Questions: Laws of Motion

Q1. State Newton's first law and explain what inertia means.

Answer: A body remains at rest or in uniform motion along a straight line unless a net external force acts on it. The law defines the natural state of motion and introduces inertia, the tendency of a body to resist a change in its velocity. Mass measures inertia: for the same force, a body of larger mass has a smaller acceleration, so a loaded truck and a bicycle respond very differently to the same push.

Hinglish: Newton ka first law kehta hai ki body rest mein ya uniform motion mein rehti hai jab tak net external force na lage. Inertia velocity change ka virodh karne ki property hai, aur mass uska measure hai. Same force ke liye zyada mass wali body ka acceleration kam hota hai. Force motion banaye rakhne ke liye nahi, badalne ke liye lagta hai.

Q2. State Newton's second law in both forms and derive F = ma from it.

Answer: In momentum form the law says the net force equals the rate of change of momentum, F = dp/dt. With p equal to mv and constant mass, the derivative is m dv/dt, which is ma. The two forms coincide only when the mass does not change; a rocket loses mass as it burns fuel, so the momentum form is the correct one there. The law is a vector relation, so each component obeys it separately.

Hinglish: Second law ka momentum form F = dp/dt hai. Agar mass constant ho to p = mv ka derivative m dv/dt = ma milta hai. Rocket ka mass ghatta hai, isliye uske liye momentum form hi sahi hai. Law vector hai, isliye har axis ke liye alag lagta hai.

Q3. Explain why the action and reaction forces do not cancel each other.

Answer: The action and reaction of Newton's third law act on two different bodies. The force that A exerts on B and the force that B exerts on A are equal and opposite, but they enter the free body diagram of different objects, so they never appear together in one equation. If a book rests on a table, the weight and the normal reaction on the book are not a third law pair: the reaction to the book's weight is the book's pull on the Earth, and the reaction to the normal is the book's push on the table.

Hinglish: Third law ke action aur reaction alag bodies par lagte hain, isliye ek hi free body diagram mein dono ek saath nahi aate aur cancel nahi hote. Book aur table wale case mein weight ka reaction Earth par hai, aur normal ka reaction table par, isliye woh pair nahi hain.

Q4. Define impulse and show that it equals the change in momentum.

Answer: Impulse is the product of force and the time for which it acts, and for a varying force it is the integral of force with respect to time. Starting from F = dp/dt and integrating over the contact time gives the impulse equal to the change in momentum. This is the impulse-momentum theorem. It explains why a longer contact time needs a smaller force to produce the same momentum change, which is the principle behind airbags and follow-through in sport.

Hinglish: Impulse force aur time ka product hai, aur variable force ke liye force ka time integral. F = dp/dt ko contact time par integrate karne se impulse change in momentum ke barabar milta hai. Isi wajah se airbag aur sports mein follow-through se contact time badhta hai aur force kam ho jaata hai.

Q5. State the principle of conservation of momentum and give one example.

Answer: If the net external force on a system is zero, the total momentum of the system remains constant. The internal forces are equal and opposite pairs by the third law, so they cannot change the total. A gun firing a bullet is a standard example: before firing the total momentum is zero, so after firing the bullet's forward momentum equals the gun's backward momentum, and the gun's recoil speed is the bullet's momentum divided by the gun's mass. A rocket works on the same principle because the exhaust carries momentum backward.

Hinglish: Jab net external force zero ho, system ka total momentum constant rehta hai. Internal forces third law se equal opposite hote hain, isliye total nahi badal sakte. Gun firing mein pehle momentum zero, baad mein bullet ka forward momentum gun ke backward momentum ke barabar; recoil speed bullet momentum divided by gun mass. Rocket isi principle par chalta hai.

Q6. A body of mass 5 kg is acted on by a net force of 20 N for 3 s. Find its change in velocity and the impulse.

Answer: The acceleration is 20/5, that is 4 m per second squared, so in 3 s the velocity changes by 12 m per second. The impulse is the force times the time, 60 N s, and this equals the change in momentum, 5 times 12, which is also 60 kg m per second. If the same impulse were delivered in 0.5 s instead, the average force would be 120 N, four times larger for the same change in momentum.

Hinglish: Acceleration 20/5 = 4 m/s^2, isliye 3 s mein velocity change 12 m/s. Impulse 20 x 3 = 60 N s, jo change in momentum 5 x 12 = 60 kg m/s ke barabar hai. Same impulse 0.5 s mein dene par average force 120 N ho jaata hai, chaar guna zyada.

Q7. Explain why a block stays at rest on an inclined plane up to a certain angle.

Answer: The component of the weight down the slope is mg sin theta and the normal reaction is mg cos theta. Static friction can rise to the coefficient of static friction times the normal reaction, so it can balance the downslope component while that component stays below the maximum. The critical angle satisfies tan theta equal to the coefficient of static friction, and it is called the angle of repose. Beyond that angle the required friction exceeds the maximum, so the block begins to slide and kinetic friction replaces static friction.

Hinglish: Slope ke along weight ka component mg sin theta hai aur normal mg cos theta. Static friction mu_s N tak badh sakta hai, isliye block tab tak rukta hai jab tak downslope component us maximum se kam ho. Critical angle par tan theta = mu_s, jise angle of repose kehte hain. Usse zyada angle par block slide karne lagta hai aur kinetic friction lagta hai.

Q8. Find the maximum safe speed of a car on a level road with friction coefficient 0.5 and a turn of radius 40 m. Take g = 10 m s^-2.

Answer: On a level road the centripetal force is supplied by static friction, so mass times speed squared over the radius must not exceed the friction coefficient times the normal reaction, which equals the weight. The mass cancels and the speed squared equals 0.5 times 40 times 10, that is 200, so the maximum speed is about 14.1 m per second, roughly 51 km per hour. Above that speed the tyres lose grip and the car skids toward the outside of the turn.

Hinglish: Level road par centripetal force static friction deta hai, isliye mv^2/r <= mu mg. Mass cancel ho jaata hai aur v^2 = 0.5 x 40 x 10 = 200, matlab maximum speed lagbhag 14.1 m/s ya 51 km/h. Isse tez chalne par grip chala jaata hai aur car bahar ki taraf skid karti hai.

Q9. Why is a banked road safer than a level road for the same turn?

Answer: On a banked road the surface is tilted so that the normal reaction gains a horizontal component toward the centre of the turn. At the design speed that component supplies the whole centripetal force, so no friction is needed and the road remains safe on a wet day when the friction coefficient is low. The banking angle satisfies tan theta equal to speed squared over the product of radius and g. On a level road the same turn depends entirely on friction, so the safe speed falls sharply when the road is wet.

Hinglish: Banked road par surface tilt hoti hai, isliye normal reaction ka ek horizontal component centre ki taraf hota hai. Design speed par woh component poora centripetal force deta hai, friction ki zaroorat nahi padti, isliye barish mein bhi road safe rehta hai. tan theta = v^2/(rg) relation banked speed deta hai. Level road par sab kuch friction par depend karta hai, isliye geeli sadak par speed bahut kam ho jaati hai.

Q10. A ball of mass 0.2 kg moving at 10 m s^-1 is hit back along the same line at 8 m s^-1. Find the impulse on the ball.

Answer: Take the initial direction as positive. The initial momentum is 0.2 times 10, which is 2 kg m per second, and the final momentum is 0.2 times minus 8, which is minus 1.6 kg m per second. The change in momentum is the final minus the initial, minus 3.6 kg m per second, so the impulse is 3.6 N s directed opposite to the initial motion.

Hinglish: Initial direction positive lo: initial momentum 0.2 x 10 = 2, final momentum 0.2 x (-8) = -1.6. Change -1.6 - 2 = -3.6 kg m/s, isliye impulse 3.6 N s initial motion ke opposite. Sign mat chhodo, kyunki ball direction badal rahi hai, isliye momentum change sirf rukne se zyada hai.

Quiz below: five questions on the three laws, impulse, friction and circular motion. Attempt them before rereading the formula sheet, and check each wrong answer against the matching page.