Notes on Newton's Second Law in Elevators

Introduction to Newton's Second Law in Elevators

• Presenter: Joe Mancino, Glastonbury High School, CT.

• Topic: Application of Newton's Second Law in the context of elevators.

• Student Feedback: Many students find the concepts involving elevators particularly challenging in AP Physics 1.

Key Terminology

Net Force

• Definition: The vector sum of all forces acting on an object.

• Importance: Necessary to consider when multiple forces are applied to an object; requires vector addition of forces.

Forces Acting on the Object in an Elevator

• Force of Gravity:

  • Exerted by Earth on the object, directed downwards.

• Normal Force:

  • Exerted by the scale on the object when it is inside the elevator, directed upwards.

Role of Mass

• The acceleration experienced by the object is influenced by both the net force acting on it and the object's mass.

• Newton's Second Law:

  • Relationship: $F_{net} = m imes a$

  • Where:

    • $F_{net}$ = net force

    • $m$ = mass of the object

    • $a$ = acceleration

• Implication of the Law:

  • Greater net force leads to greater change in motion (acceleration).

  • Greater mass results in less acceleration, given the same net force.

Understanding Forces in the Elevator

Vector Sum of Forces

• The net force is determined by the difference in magnitudes between the upward force from the scale and the downward force of gravity.

• Cases of Net Force:

  • Balanced Forces: When forces acting on the object are equal in magnitude, leading to zero acceleration (constant velocity).

  • Unbalanced Forces: When forces are not equal, leading to acceleration in the direction of the net force.

Example Scenario: Riding an Elevator

Observations from Riding an Elevator

• Path through the elevator experience:

  1. Starting from rest at the bottom (Ground Floor).

  2. Speeding up while moving upward.

  3. Cruising at a constant speed through the middle floors.

  4. Slowing down near the top.

  5. Coming to rest at the top.

Personal Experience of Forces

• Different sensations experienced during the elevator ride:

  • At the Bottom (Speeding Up): Felt "extra heavy" due to increased normal force.

  • Middle Floors (Constant Speed): Felt "regular weight"; forces were balanced and acceleration was zero.

  • At the Top (Slowing Down): Felt "extra light" due to decreased normal force.

Data Analysis

Scale Readings

• Data points observed during the elevator ride:

  • Ground Floor: Scale reading at rest, upward force = downward force (gravity).

  • Middle Floors: Constant speed indicates balanced forces.

  • Near Top: Scale reading shows evidence of unbalanced forces.

Numerical Example

1. At Bottom (Speeding Up):

   • Downward Force (Gravity): 800 Newtons

   • Upward Force (Scale): 885 Newtons

   • Net Force: 885 N - 800 N = 85 Newtons (upward)

   • Mass of the object: 80 kg

   • Acceleration Calculation:

     • Using the formula $a = \frac{F_{net}}{m}$,

     • Result: $a = \frac{85 ext{ N}}{80 ext{ kg}} \approx 1.06 ext{ m/s}^2$ (upward).

2. At Top (Slowing Down):

   • Downward Force (Gravity): 800 Newtons

   • Upward Force (Scale): 705 Newtons

   • Net Force: 705 N - 800 N = -95 Newtons (downward)

   • Acceleration Calculation:

     • $a = \frac{-95 ext{ N}}{80 ext{ kg}} \approx -1.19 ext{ m/s}^2$ (downward).

Additional Calculations

Estimating Constant Velocity

• Using average forces during the cruise phase of upward motion:

  • Average upward force: 855 Newtons.

  • Net force: 855 N - 800 N = 55 N (upward).

  • Average acceleration:

  • $a = \frac{55 ext{ N}}{80 ext{ kg}} \approx 0.6875 ext{ m/s}^2$

  • Duration of acceleration: Approximately 3.5 seconds, leading to change in speed calculation:

  • $\Delta v = a \times t = 0.6875 ext{ m/s}^2 \times 3.5 ext{ s} \approx 2.40625 ext{ m/s}$.

Conclusion

Key Takeaways

• Understanding net force and unbalanced forces is crucial in analyzing motion.

• A graph of the forces acting during an elevator ride helps in estimating net force, acceleration, and velocity.

• The dynamics within an elevator provide practical applications of Newton's Second Law in real-world scenarios.

• Emphasis on how experiences in elevators relate to fundamental physics concepts

• Closing Remarks: Thank you and anticipation for the next lesson.