SEMANA 3, ONCE, CAÍDA LIBRE

Caída Libre: Conceptos Fundamentales

Introducción a la Caída Libre

• La clase se centra en el concepto de caída libre, que es el movimiento vertical influenciado por la gravedad.

• Se establece que la aceleración debida a la gravedad es de 9.8 m/s², y se considera un entorno sin resistencia del aire (vacío).

• Se menciona que en otros cuerpos celestes, como la luna, la gravedad varía significativamente.

Movimiento Vertical y Gravedad

• Al lanzar un objeto hacia arriba, alcanzará una altura máxima donde su velocidad instantánea será cero.

• En este punto máximo, el objeto comenzará a descender; su velocidad inicial al lanzarlo hacia arriba es positiva y disminuye hasta llegar a cero.

Relación entre Velocidades

• La rapidez de subida es igual a la rapidez de bajada; esto implica simetría en el movimiento vertical.

• El tiempo que tarda un objeto en subir es igual al tiempo que tarda en bajar desde el mismo nivel.

Factores Clave en Caída Libre

Variables Importantes

• Se introducen variables clave: H (desplazamiento vertical), t (tiempo), v₀ (velocidad inicial), v_f (velocidad final), y g (gravedad).

Ejemplo Práctico

• Un cuerpo se deja caer cerca de la superficie terrestre; después de 3 segundos ha descendido 10.9 m con una rapidez final de 59 m/s.

• Se identifica cada variable: tiempo = 3 s, desplazamiento vertical = 10.9 m, velocidad inicial = 0 m/s antes de caer.

Cálculo y Fórmulas

• La gravedad se mantiene constante en 9.8 m/s² para los cálculos; algunos problemas pueden aproximar esta cifra a 10 m/s² según las indicaciones del problema.

Conclusiones sobre Caída Libre

Resumen de Conceptos Clave

• En altura máxima, la velocidad instantánea es cero; esto resalta cómo los objetos experimentan cambios significativos durante su trayectoria ascendente y descendente.

Understanding Motion: Time of Ascent and Descent

Key Concepts in Motion

• The time taken for an object to ascend is equal to the time taken for it to descend, emphasizing symmetry in motion.

• Four key formulas are introduced, each missing a variable that is deemed unnecessary for calculations.

• The height (H) is not considered in some formulas; instead, focus is placed on initial velocity, final velocity, gravity, and time.

• Each formula has one variable that cannot be used simultaneously with others; this ensures only one unknown variable per equation.

• Positive values are assigned when an object descends and negative when it ascends.

Practical Application: Problem Solving

• A scenario involving a cat dropping a flower pot from a second floor (20 m high) sets the stage for applying learned concepts.

• A diagram illustrates the situation where the cat drops the pot; identifying known variables like height (H = 20 m).

• Gravity is established at 9.8 m/s²; initial velocity is zero since the pot starts from rest.

• The relevant formula chosen excludes final velocity as it's not needed for this calculation.

Calculation Steps

• Formula three is applied: H = (initial velocity * time) + (0.5 * gravity * time²), focusing on downward motion which adds positive value due to direction.

• Substituting known values into the formula leads to setting up an equation to solve for time squared.

• After simplifying, 20 = 4.9 * t² results in isolating t² by dividing both sides by 4.9.

Finalizing Results

• Calculating gives t² = 4.08; taking the square root yields t ≈ 2.02 seconds as the total fall time of the pot.

• Emphasis on units confirms that calculated time should be expressed in seconds, reinforcing understanding of physical dimensions involved.

This structured approach provides clarity on how fundamental principles of physics apply to real-world scenarios while ensuring comprehension through step-by-step problem-solving techniques.

Understanding Motion: Time and Height Calculations

Initial Problem Setup

• The discussion begins with the introduction of units in the International System, emphasizing that height (H) is measured in meters, initial and final velocities in meters per second, and gravity in meters per second squared.

• The speaker solves a problem where a mass takes 2.02 seconds to reach a certain point, demonstrating the process of identifying given information and unknown variables.

Analyzing Vertical Motion

• A new exercise is presented involving an object launched upwards at 32 m/s. The goal is to determine both the time it takes to reach maximum height and the value of that height.

• The initial velocity of 32 m/s is confirmed as the launch speed. The problem requires finding two key pieces of information: time to maximum height and maximum height itself.

Key Variables Identified

• Gravity is consistently noted as 9.8 m/s² throughout calculations, which remains unchanged for this scenario.

• At maximum height, the final velocity becomes zero since the object stops ascending before descending.

Calculating Time to Maximum Height

• To find time, the speaker uses a formula relating final velocity (0), initial velocity (32 m/s), gravity (-9.8 m/s²), and time (unknown).

• Rearranging gives an equation where gravity multiplied by time equals initial velocity; thus, time can be calculated by dividing initial velocity by gravity.

Solving for Time

• After rearranging terms, it’s established that t = frac32 text m/s9.8 text m/s^2 .

• Using dimensional analysis confirms that units simplify correctly to seconds when calculating time.

Final Calculation Results

• Performing calculations yields a result of approximately 3.27 seconds for reaching maximum height.

Finding Maximum Height

• To calculate maximum height, another formula involving average velocity over time is introduced.

• The average velocity during ascent combines initial (32 m/s) and final velocities (0 m/s), resulting in an average of 16 m/s.

Completing Height Calculation

• Substituting known values into the formula for height results in H = 16 text m/s times t .

• With t = 3.27 text s , multiplying gives a total height of approximately 52.32 meters achieved by the object during its ascent.

How to Calculate Maximum Height and Time in Free Fall?

Understanding the Problem

• The discussion begins with a question about determining how long it takes for an object to reach its maximum height, which is stated as 3.27 seconds, and what that maximum height value is.

Solving Problems with Formulas

• The speaker emphasizes the importance of using given data to solve various problems by rearranging formulas. This involves isolating a variable and substituting results into other equations to find solutions.

Concepts of Free Fall

• A new problem is introduced where the object moves upwards instead of downwards. The class concludes with a definition of free fall: vertical movement influenced solely by gravity, which is consistently 9.8 m/s², ignoring air resistance or other external factors.

Velocity Changes During Motion

• It’s explained that the sign in formulas changes based on the direction of motion; positive when moving downwards and negative when moving upwards. At maximum height, velocity reaches zero since it's the peak point.

Symmetry in Motion

• The initial launch speed will equal the speed at which the object returns to its original launch point. Additionally, the time taken to reach maximum height equals the time taken to descend back down, illustrating symmetry in projectile motion.