Forces and Newton's Laws

Forces Overview

• Forces are pushes or pulls affecting an object's motion.
• Contact forces involve physical touching between objects.
• Non-contact forces, like gravity, magnetism, and electrostatic force, do not require physical touching.

Newton's First Law: Inertia

• An object remains at rest or moves at a constant velocity unless acted upon by an external force.
• Inertia is the resistance of an object to changes in its state of motion and is related to mass.
• Drag force and frictional force are external forces in the real world that can cause an object to slow down.

Newton's Second Law: F = ma

• Force equals mass times acceleration (F = ma).
• The unit of force is the Newton (N), equivalent to kg*m/s².
• One Newton is the force required to accelerate a 1 kg mass at 1 m/s².
• The mass of an object does not affect the direction of acceleration.
• Force and acceleration have a direct relationship: increasing force increases acceleration proportionally.
• Mass and acceleration have an inverse relationship: increasing mass decreases acceleration, and vice versa, given a constant force.

Newton's Third Law: Action-Reaction

• Every action has an equal and opposite reaction.
• When a box rests on a table, gravity pulls down on the box (action), and the box pulls up on the Earth (reaction) with an equal force.
• The box applies a downward force on the table (due to its weight), and the table applies an equal and opposite restoring force upwards on the box.
• The box experiences more acceleration than the earth because it is less massive.

Free Body Diagrams

• Free body diagrams model the magnitude and direction of forces acting on objects.
• Arrows represent forces, with length indicating magnitude (longer arrow = stronger force).
• Diagrams focus on forces acting on a single body.
• Force vectors originate from the center of mass.
• All forces must be clearly labeled.
• Free body diagrams can illustrate various situations, such as a falling ball (gravity only), a ball on the ground (gravity and support force), or an accelerating ball (applied force, friction, gravity, and support force).

Translational Equilibrium

• Translational equilibrium occurs when an object has a constant velocity (including zero).
• This happens when the net force on the object is zero.
• A basket suspended by two ropes at different heights can be in translational equilibrium if the forces balance in both the vertical and horizontal dimensions.
• In the vertical dimension, the upward tension force from one rope equals the downward force of gravity.
• In the horizontal dimension, the tension forces from the two ropes oppose each other and are equal in magnitude.
• Trigonometry can be used to calculate the force values of the tension to determine if it is indeed in equilibrium

Elastic Restoring Force

• Springs produce an elastic restoring force when extended or compressed.
• The force is directly related to the extension of the spring (Hooke's Law: F = kx).
• k is the spring constant, representing the stiffness of the spring.
• In a series system of multiple springs, the reciprocal of the equivalent spring constant is the sum of the reciprocals of individual spring constants: 1/k' = 1/k_a + 1/k_b.
• In a parallel system, the equivalent spring constant is the sum of individual spring constants: k' = k_a + k_b

Buoyancy Force

• Buoyancy force acts upwards on an object submerged in a fluid.
• Density (ρ) is mass (m) per unit volume (V): ρ = m/V.
• The unit for density is kilogram per M cubed.
• The buoyancy force is equal to the density of the fluid times the volume of the displaced fluid times G.
• Neutral buoyancy occurs when the densities of the fluid and object are equal.
• An object sinks if its density is greater than the fluid's density.
• An object floats if its density is less than the fluid's density.

Frictional Force

• Frictional force opposes the motion of objects in contact.
• Static friction prevents initial motion, while dynamic friction opposes motion once it has started.
• Dynamic friction is typically less than static friction.
• The force of friction depends on the normal force (weight of the object) and the coefficient of friction (µ), which represents the type of surfaces in contact.
• The value to solve for frictional force is the same for both static and dynamic, but each has a different coefficient of friction to account for the different forces.

Air Resistance & Terminal Velocity

• Air resistance is the force exerted by air molecules on an object moving through the atmosphere.
• The drag force is the average force from air molecules contacting the object.
• A falling skydiver experiences increasing air resistance as their speed increases.
• Terminal velocity is reached when the drag force equals the gravitational force, resulting in a zero net force and constant velocity.
• Parachutes increase surface area, increasing the drag force and slowing the descent.

Stokes's Law

• Stokes's Law calculates the drag force on objects moving through fluids, considering fluid viscosity.
• Viscosity measures a fluid's resistance to deformation.
• Stokes's Law: drag force = 6πηrv, where η is viscosity, r is the object's radius, and v is its velocity.
• By applying Stokes's Law and free body diagrams, the terminal velocity of a ball falling through the air can be determined by summing the forces from gravity, buoyancy, and drag to be equal to zero