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.
Compare how extending or reducing contact time modifies impulsive force, and how follow-through enhances impulse.
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 \(F\).
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 \(F\).
In every collision, the action force and reaction force are equal in magnitude and opposite in direction, acting on different bodies.
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.
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
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.
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.
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.
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 \(F = \dfrac{0.04593(50) - 0.04593(0)}{0.005} = 459.3\ \mathrm{N}\).
Answer in your mind, then press “Check Answer”.
Why does a high jumper or long jumper bend their knees upon landing?
State Newton's Third Law of Motion.
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?
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 \(F\).
Objective: Identify impulse, impulsive force, impact time and Newton's Third Law.
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?
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 .
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.
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