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Answers toStudent Questions

Physics

How to find total mechanical energy?

Mechanical energy is defined as the sum of an object’s energies due to its motion and position. The amount of mechanical energy an object possesses determines the amount of work it can do on other objects, or in other words, the amount of energy it is capable of transferring to other objects. Given the above definition, we can be more specific about the types of energy that contribute to the total mechanical energy of an object: - Kinetic energy $E_k$ is the energy associated with an object’s motion and is given by the formula $E_k = \dfrac{1}{2}mv^2$ where $m$ is the mass of the object and $v$ is its speed. Note that this is the macroscopic energy of motion of the particle, and does not include the microscopic energy of the movement of its particles which contributes to the object's internal energy. The energy associated with an object’s position is called its potential energy. Two main types of potential energy will contribute to mechanical energy: - Gravitational potential energy $E_p$ is the energy of an object due to its position in a gravitational field. For an object at a height $h$ above a reference point, its gravitational potential energy is calculated with the formula $E_p = mgh$, where $m$ is the mass of the object and $g$ is the gravitational field strength. At the Earth’s surface, the value for $g$ is 9.8 N kg$^{-1}$. - Elastic potential energy $E_H$ is is the energy stored due to the deformation of an elastic object. Work can be done in changing the shape of an object, for example stretching or compressing a string, and energy is stored in the object as a result. This stored energy is released when the object returns to its original shape. The standard formula for elastic potential energy is derived from Hooke's Law: $E_H = \dfrac{1}{2}kx^2$. Where $k$ is the spring constant and $x$ is the displacement from the equilibrium position. Another potential energy that can be considered to contribute to total mechanical energy is electric potential energy. Like gravitational potential energy, a charged object will have stored energy due to its position in an electric field. Because the idea of mechanical energy is normally applied to larger objects and not small charged particles, we will ignore it here. Having discussed the different types of energy that contribute to the mechanical energy of an object, we can create a formula for total mechanical energy. In words, the formula is $\hspace{3em} $ Mechanical Energy = Kinetic Energy + Potential Energy or more specifically $\hspace{3em} $ Mechanical Energy = Kinetic Energy + Gravitational Potential energy + Elastic Potential Energy In the form of an equation, the total mechanical energy can be expressed as $\hspace{3em} E_{tot}=E_k + E_p + E_H$ or $\hspace{3em} E_{tot}=\dfrac{1}{2}mv^2+ mgh+ \dfrac{1}{2}kx^2$

Biology

How do we determine if genes are autosomal vs sex linked?

To determine whether genes are autosomal or sex-linked, we first need to understand the difference between the two. Autosomal genes are located on the autosomes, which are the 22 pairs of non-sex chromosomes in humans. These chromosomes are present in both biological males and females in equal number, so traits governed by autosomal genes typically show similar inheritance patterns across sexes. In contrast, sex-linked genes are located on the sex chromosomes, primarily the X chromosome. Since biological males have one X and one Y chromosome, and biological females have two X chromosomes, the inheritance of sex-linked traits differs between sexes. Y-linked traits, though rare, are located on the Y chromosome and are passed strictly from father to son, affecting only biological males. To identify whether a gene is autosomal or sex-linked, we look at inheritance patterns by examining how traits are passed down through generations. For human traits these studies often include the use of pedigree charts, which are visual diagrams showing family relationships and the presence or absence of specific traits. Pedigree charts use standardised symbols to represent individuals, their biological sex, and whether they express or carry a trait. By analysing these charts, we can observe patterns of inheritance that help distinguish between autosomal and sex-linked traits. For example, autosomal traits usually affect males and females equally. Recessive autosomal traits can skip generations. In contrast, X-linked traits often appear more frequently in biological males because they have only one X chromosome. A recessive allele on that chromosome will be expressed, whereas biological females need two copies of the recessive allele (one on each X chromosome) to express the trait. If a biological female is a carrier of a recessive X-linked trait, each of her sons has a 50% chance of inheriting the allele and expressing the trait, while each daughter has a 50% chance of being a carrier. Daughters will only express the trait if they inherit the recessive allele from both parents. Classic examples of X-linked recessive conditions include haemophilia (as stated in the IB Biology syllabus subtopic D3.2) and red-green colour blindness, both of which disproportionately affect biological males Further patterns help confirm sex linkage. If a biological male with an X-linked trait has children, all his daughters will inherit the allele (since daughters receive his X chromosome), but none of his sons will (since they inherit his Y chromosome). In contrast, autosomal traits do not show sex-specific inheritance; both sons and daughters have an equal chance of inheriting the allele from either parent. In addition to human studies, genetic crosses in model organisms like fruit flies (*Drosophila*) and mice provide valuable insights into the inheritance of sex-linked and autosomal traits. For example, in fruit flies, X-linked traits like white eye colour appear more frequently in males because they have only one X chromosome, while females need two copies of the recessive allele to express the trait. By performing controlled crosses, scientists can predict inheritance patterns and distinguish between autosomal and sex-linked genes. In summary to determine whether genes are autosomal or sex-linked, we analyse inheritance patterns through tools like pedigree charts. Autosomal genes are located on non-sex chromosomes and are inherited equally by both sexes, while sex-linked genes are found on the sex chromosomes and show different inheritance patterns between males and females. Genetic crosses in organisms like fruit flies and mice help confirm these patterns, providing additional insights into the inheritance of sex-linked and autosomal traits.

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