Lecture Notes on Gravity, Weight, and Normal Force

Lecture Overview

• Course: PHYS 225 - Fundamentals of Physics: Mechanics

• Instructor: Prof. Meng (Stephanie) Shen

• Institution: California State University, Fullerton

Learning Goals

• Understand the concept of Weight

• Comprehend the Force of Gravity in general

• Learn about Normal Force

• Analyze Free Body Diagrams (FBD)

Key Concepts in Gravity and Forces

1. Weight

• Weight is defined as the force of gravity acting on an object near the Earth’s surface.

• Mathematically expressed as:
  $W = F<em>g = m a</em>y = -g \boldsymbol{j} ext{ where } g ext{ is approximately } 9.8 ext{ m/s}^2$

2. Free Fall in a Vacuum

• A feather and a penny dropped from the same height will land at the same time in a vacuum due to the absence of air resistance.

3. Newton’s Law of Gravity

• An attractive force described by:
  $|F<em>g| = G rac{m</em>1 m_2}{r^2}$

• G = Gravitational constant

• The direction of force is always towards the other object.

4. Earth-Moon Gravity Interactions

• Both Earth and Moon exert equal gravitational forces on one another, thus:

  • Answer: c) They pull on each other equally.

5. Force of Gravity Example: Earth

• Parameters:

  • Earth radius (R_E) = 6371 km

  • Earth mass (M_E) = $5.972 imes 10^{24} ext{ kg}$

  • Gravitational constant (G) = $6.674 imes 10^{-11} ext{ N m}^2 ext{ kg}^{-2}$

• The acceleration due to gravity on Earth's surface can be calculated as:
  $a <br>ightarrow (6.674 imes 10^{-11})(5.972 imes 10^{24}) / (6.371 imes 10^6)^2 <br>ightarrow a ext{ is approximately } 9.8 ext{ m/s}^2$

6. Relationship Between Gravity and Weight

• For an object of mass m:
  $|F<em>g| = G rac{m M</em>E}{R_E^2}$

• Force of gravity or weight can also be expressed as:
  $F_g = W = -m g \boldsymbol{j}$

• Where $g ext{ is equivalent to } 9.8 ext{ m/s}^2$ on Earth.

7. Normal Force

• The normal force is the support force exerted by a surface that supports the weight of an object resting on it.

• Direction: Always perpendicular to the surface.

• Magnitude: Adjusts to be exactly equal to the weight force when in equilibrium.

8. Free Body Diagrams (FBD)

• FBDs provide a visual representation of all forces acting on an object.

• Each force is shown as a vector to indicate direction.

• Forces not aligned with coordinate axes should be decomposed along these axes.

Steps to Draw a Free Body Diagram (FBD)

1. Draw the coordinate system (x, y, z axes).

2. Indicate all forces acting on the object or system.

3. Decompose any non-axial forces as necessary.

Example Problem

• Scenario: A block of mass 1 kg sliding with external forces F1 = 2N and F2 = 8N along a frictionless surface.

• Use FBD to solve for acceleration and normal force acting on the block.

Conclusion

• This lecture emphasized understanding gravity, how to analyze forces in free fall, normal forces, and using Free Body Diagrams for problem-solving in mechanics.

Key Equations and Concepts

1. Weight
   Weight (bW) is defined as the force of gravity acting on an object near the Earth’s surface.
   Mathematically expressed as:
   $W = F<em>g = m a</em>y = -g \boldsymbol{j} \text{ where } g \text{ is approximately } 9.8 \text{ m/s}^2$

2. Free Fall in a Vacuum
   A feather and a penny dropped from the same height will land at the same time in a vacuum due to the absence of air resistance.

3. Newton’s Law of Gravity
   An attractive force described by:
   $|F<em>g| = G \frac{m</em>1 m_2}{r^2}$

   • G = Gravitational constant

   • The direction of force is always towards the other object.

4. Force of Gravity Example: Earth
   Parameters:

   • Earth radius (R_E) = 6371 km

   • Earth mass (M_E) = $5.972 \times 10^{24} \text{ kg}$

   • Gravitational constant (G) = $6.674 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2}$

   • The acceleration due to gravity on Earth's surface can be calculated as:
     $a \rightarrow \frac{(6.674 \times 10^{-11})(5.972 \times 10^{24})}{(6.371 \times 10^6)^2} \rightarrow a \text{ is approximately } 9.8 \text{ m/s}^2$

5. Relationship Between Gravity and Weight
   For an object of mass m:
   $|F<em>g| = G \frac{m M</em>E}{R<em>E^2}$ Force of gravity or weight can also be expressed as: $F</em>g = W = -m g \boldsymbol{j}$
   Where $g \text{ is equivalent to } 9.8 \text{ m/s}^2$ on Earth.

6. Normal Force
   The normal force is the support force exerted by a surface that supports the weight of an object resting on it.

   • Direction: Always perpendicular to the surface.

   • Magnitude: Adjusts to be exactly equal to the weight force when in equilibrium.

7. Free Body Diagrams (FBD)
   FBDs provide a visual representation of all forces acting on an object.

   • Each force is shown as a vector to indicate direction.

   • Forces not aligned with coordinate axes should be decomposed along these axes.