Lec 07: Weight, Perceived Gravity, and Weightlessnes | 8.01 Classical Mechanics (Walter Lewin)

Scientific concepts, discoveries, and nature/physical phenomena presented

1) Definition of weight (force vs. mass)

• Weight is defined operationally as the normal force / tension / scale reading—i.e., the force transmitted to the person/object by a support.
• In a stationary frame on Earth:
  • Gravity exerts force (mg) downward.
  • A scale pushes upward with force (F_{\text{scale}} = mg).
  • Therefore, the scale reading equals the object’s weight.

2) Apparent weight in an accelerating elevator

• Upward acceleration (elevator accelerating upward):

  • Scale force increases: [ F_{\text{scale}} = m(g+a) ]

  • Apparent weight increases.

  • Downward acceleration (elevator accelerating downward):

  • Scale force decreases: [ F_{\text{scale}} = m(g-a) ]

  • Apparent weight decreases.

  • Free fall / weightlessness condition:
  • If the elevator cable is cut, then (a=g) downward.

  • Scale force becomes zero: [ F_{\text{scale}} = m(g-a)=0 ]

  • The object becomes weightless, even though gravity still acts.

3) Free fall and what “weightless” means

• Free fall occurs when the only force is gravity (no contact forces).
• Objects in free fall are weightless because they have no support force (no scale/tension/normal force).
• Similarity emphasized:
  • Astronauts in orbit / free-falling elevator / free-falling objects: no weight (contact force vanishes).

4) Weightlessness during vertical circular motion

For a person/bucket on a string moving in a horizontal circle:

• The tension depends on centripetal acceleration: [ a_c=\omega^2R ]

• At the bottom of the circle: [ T=m(a_c+g) ] → increased weight (larger tension).

• At the top of the circle: [ T=m(a_c-g) ] → decreased weight.

• If (a_c=g), then (T=0):

  • the string goes slack → weightlessness.

5) Momentary weightlessness while jumping; impact causes large forces

• Demonstration: jumping off a table (ignoring air drag) gives brief free-fall:
  • the scale reading drops to ~0.
• During impact:
  • To stop the motion, acceleration is upward and large.
  • Scale reading increases dramatically during the short stopping time (high apparent weight).

6) “Equal weights” in a massless-string, frictionless-pulley/pin setup (counterintuitive result)

Setup:

• A frictionless pin with massless strings on both sides.
• Masses (m_1) and (m_2) with (m_2>m_1).

Key constraint (ideal strings/pin):

• Tension is the same on both sides: [ T_L=T_R=T ]

Because weight is defined via tension/scale reading:

• Both masses have the same apparent weight, even though their masses differ.

Solved results:

• Acceleration: [ a=\frac{m_2-m_1}{m_1+m_2}g ]

• Tension (apparent weight on both sides): [ T=\frac{2m_1m_2}{m_1+m_2}g ] (also presented as (T=\frac{2mg}{m_1+m_2}) in the lecture)

Limiting cases:

• If (m_1=m_2): [ a=0,\quad T=mg ]

• If (m_1\to 0): [ a\to g,\quad T\to 0 ] (the heavier mass effectively enters free fall)

7) “Zero gravity” airplane experiments and the misconception

• “Zero gravity” is a misnomer:
  • Gravity is not zero near Earth.
  • The key phenomenon is zero weight (free-fall).
• KC-135 flight profile:
  • The aircraft follows a parabolic free-fall arc.
  • During free-fall: passengers and airplane are weightless.
  • During pull-up/pullout: upward acceleration causes increased apparent weight (roughly up to about double weight, i.e., “2g peak”).
• Cyclic pattern:
  • Weightlessness (~30 s), then increased weight during pull-up, then normal weight, repeating on a cycle (~90 s).

8) Practical consequence: motion sickness and changing apparent weight

• Purpose described: experiments on motion sickness due to weightlessness (parabolic flights; also referenced later for shuttle).
• Safety note emphasized:
  • When weight returns/doubles quickly, people must orient correctly to avoid injury.

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Methodology / calculation “recipes” outlined (as implied by the lecture)

Elevator method (apparent weight)

1. Choose a coordinate sign for acceleration.

2. Apply Newton’s 2nd law to the person/object.

   • Use either:

     • Upward acceleration case: [ F_{\text{scale}}-mg=ma ]

     • Downward acceleration case: [ mg-F_{\text{scale}}=ma ]

3. Solve for scale force:

   • Upward accel: [ F_{\text{scale}}=m(g+a) ]

   • Downward accel: [ F_{\text{scale}}=m(g-a) ]

4. Weightless condition:

   • If (a=g), then (F_{\text{scale}}=0).

Vertical circular motion method

1. Compute centripetal acceleration: [ a_c=\omega^2R ]

2. Apply Newton’s 2nd law radially using tension and gravity.

   • Bottom: [ T-mg=ma_c ]

   • Top: [ T+mg=ma_c ] (with sign conventions leading to (T=m(a_c-g))).

3. Check slack condition:

   • If the required tension becomes unphysical (e.g., (T<0)), the string cannot maintain that tension.

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Featured researchers / sources

• Walter Lewin (lecturer; video source)
• Professor Dave Trumper (built the fast-response scale demonstration device)
• Professor Young (led/featured in airplane “zero weight” experiments on airsickness)
• Professor Oman (co-developed/featured in the airplane experiments at the Aeronautics Department)
• Kepler’s Law (mentioned as a later topic related to orbits; not a featured person in this excerpt)