8.01x - Lect 6 - Newton's Laws

Main Ideas and Lessons

Newton’s First Law: Inertia

• A body at rest remains at rest, and a moving body continues at constant velocity in a straight line unless an external force acts on it. Galileo described this as the law of inertia; Newton stated a similar principle in the Principia.
• Everyday objects seem to stop because forces such as friction and air resistance act on them. The law describes what would happen if those forces were absent.
• The First Law applies in inertial reference frames—frames that are not accelerating. An accelerating observer may perceive motion in a way that makes the law appear not to hold.
• No real location is perfectly inertial: Earth rotates, orbits the Sun, and moves with the Solar System. Lewin estimates that Earth’s rotational acceleration at the equator is about 0.034 m/s², far smaller than gravitational acceleration. The lecture hall is therefore treated as a sufficiently good approximation to an inertial frame.
• The law cannot be proven absolutely because it is impossible to establish that a reference frame has no acceleration at all. It is accepted because experiments are consistent with it within measurement uncertainty.

Newton’s Second Law: Force and Acceleration

• Lewin illustrates the relationship using a stretched spring. With the same spring extension—and therefore the same pull—different masses acquire different accelerations. Experimentally, the products of mass and acceleration are equal for the same pull.
• This motivates the definition and equation F = ma:
  • Acceleration is in the direction of the net force.
  • Its magnitude is proportional to the force and inversely proportional to the mass.
  • One newton is 1 kg·m/s².
• The Second Law, like the First, is stated to apply in inertial reference frames and is supported by experimental agreement rather than absolute proof.
• Mass can be compared without relying on gravity. For instance, two identical pieces of cheese together have twice the mass of one, based on their amount of matter.
• Near Earth’s surface, an object’s gravitational force (weight) is mg. If an object is held at rest, another force must balance its weight so the net force is zero.
• The equation does not require a particular speed, but Newtonian mechanics is not adequate when speeds approach the speed of light; special relativity is then needed.

Newton’s Third Law: Action and Reaction

• If one object exerts a force on another, the second exerts an equal force in the opposite direction on the first: action equals minus reaction.
• The paired forces act on different objects; they do not cancel each other on a single object.
• Examples include:
  • A hand and a ball exerting equal, opposite forces on each other.
  • A person pushing on a wall and the wall pushing back.
  • A person walking by pushing backward on the floor while the floor pushes forward on the person.
  • A hose or balloon recoiling as water or air is expelled.
  • A gun recoiling when it pushes a bullet forward.
  • Steam expelled from Hero’s engine causing the device to rotate.
• In a two-block example, a 20 N force accelerates a 5 kg block and a 15 kg block together. Their combined mass is 20 kg, so the acceleration is 1 m/s². The contact force between the blocks is 15 N in either direction, with opposite signs.

Earth and a Falling Object

• Newton’s Third Law means Earth is pulled toward a falling object just as strongly as the object is pulled toward Earth.
• For a 0.5 kg apple falling from 100 m, Lewin estimates a fall time of about 4.5 seconds. The apple’s force on Earth is about 5 N, but Earth’s enormous mass makes its acceleration tiny—about 8 × 10⁻²⁵ m/s². Over the fall, Earth moves only about 8 × 10⁻²⁴ m toward the apple.
• The displacement is immeasurably small, but the example illustrates that the mutual forces are equal even when the resulting accelerations are vastly different.

Finding Tensions in Two Supporting Strings

Lewin works through a mass held at rest by two strings: one at 30° to the vertical and the other at 45° to the vertical.

1. Draw the forces on the mass: the two string tensions and its weight, mg.
2. Since the mass is not accelerating, set the net force to zero in both the horizontal and vertical directions.
3. Resolve each tension into components:
   • Horizontal balance: T₁ cos 60° − T₂ cos 45° = 0
   • Vertical balance: T₁ sin 60° + T₂ sin 45° − mg = 0
4. Solve the simultaneous equations:
   • T₁ = 2mg / (1 + √3)
   • T₂ = T₁ / √2
5. For a 4 kg mass, using g ≈ 10 m/s², the tensions are approximately 29.3 N and 20.7 N.
6. Alternatively, construct a force triangle: the two tension vectors must combine to balance the weight. The known angles and the magnitude of the weight can then be used to find the tensions geometrically.

The lecture also demonstrates spring-based tension meters and notes that experimental readings depend on calibration, the accuracy of the angles, and measurement uncertainty.

Final String-Breaking Demonstration

• Lewin shows two nearly identical strings, one above a 2 kg block and another below it. Pulling on the lower string produces different outcomes in repeated trials: sometimes the lower string breaks, and sometimes the upper one does.
• The changing result highlights that how a force is applied matters in a real demonstration. The lecture ends by asking students to think about the result rather than giving a definitive explanation in the subtitles.

Speakers and Sources Featured

• Walter Lewin — lecturer and demonstrator.
• Students in the lecture hall — answer questions and vote during the string-breaking demonstration. One student is addressed as “Alicia” and then “Georgia, close enough,” so the name is unclear in the subtitles.
• Galileo — quoted by Lewin for the law of inertia; not a live speaker.
• Isaac Newton — quoted by Lewin for the First and Second Laws; not a live speaker.