W PHYS 2130: Physics for the Life Sciences I
UNIT 3: Forces and Newton's Laws
Emphasis on understanding mechanical forces.
3-1: Principles of motion & net force
Key Principles for Motion Investigation:
Inertia: Resistance of an object to change in its state of motion.
Mass: Amount of substance in an object.
Interactions: Forces acting between objects.
Egotism: Objects react only to immediate influences on them.
Reciprocity: Interaction forces occur in pairs between objects.
Superposition: Net force is the vector sum of all individual forces.
Definition: An object at rest remains at rest; an object in motion remains in motion unless acted upon by an external force.
Equivalent Statement: An object maintains its velocity (including zero) without external influence.
Mass: Quantifies the amount of substance.
Forces: Changes in velocity occur through interactions (push/pull).
Contact Forces: Direct physical contact between objects.
Non-contact Forces: Forces acting at a distance without direct contact.
Vectors Model: Forces are represented mathematically as vectors.
Magnitude: Strength of the force.
Direction: Direction of the force.
All forces, whether contact or non-contact, are modeled as vectors.
Egotism: Objects respond only to present influences; influences applied to other objects do not affect motion of the influenced object.
Reciprocity: Forces between two interacting objects are equal and opposite, expressed as:( F_{B \to A} = - F_{A \to B} )
Net Force: Resultant force acting on an object, calculated as the vector sum of all acting forces.
Condition of equilibrium: If ( F_{net} = 0 ), forces balance with no change in velocity.
Component Addition:
Net force equation ( ( \vec{C} = \vec{A} + \vec{B} ) ) breaks down to separate x and y components.
Ensure proper handling of sign directions in calculations.
Equations:
( F_{net,x} = F_{1,x} + F_{2,x} + ... )
( F_{net,y} = F_{1,y} + F_{2,y} + ... )
3-2: System diagrams & free body diagrams.
3-3: Impulse
Modeling Techniques: Use diagrams to visualize objects and interactions.
Scenario: Two blocks at rest with interactions and contact forces.
Forces acting on blocks include:
Normal forces
Gravitational force
Applied push
Create diagrams for stacked blocks: Illustrate forces acting on and among the blocks.
Diagram Components:
Coordinate axes
Dot representing the object
Labeled force vectors and net force vector
Impulse: Represent physical quantities like force and impulse using vectors.
Impulse Equation: ( I = F \Delta t = m \Delta v )
Cumulative impulse can be graphically determined as area under force-time graph.
3-4: Newton's first law
3-5: Newton's second law
Application: Use vector representation for forces in an object’s motion evaluation.
Objects maintain a constant velocity in the absence of net forces:( \vec{F}_{net} = 0 ) results in ( v = 0 )
Net Force Definition: Sum of all acting forces.
Separate balance equations for x and y components indicating independent interaction.
Quantitative predictions of object behavior using Newton's laws understanding.
Basic Law: ( F = ma ) (acceleration ratio)
Consistent application in spatial dimensions.
Acceleration and net force session directionality.
Balanced forces leading to constant velocity inertia understanding.
3-6: Newton's third law
Analysis of forces affecting object in motion using directed interactions.
Gravity Force Interaction: Action and reaction pairs between two bodies.
Equal and opposite forces, emphasizing action/reaction scenarios.
3-8: Gravitational force & weight
3-9: Free fall motion
Explanation of gravity as an attractive force between massive objects.
Utilize gravitational constant and proportional equations.
Demonstrated proportions including distance separation and mass interaction.
Distinguishing conditions for free fall regarding absence of other forces.
All objects fall at the same acceleration due to gravity regardless of mass.
Weight Force: Gravitational attraction for an object towards Earth.
Expressed mathematically with weight equation: ( W = mg ).
Analysis of mixed motion components in free fall context.
Independence Principle: X and Y motion directions are separately assessed showcasing acceleration effects.
Assumptions maintaining constant forces in specific motion axes during motion considerations.
Breakdown of example involving velocity components at given time intervals.
Evaluation of displacement in trajectory during motion intervals.
Finding landing distance through gravitational time intervals for projectile.
3-10: Spring force & Hooke’s law
3-11: Normal & tension forces
Exploring spring mechanics and the concept of restoring forces.
Definitions and the mathematical foundation given by Hooke’s law: ( F_{sp} = k \Delta x ).
Relationship between spring constant and linear force application demonstrated.
Hooke's law application limitations and non-linear behavior interpretations.
Clarification of the force responsible for maintaining the contact between an object and surface.
Interaction and nature of normal force in support and weight relations.
Upward normal force reaction against applied downward pressure on a resting object.
Comparing magnitudes of forces against gravitational weight establishing equilibrium situations.
3-12: The friction force
3-13: Viscous & drag forces
Understanding friction's nature and its dependency on surfaces interacting.
Definition: Friction between sliding surfaces and factors affecting friction coefficients.
Kinetic & Static Friction:
Opposing forces based on conditions of motion or rest.
Static friction only permits motion once a threshold force applies.
Kinetic friction as a constant force contrasting with adaptable static friction.
Practical example defining static friction from applied forces.
Emphasizing non-movement leading to friction equils applied force illustrations.
Understanding resistive forces based on relative motion through fluids.
Distinction between drag and viscous forces corresponding with speed.
Relation of viscous forces with speed of object through a fluid.
Drag as proportional to the square of relative velocity in motion analysis.
Comparison of drag and viscosity focusing on importance in specific scenarios.
Visual representation of various resistive forces demonstrated through graph analysis.
Matching examples of resistive forces to respective graph lines.
3-14: Electric charge
3-15: The electric force
Predicting distributions of electric charges based on conservation principles.
The role of electric interactions at cellular levels and effects on biological molecules.
Fundamental nature of electric charge and force between charged objects.
Charge Intricacies: Positive and negative charge characteristics.
Magnitude defined in specific units.
Importance of net charge being quantized and unequal composition effects.
Conservation principle ensuring constant net charge in closed systems.
Differences in electrical charge movement across various materials.
Mechanisms of charge separation leading to attraction effects.
Evaluating attractive and repulsive forces systematically through object interactions.
Coulomb’s Law application details regarding force magnitude between two charged objects.