Chapter 3 · Impulsive force and impulseTextbook pages 66–67

Impulsive Force & Impulse ആവേഗബലവും ബലത്തിന്റെ ആവേഗവും

Why does a good fielder pull the hands back while catching? Why is there a thick foam bed in the pole-vault pit, and straw around glass bottles in a box? One idea answers all of these: for the same change of momentum, a longer time means a smaller force. On this page: a catch lab, four “give reasons” animations, airbags and helmets – and a surprise link back to the first law.

📖 What you need (pages 8 and 9 of this guide)

Momentum p = mv (unit kg m/s). Change of momentum Δp = mv − mu.
Second law: F = rate of change of momentum = m(v − u)/t = ma (unit N = kg m/s²).
Force is a vector: choose one direction as positive; a negative answer means “the opposite way”.

1. Big forces for a very short time

ചുറ്റിക ഉപയോഗിച്ച് ആണി അടിച്ച് കയറ്റുമ്പോൾ ആണിയിലേക്ക് ബലം കൈമാറ്റം ചെയ്യുന്ന സമയ ഇടവേള എത്രയെന്ന് ചിന്തിച്ചിട്ടുണ്ടോ? ഒരു സെക്കന്റിന്റെ വളരെ ചെറിയ ഒരംശം മാത്രമല്ലേ ഇത്? ഇത്തരം ബലങ്ങളുടെ സവിശേഷതകൾ പരിശോധിക്കാം. When a nail is driven in with a hammer (Fig 3.10), have you thought about how long the hammer actually pushes on the nail? Isn't it only a very tiny fraction of a second? Let us look at the special features of such forces. ചുവടെ കൊടുത്തിരിക്കുന്ന സാഹചര്യങ്ങളിൽ ബലങ്ങളുടെ പ്രത്യേകത എന്താണെന്ന് കണ്ടെത്താമോ? • ക്രിക്കറ്റ് ബാറ്റ് കൊണ്ട് ബോൾ അടിച്ചു തെറിപ്പിക്കുന്നത്. • ഫുട്ബോൾ കളിക്കുമ്പോൾ പന്ത് കാലുകൊണ്ട് അടിക്കുന്നത്. Can you find what is special about the forces in these situations? • A cricket bat hitting the ball away. • Kicking the ball while playing football.

🎬 Three impulsive forces – and their force–time graphs

The masses, speeds and contact times in the animation are typical values (not from the textbook) to show the size of these forces. 1 ms = 1 millisecond = 1/1000 s.

ഇവിടെയെല്ലാം വലിയ ബലം വളരെ ചെറിയ സമയത്തേക്കല്ലേ പ്രയോഗിക്കപ്പെടുന്നത്. ഇത്തരം ബലമാണ് ആവേഗബലം (impulsive force). In all of these, isn't a large force applied for a very short time? Such a force is called an impulsive force (ആവേഗബലം).

2. Impulse of a force ബലത്തിന്റെ ആവേഗം

⭐ Impulsive force and impulse (textbook page 67)

വളരെ ചെറിയ സമയത്തേക്ക് പ്രയോഗിക്കുന്ന വലിയ ബലമാണ് ആവേഗബലം. ഈ ബലത്തിന്റെയും സമയത്തിന്റെയും ഗുണനഫലമാണ് ബലത്തിന്റെ ആവേഗം. ബലത്തിന്റെ ആവേഗം (I) = ബലം (F) × സമയം (t), I = F × t.

A large force applied for a very short time is an impulsive force. The product of this force and the time for which it acts is the impulse of the force: impulse (I) = force (F) × time (t), I = F × t.

ബലം ഉണ്ടാക്കുന്ന ആവേഗത്തിന്റെ യൂണിറ്റ് = ബലത്തിന്റെ യൂണിറ്റ് × സമയത്തിന്റെ യൂണിറ്റ് = ........ × ........ = ........ Unit of impulse = unit of force × unit of time = ........ × ........ = ........

Unit of impulse = N × s = N s (newton second).
Since 1 N = 1 kg m/s², 1 N s = 1 kg m/s² × s = 1 kg m/s – exactly the unit of momentum. That is a big clue for the next box!

Now put the second law, F = m(v − u)/t, into I = F × t:

🎬 From F = m(v − u)/t to the impulse–momentum principle

⭐ Impulse–momentum principle – ആവേഗമൊമെന്റതത്വം (textbook page 67)

ഒരു ബലത്തിന്റെ ആവേഗവും അതുണ്ടാക്കുന്ന മൊമെന്റവ്യത്യാസവും തുല്യമായിരിക്കും. ഇതാണ് ആവേഗമൊമെന്റതത്വം (impulse–momentum principle).

The impulse of a force is equal to the change in momentum it produces. This is the impulse–momentum principle: Ft = mv − mu.

🔑 Read it backwards

If the change of momentum (mv − mu) is fixed – say a ball must be brought to rest – then F × t is fixed. Make t bigger and F must get smaller; make t tiny and F becomes huge. Everything else on this page follows from this one line.

3. Catching a ball – the textbook question

❓ 200 g മാസുള്ള ഒരു പന്ത് 30 m/s പ്രവേഗത്തിൽ ചലിക്കുന്നു. ഒരാൾ ഈ പന്ത് പിടിക്കുന്നു. a) പന്തിനെ പിടിച്ച് നിശ്ചലമാക്കാനെടുത്ത സമയം താഴെ കൊടുത്ത പ്രകാരമെങ്കിൽ ഓരോ സന്ദർഭത്തിലും കൈയിൽ അനുഭവപ്പെടുന്ന ബലം എത്രയായിരിക്കും? i) 0.3 s ii) 0.2 s iii) 0.1 s b) ഇവിടെ നിങ്ങൾക്ക് ലഭിച്ച ഉത്തരങ്ങളിലെല്ലാം ബലത്തിന്റെ അളവ് നെഗറ്റീവാണല്ലോ. ഇത് എന്തിനെ സൂചിപ്പിക്കുന്നു? c) ഈ ഉത്തരങ്ങൾ വിശകലനം ചെയ്ത് ഒരു പൊതുനിഗമനം രൂപീകരിക്കുക. A ball of mass 200 g moves with a velocity of 30 m/s. A person catches it.

If the time taken to catch the ball and bring it to rest is as given below, what is the force felt on the hand in each case? (i) 0.3 s (ii) 0.2 s (iii) 0.1 s
All your answers for the force are negative. What does this indicate?
Analyse these answers and arrive at a general conclusion.

Convert 200 g to kg. The change in momentum is the same in all three cases: m(v − u) with v = 0. Then F = change in momentum ÷ time.

📝 Quick answer (full exam layout on page 10)

Take the ball's direction of motion as positive. m = 200 g = 0.2 kg, u = 30 m/s, v = 0.
Change in momentum = m(v − u) = 0.2 × (0 − 30) = −6 kg m/s (the same every time).
(a) F = m(v − u)/t: (i) −6 ÷ 0.3 = −20 N (ii) −6 ÷ 0.2 = −30 N (iii) −6 ÷ 0.1 = −60 N.
(b) The minus sign shows that the force acts opposite to the ball's motion – it is a stopping force.
(c) For the same change in momentum, the longer the time taken, the smaller the force (F × t stays −6 N s).
👉 Worked step by step, with figures: In-text numericals – Solutions (page 10).

🤔 Force on the ball or on the hand?

Strictly, F = m(v − u)/t is the force the hand exerts on the ball (−20 N: backwards, against the ball's motion). The ball pushes the hand with an equal force the other way, +20 N, in the ball's direction of motion – that is the push you feel in your palm. This pairing is Newton's third law – the topic of the next page.

Virtual lab – the catch lab

Choose how long the hands take to stop the ball, press ▶ Catch (slow motion) and then 📋 Record. Record at least four different times, including 0.3 s, 0.2 s and 0.1 s.

⚠ In real life practise catching with a tennis ball or a soft rubber ball. Catch a hard (leather) cricket ball only with proper coaching – fingers pointing up or down, never straight at the ball – it can break a finger.

🧤 Catch lab – 200 g ball at 30 m/s

stopping time t (s)

Stopping time t (s)	Change in momentum m(v − u) (kg m/s)	Force on the ball F = m(v − u)/t (N)	Impulse F × t (N s)

Positive direction = the ball's direction of motion (to the right). The amber block in the middle panel is the force–time graph of the catch (average force): it gets tall and thin for a quick stop and low and wide for a slow one – but its area, F × t, is always 6 N s.

🔎 Inference

The change in momentum is −6 kg m/s in every row, so the impulse F × t is −6 N s in every row.
Double the stopping time → half the force; half the time → double the force. Force and stopping time are inversely proportional (F = −6/t).
Conclusion: for the same change in momentum, the longer the time, the smaller the force. That is why a gentle catch does not hurt.

4. Give reasons – four everyday cases

ഇവിടെ രൂപീകരിച്ച നിഗമനത്തിന്റെ അടിസ്ഥാനത്തിൽ ചുവടെ കൊടുത്ത പ്രസ്താവനകൾക്ക് കാരണം കണ്ടെത്തുക. On the basis of the conclusion you have just formed, find reasons for the following statements. In each animation the same object with the same speed is stopped twice – once quickly (left), once slowly (right). Press ▶ to compare.

(a) The cricketer pulls the hands back

a) ക്രിക്കറ്റ് കളിക്കാർ വേഗത്തിൽ വരുന്ന പന്ത് പിടിക്കുന്നതിനൊപ്പം കൈ പുറകോട്ട് ചലിപ്പിക്കുന്നു. Cricketers move their hands backwards along with a fast-moving ball while catching it (Fig 3.11).

🏏 Stiff hands vs hands that “give”

The ball must lose all its momentum: the change in momentum m(v − u) is fixed. By the impulse–momentum principle F × t = m(v − u). By moving the hands back with the ball, the cricketer increases the time taken to stop it, so the force on the hands becomes smaller – the catch does not hurt and the ball is less likely to bounce out.

(b) The goalkeeper's hands move back

b) ഫുട്ബോൾ കളിയിൽ ഗോൾമുഖത്തേക്ക് വരുന്ന പന്ത് ഗോളി പിടിക്കുമ്പോൾ പന്തിനൊപ്പം കൈകൾ പുറകോട്ട് ചലിപ്പിക്കുന്നു. In football, when the goalkeeper catches a ball coming towards the goal, the hands are moved backwards along with the ball.

⚽ Rigid arms vs arms drawn in to the chest

The ball's change in momentum is the same however it is caught. Moving the hands back with the ball lengthens the time of contact, so the force needed to stop it (F = change in momentum ÷ time) is smaller. The goalkeeper's hands and wrists are not hurt and the ball does not rebound out of the hands.

(c) A foam bed in the pole-vault pit

c) പോൾവാൾട്ട് പിറ്റിൽ ഫോം ബെഡ് ഇടുന്നു. A foam bed is placed in the pole-vault pit.

🤸 Landing on hard ground vs on a foam bed

The athlete falls from a great height (about 5 m) and reaches the pit with a large momentum, which must become zero. The soft foam bed sinks in slowly, so the athlete takes a much longer time to stop. Since F × t = change in momentum (fixed), the force on the athlete's body is much smaller, and injuries to the bones and joints are avoided.

(d) Sponge or straw around glassware

d) ഗ്ലാസ് പാത്രങ്ങൾ അടുക്കി വച്ചിരിക്കുന്ന പാക്കറ്റുകളിൽ സ്പോഞ്ച് അല്ലെങ്കിൽ വൈക്കോൽ നിറയ്ക്കുന്നു. Sponge or straw is packed into boxes in which glassware is stacked.

📦 A jolt in a box – bare cardboard vs sponge packing

When the box is dropped or jerked, the glass vessels move and have to be stopped. If they hit the hard box (or each other) directly they stop in a tiny time and a large impulsive force breaks them. Sponge or straw is soft: it squeezes slowly and increases the time of impact, so the force on the glass is much smaller and the glassware does not break.

⚠️ Common trap

Writing “the foam/sponge reduces the momentum”. It does not – the object still goes from its speed to rest, so the change in momentum is exactly the same. The soft material only increases the time, and that is what reduces the force.

5. Safety by design – longer time, smaller force

🎈

Airbags

In a crash the airbag inflates in about 1/30 s and lets the head sink in slowly, so it stops in a longer time – the force on the head and chest is much smaller than hitting the steering wheel.

⛑️

Helmets

The thick foam (thermocol-like) liner inside a two-wheeler helmet crushes on impact, increasing the stopping time of the head. Kerala's helmet rule for riders and pillion riders is pure physics.

🚗

Crumple zones

The front and back of a modern car are designed to fold up slowly in a crash, so that the passenger cabin stops over a longer time.

🏖️

Long-jump sand pit

Loose, dug-up sand lets the jumper's feet sink in – a long stopping time. Landing on hard ground from the same jump could injure the ankles.

🚌

Shock absorbers

KSRTC buses and autorickshaws have springs and shock absorbers that spread each jolt from a pothole over a longer time, so the force on the passengers is smaller.

👟

Bending the knees

When you jump down from a wall you bend your knees on landing. This increases the stopping time and reduces the force on your legs – try landing stiff-legged (don't!) and you will feel why.

🌴 Kerala corner – coconuts and soft soil

A coconut falling from a tall tree onto hard laterite or a concrete yard often cracks; one falling into freshly dug, loose soil in the coconut basin usually survives. The soft soil gives way and stops the coconut in a longer time, so the impulsive force on it is smaller. (That is also why the coconut makes a pit – the soil is pushed aside while the nut is stopped.)

🥚 Try at home – the egg drop. Drop a raw egg, sealed inside a small plastic bag, from about 50 cm onto a folded thick towel or a pillow. Then imagine dropping it on the floor. Same egg, same height, same change of momentum – only the stopping time differs.

⚠ Do this over a tray or outside, with an adult's permission; wash your hands after handling raw egg.

6. When F = 0 – the second law gives the first law

രണ്ടാം ചലനനിയമം പരിഗണിക്കുമ്പോൾ ബലം പ്രയോഗിക്കാത്ത ഒരവസരത്തെപ്പറ്റി ചിന്തിച്ചു നോക്കൂ. F = ma, a = F/m; F = 0 എങ്കിൽ a = 0. ബലം പ്രയോഗിക്കാത്ത അവസരങ്ങളിൽ വസ്തുവിന് ത്വരണം ഉണ്ടാകില്ലല്ലോ. ത്വരണമുണ്ടാകാത്ത അവസ്ഥയിൽ ചലിച്ചുകൊണ്ടിരിക്കുന്ന വസ്തു നേർരേഖാപാതയിൽ തുടരുകയോ ചലനമില്ലാത്ത വസ്തു നിശ്ചലാവസ്ഥയിൽ തുടരുകയോ ചെയ്യും. ഇത് ഒന്നാം ചലന നിയമമല്ലേ? ഇതിൽ നിന്നും രണ്ടാം ചലന നിയമം ഒന്നാം ചലന നിയമവുമായി ഒത്തുപോകുന്നതായല്ലേ മനസ്സിലാകുന്നത്? Using the second law, think about a situation where no force is applied. F = ma, so a = F/m. If F = 0, then a = 0. When no force acts, the object has no acceleration. Without acceleration, a moving object continues along a straight line (at the same speed), and an object at rest stays at rest. Isn't this the first law? So the second law agrees with the first law.

🧪 Set the unbalanced force to zero

unbalanced force F (N) start

A 2 kg trolley on a frictionless track; positive = to the right. With F = 0 the v–t graph is a flat line: uniform velocity (or rest) – exactly the first law.

🔗 How the laws fit together

First law: no unbalanced force → no change in motion. Second law: an unbalanced force F → change of momentum at the rate F (F = ma; F × t = mv − mu). Put F = 0 in the second law and you get the first law back. The third law (next page) tells us that forces always come in pairs.

🌐 Explore online needs internet · opens in a new tab

▶️ Demonstrating How Helmets Affect Impulse and Impact Force YouTube – Flipping Physics · 4:20
A force sensor shows a helmet stretches the impact time and cuts the force.
▶️ WILL IT BREAK? Egg Drop Physics (Full Length) YouTube – TAMU Physics & Astronomy · 1:10
Texas A&M physicists show why a soft landing saves the egg: same momentum change, longer time.
▶️ How Airbag Works In Car | How Do Airbags Make a Car Safer? YouTube – BYJU'S · 3:29
How airbags reduce the force on you by increasing the stopping time.
▶️ The Physics of Car Crashes YouTube – minutephysics · 3:09
Why crumple zones are designed to crush.
📄 Momentum and Impulse – Real-World Applications The Physics Classroom
Airbags, padded dashboards, boxing and catching explained with impulse.

Check yourself

Next: Newton's third law – action and reaction ▶