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 \(F\).
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 \(F\).
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.
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”.
Why does a high jumper or long jumper bend their knees upon landing?
Check Answer
State Newton's Third Law of Motion.
Check Answer
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
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
A follow-through kick increases the force exerted by the foot on the ball.
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.
Impulse and impulsive force are the same physical quantity.
Impulse is the change of momentum \(mv - mu\), while impulsive force is the rate of change of momentum \(\dfrac{mv - mu}{t}\).
Extending impact time reduces the change of momentum.
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.
