Newton's Laws — Set 5

Correct Answer: B. Isaac Newton

• **Isaac Newton** = Isaac Newton published his laws of motion and universal gravitation in 'Philosophiæ Naturalis Principia Mathematica' in 1687. • **1687** — the Principia is considered one of the most important scientific works ever published. • 💡 Wrong-option analysis: Johannes Kepler: Kepler formulated the laws of planetary motion, not the Principia; Albert Einstein: Einstein published the theory of relativity in the 20th century; Galileo Galilei: Galileo contributed foundational experimental work but did not publish the Principia.

Correct Answer: B. Zero acceleration

• **Zero acceleration** = Balanced forces have a vector sum of zero; by Newton's Second Law F = ma, zero net force means zero acceleration. • **ΣF = 0 → a = 0** — the object either remains at rest or moves at constant velocity (Newton's First Law). • 💡 Wrong-option analysis: Acceleration: acceleration requires nonzero net force; Change in direction: changing direction requires a net force (centripetal); Increase in mass: mass is invariant in classical mechanics.

Correct Answer: C. No external force acts

• **No external force acts** = The law of conservation of momentum: the total momentum of a system is conserved only when the net external force acting on the system is zero. • **F_ext = 0 → p_total = constant** — internal forces between parts of the system cancel in pairs (Newton's Third Law). • 💡 Wrong-option analysis: Friction is high: high friction is an external force that would change total momentum; Internal forces are zero: internal forces always cancel in pairs and do not affect total momentum — the condition for conservation is zero external force; Gravity is zero: gravity being zero is one way to have zero net external force, but is not the general condition.

Correct Answer: C. Static friction being higher

• **Static friction being higher** = Static friction (which must be overcome to start motion) is generally greater than kinetic friction, requiring the horse to exert more effort at the start. • **μs > μk** — once the cart is moving, the lower kinetic friction takes over and the horse needs less force. • 💡 Wrong-option analysis: Kinetic friction being higher: wrong — kinetic friction is generally lower than static friction; Air resistance: air resistance is negligible for a slow-moving cart compared to ground friction; Gravity: gravity is a vertical force and does not directly oppose horizontal motion on flat ground.

Correct Answer: B. Second Law

• **Second Law** = Newton's Second Law F = ma relates force, acceleration, and mass — through this equation, mass is defined as the 'quantity of matter' (resistance to acceleration). • **m = F/a** — mass can be determined by measuring force and acceleration, making it a quantitative measure of matter. • 💡 Wrong-option analysis: First Law: the first law defines force qualitatively (as what changes motion) — it does not quantify mass; Third Law: the third law deals with action-reaction pairs, not with defining mass; None of these: the second law is indeed the correct answer.

Correct Answer: A. Action and reaction are on different bodies

• **Action and reaction are on different bodies** = Newton's Third Law forces always act on two different objects; since they act on different bodies, they cannot cancel each other. • **different bodies** — e.g., Earth pulls you down (action on you); you pull Earth up (reaction on Earth). • 💡 Wrong-option analysis: Reaction is smaller than action: wrong — they are always equal in magnitude; Action and reaction cancel out: wrong — they act on different bodies and therefore do not cancel; Action precedes reaction: wrong — action and reaction occur simultaneously.

Correct Answer: B. Force

• **Force** = The slope of a momentum–time graph = dp/dt = F; force equals the rate of change of momentum (Newton's Second Law). • **slope of p–t graph = F** — a steeper slope means a larger net force acting on the object. • 💡 Wrong-option analysis: Acceleration: acceleration is the slope of a velocity–time graph, not a momentum–time graph; Velocity: velocity is the slope of a displacement–time graph; Work: work = F·s and cannot be read as a slope of a p–t graph.

Correct Answer: D. Sand increases the time of impact

• **Sand increases the time of impact** = Sand is soft and yields on impact, increasing the time Δt over which the person's momentum changes; by F = Δp/Δt, a larger Δt means a smaller impact force. • **F = Δp/Δt** — same momentum change over longer time → smaller force → less injury. • 💡 Wrong-option analysis: Cemented floor increases momentum: momentum change is determined by initial momentum, not the floor material; Cemented floor is harder: hardness means smaller time of impact, giving larger force — the mechanism is about time not hardness per se; Sand decreases the force of gravity: gravity is the same on both surfaces.

Correct Answer: D. Opposite to motion

• **Opposite to motion** = Kinetic (sliding) friction always acts in the direction that opposes the relative motion between surfaces in contact. • **friction = −v/|v| × f** — friction decelerates the block; it acts backward along the surface. • 💡 Wrong-option analysis: Same as motion: friction in the direction of motion would accelerate the object — it cannot oppose motion; Downward: friction acts along the surface (horizontally for a horizontal block), not vertically downward; Perpendicular to motion: the normal force is perpendicular to motion, not friction.

Correct Answer: A. Inertia

• **Inertia** = Inertia is the property of a body by which it maintains its current state — resisting both starting motion from rest and stopping from uniform motion. • **First Law = Law of Inertia** — no external force means no change in state; this is what allows objects to coast indefinitely in space. • 💡 Wrong-option analysis: Friction: friction is an external force that opposes motion — it does not maintain the state; Weight: weight is the gravitational force acting downward — it does not explain horizontal constant motion; Force: force is what changes the state of motion, not what maintains it.