5.6 Common Forces

Forces shape our physical world, from the normal force keeping us on the ground to tension in ropes and cables. Understanding these common forces helps us analyze everyday situations and complex systems, connecting the abstract concepts to tangible experiences.

Newton's_Laws_0### provide a framework for understanding motion and interactions between objects. By applying these laws to real-world scenarios, we can predict and explain the behavior of objects under various forces, bridging the gap between theory and practical applications.

Common Forces

Normal and tension forces

• Normal force acts perpendicular to surface of contact prevents object from sinking into surface (book on table, person standing on ground)
• Magnitude of normal force depends on weight of object and surface properties (hardness, elasticity)
• Tension force exerted by rope, string, cable when pulled taut always along length of object (person hanging from rope, clothesline with clothes)
• Magnitude of tension force equal at both ends of object determined by weight of suspended object and angle of rope

Real vs fictitious forces

• Real forces exist in nature caused by interaction between objects (gravitational, electromagnetic, strong and weak nuclear)
• Fictitious forces apparent due to acceleration of reference frame do not exist in inertial reference frame
  • Centrifugal force appears to push objects away from center of rotation (person in rotating car pushed against door)
  • Coriolis force deflects moving objects in rotating reference frame (wind patterns on Earth affected by rotation)
• Fictitious forces useful for analyzing motion in non-inertial reference frames (rotating platforms, accelerating vehicles)

Newton's laws in complex systems

• Newton's 1st law (inertia): object maintains state of rest or constant velocity unless acted upon by net external force (equilibrium)
• Newton's 2nd law: $\vec{F}_{net} = m\vec{a}$, acceleration directly proportional to net force inversely proportional to mass
• Newton's 3rd law: action-reaction force pairs equal in magnitude opposite in direction act on different objects
• Solving problems with multiple forces:
  1. Identify all forces acting on object
  2. Draw free-body diagram representing object and forces (force)
  3. Choose coordinate system (x and y axes)
  4. Resolve forces into components along chosen axes
  5. Apply Newton's 2nd law to each axis separately ($\sum F_x = ma_x$, $\sum F_y = ma_y$)
  6. Solve resulting equations for desired quantities (acceleration, tension, normal force)
• Examples:
  • Block on inclined plane with friction (normal force, friction force, gravitational force)
  • Atwood machine with unequal masses (tension forces, gravitational forces)

Friction and Work-Energy

• Friction is a force that opposes motion between surfaces in contact
  • Static friction prevents objects from starting to move (static friction)
  • Kinetic friction acts on objects already in motion (kinetic friction)
• Work is done when a force moves an object over a distance (work)
• Energy is the capacity to do work and comes in various forms (energy)