Physics 2211K: Study Notes on Newton's Laws

Newton's Laws of Motion Overview

Basic Concepts of Newton's Laws

• Newton's Laws of Motion are foundational principles that describe the relationship between the motion of an object and the forces acting upon it.

• There are three primary laws:

  • First Law (Law of Inertia): An object at rest will remain at rest and an object in motion will remain in motion at a constant velocity unless acted upon by a net external force.

  • Second Law (Law of Acceleration): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically expressed as:
    $F = ma$
    where

  • $F$ is the net force,

  • $m$ is the mass of the object, and

  • $a$ is the acceleration.

  • Third Law (Action-Reaction Law): For every action, there is an equal and opposite reaction. This means that forces always occur in pairs; if object A exerts a force on object B, then object B exerts an equal and opposite force on object A.

Example Problems

Problem 1: Skydiver

• A skydiver of mass 72 kg is descending with a parachute, experiencing an acceleration of 1.2 m/s². The problem is to determine the magnitude and direction of the force exerted by the parachute harness on the diver.

  • Calculation: Using Newton's second law,
    $F = ma$

  • Given:

  • $m = 72$ kg

  • $a = 1.2$ m/s²

  • Thus,
    $F = 72 imes 1.2 = 86.4 ext{ N (net force)}$

  • The gravitational force ($Fg$) acting on the diver: $F</em>g = mg = 72 imes 9.8 = 705.6 ext{ N downward}$

  • The force of the parachute harness ($F_H$) is 619.2 N upward, balancing out the forces involved during descent.

Problem 2: Block on Incline

• A 50 kg block is resting on a 25° rough incline.

  • Objective:

  • A) Find the magnitude of the normal force ($F_N$) acting on the block.

  • B) Find the magnitude of the static friction force ($F_S$) acting on the block.

• Calculations:

  • The normal force can be calculated as follows:
    $F_N = mg imes ext{cos}(25°)$

  • Given:

  • $m = 50$ kg

  • Gravitational force:
    $F_g = 50 imes 9.8 = 490 ext{ N}$

  • Therefore,
    $F<em>N = 490 imes ext{cos}(25°) ightarrow F</em>N = 444.1 ext{ N}$

  • Static friction force can be calculated as follows:
    $F<em>S ext{ (approx.)} = ext{friction coefficient} imes F</em>N <br>ightarrow ext{Assuming applicable coefficient here, } F_S = 207.1 ext{ N}$

Problem 3: Atwood Machine

• Description: An Atwood machine consists of two masses connected by a light string over a massless pulley.

• Given mass $m1 = 31$ kg on one side and $m2 = 22$ kg on the other:

• To find acceleration ($a$), consider the difference in weight:
  $F<em>{net} = m</em>1g - m<em>2g = (m</em>1 - m_2)g$

• Substituting the values results in:
  $m<em>1 = 31 ext{ kg}, m</em>2 = 22 ext{ kg}, g = 9.8 ext{ m/s²}$
  $F_{net} = (31-22) imes 9.8 = 88.2 ext{ N}$

• The mass of the system:
  $m<em>{total} = m</em>1 + m_2 = 31 + 22 = 53 ext{ kg}$

• The acceleration is thus:
  $a = rac{F<em>{net}}{m</em>{total}} = rac{88.2}{53} <br>ightarrow a = 1.66 ext{ m/s²}$

Multiple Choice Questions

1. Acceleration Graph of a Pulled Cart: Options include various forms of graphs; understanding the nature of constant force and resultant acceleration is crucial here.

2. Train and Wall Collision: Regarding the collision between a train and a wall:

   • Correct Option: C. The train exerts the same force on the wall as the wall exerts on the train, illustrating Newton's third law.

3. Tension in Ropes: In a system with multiple ropes, options examine the relationship between tensions depending on mass distribution and positioning.

4. Free-Body Diagram for a Car Engine: Understanding the forces to include (tensions in chains) in a free-body diagram is essential for analyzing static or dynamic situations.

5. Frictionless Surface and Tension Forces: Exploring scenarios of blocks on a frictionless surface, the tension forces reflect directly on the block's mass and movement dynamics.

6. Free-Body Diagram for Crate on Surface: Determining relevant forces acting on crate B demonstrates understanding of inter-object interactions and forces of nature.

• Encouragement to work in groups to solve problems signifies the importance of collaborative learning in physics problem-solving.

• Solutions to problems (1-16, 17-19) are to be checked with instructors or teaching assistants as a means of verifying understanding.