  • !Misunderstanding action-reaction pairs by thinking they cancel each other out on the same object, rather than acting on two completely different objects.

Concept Misunderstandings

Misunderstanding

A follow-through kick increases the force exerted by the foot on the ball.

Correct Concept

Follow-through maintains contact between the foot and the ball for a longer time interval \(t\), which increases the total impulse \(Ft\) and final velocity, not necessarily the peak applied force.

Misunderstanding

Impulse and impulsive force are the same physical quantity.

Correct Concept

Impulse is the change of momentum \(mv - mu\), while impulsive force is the rate of change of momentum \(\dfrac{mv - mu}{t}\).

Misunderstanding

Extending impact time reduces the change of momentum.

Correct Concept

For a car brought to a complete stop from a fixed speed, the total change of momentum \(mv - mu\) is constant; extending impact time only reduces the average impulsive force \(F\).

Summary

  • Impulse \(J = mv - mu = Ft\), measured in \(\mathrm{N\,s}\).
  • Impulsive force \(F = \dfrac{mv - mu}{t}\), measured in \(\mathrm{N}\).
  • When change in momentum is constant, \(F \propto \dfrac{1}{t}\).
  • Increasing \(t\) decreases impulsive force, such as crumple zones and bending knees.
  • Decreasing \(t\) increases impulsive force, such as pestle and mortar.
  • Follow-through increases contact time \(t\) to maximize impulse and final velocity.
  • Newton's Third Law: every action force has an equal and opposite reaction force acting on separate bodies.

Short Activity

Objective: Identify impulse, impulsive force, impact time and Newton's Third Law.

A. Objective Quiz

1 What is the primary purpose of a car's crumple zone during a collision?

2 Which of the following describes Newton's Third Law of Motion?

B. Fill in the Blanks

3 Impulsive force is defined as the rate of change of in a collision or impact in a short period of time.

4 If the change of momentum is constant, the impulsive force is inversely proportional to the impact .

C. Matching / Drag and Drop

Drag each application or law to the correct physical effect or explanation. If using a phone, tap the answer first, then tap the matching box.

Application / Law
Follow-through in football
Crumple zone of a car
Mortar and pestle
Newton's Third Law of Motion
Physical Effect / Explanation
Lengthens contact time to produce a larger impulse and higher velocityCorrect ✓Try againEmpty
Extends impact time during collision to reduce impulsive forceCorrect ✓Try againEmpty
Shortens impact time to produce a large impulsive forceCorrect ✓Try againEmpty
Action and reaction forces are equal in magnitude and opposite in directionCorrect ✓Try againEmpty
 

Keywords

Impulse Impulsive Force Impact Time Follow-through Newton's Third Law of Motion Crumple Zone