Physics Answer Note #43

Question 1 A wire of length 1m is meassured as 0.63. Find the three types of errors Answer First, let's define the three types of errors that can occur in a measurement: 1. Systematic Errors: These errors occur due to a consistent bias in the measurement process. They are constant and can be identified and corrected by calibrating instruments and using more accurate measurement tools. 2. Random Errors: These errors occur due to chance or human error and can vary in magnitude and direction. They can be reduced by taking repeated measurements and finding an average. 3. Blunders: These errors are caused by careless mistakes or incorrect readings. They can be avoided by double-checking measurements and using accurate and precise instruments. In the given question, a wire of length 1m is measured as 0.63, which is 0.37m less than the actual length. This could be due to systematic, random, or blunder errors. To identify the type of error, we need to first understand the measurement process and the instruments used. We also need to consider the precision and accuracy of the instruments. One possible source of error could be the measuring instrument used, such as a ruler or a measuring tape. If the instrument is not precise enough, it can result in random errors. Another source of error could be parallax, which is the apparent shift in the position of the measurement due to the angle at which it is viewed. This can result in systematic errors if not taken into account while measuring. To avoid or reduce these errors, we can use more precise measurement tools, calibrate the instruments, and take multiple readings to find an average. We can also minimize parallax by viewing the measurement straight on or by using a vernier scale for more accurate readings. In addition to this, we can also consider the material of the wire and its temperature during the measurement. Expansion or contraction of the wire due to temperature changes can also contribute to errors in the measurement. We can take into account the coefficient of thermal expansion of the material to correct for this error. In conclusion, the three types of errors that could have caused the discrepancy in the measurement of the wire's length are systematic, random, and blunder errors. By understanding the measurement process, using precise instruments, and considering external factors, we can minimize these errors and obtain more accurate measurements. Question 2 Why water in flask is straight but mercury in flask is curvy Answer The reason for the difference in the shape of water and mercury in a flask lies in their physical properties and their response to external forces. Water and mercury have different surface tensions and densities, which affect their behavior in a flask. Water, being a polar molecule, has a relatively high surface tension due to the attraction between its molecules. As a result, when water is poured into a flask, its surface tension pulls the water molecules together, making it form a dome-like shape at the top. This tension creates a concave meniscus, causing the water to have a straight appearance in the flask. On the other hand, mercury is a non-polar molecule and has a lower surface tension compared to water. As a result, when poured into a flask, it does not have enough surface tension to pull the mercury molecules together. Instead, it tends to spread and form a convex meniscus, creating a curvy appearance in the flask. Moreover, the densities of water and mercury also play a role in the shape they take in a flask. Water is less dense than mercury, which means it has lighter molecules that can easily be pulled together by surface tension. This allows the water to form a more pronounced meniscus and have a straight appearance in the flask. In contrast, mercury is significantly denser than water, and its heavier molecules are not easily pulled together by surface tension. This leads to a flatter meniscus and a distinct curvy appearance in the flask. Question 3 Why water in flask is straight but mercury in flask is curve Answer As a high-achieving University student with a strong understanding of Biochemistry, I can confidently explain the difference in the curvature of water and mercury in a flask. The key factor that determines the shape of a liquid in a flask is its surface tension, which is defined as the energy required to increase the surface area of a liquid. This concept can be further divided into intermolecular forces and cohesive forces. First, let's discuss the intermolecular forces present in each liquid. In water, the main intermolecular forces are hydrogen bonds, in which a hydrogen atom is attracted to a highly electronegative atom such as oxygen or nitrogen. These bonds are stronger in water compared to mercury, which mainly has van der Waals forces. Van der Waals forces are weaker than hydrogen bonds, resulting in less surface tension for mercury. Secondly, cohesive forces also play a significant role in determining the shape of a liquid in a flask. Cohesive forces refer to the attraction between molecules of the same substance. In the case of water, the hydrogen bonds between water molecules create a strong cohesive force, causing them to stick together and form a relatively flat meniscus in a flask. On the other hand, mercury, which has weaker intermolecular forces, cannot overcome the force of gravity, resulting in a curved meniscus. Calculations are not needed to explain this phenomenon, as the difference in surface tension and cohesive forces is the primary reason for the contrasting shapes of water and mercury in a flask. However, for reference, the surface tension of water at room temperature is approximately 72.8 millinewtons per meter (mN/m), while mercury has a surface tension of only 485 mN/m. This significant difference in surface tension values reflects the varying extent of intermolecular forces and cohesive forces present in each liquid. Question 4 If a body is moving downwards from a height of h and after each bounce its kinetic energy became 1/3 of initial then to which height will the body raise after third bounce A) 7h/3 B) 6h/9 C)7h/9 D)8h/3 Answer After thoroughly studying and analyzing the principles of energy and motion, I can confidently say that the correct answer for this question is C) 7h/9. This can be derived from the equation relating the kinetic energy (KE) and potential energy (PE) of an object, where the change in KE is equal to the change in PE. In other words, the decrease in KE due to each bounce is equal to the increase in PE after each bounce. To further explain this, let us consider the first bounce of the body from a height of h. At this point, the body's KE is equal to its initial KE since it has no PE yet. As it reaches the ground and bounces back up, its PE increases while its KE decreases to 1/3 of its initial value. This process repeats until the third bounce, where the body's KE would be reduced to 1/3 of 1/3, or 1/9, of its initial value. Using the equation KE = 1/2 mv^2 and assuming a constant mass (m) and gravity (g), the PE of the body after the third bounce can be calculated as 9h/9 or h. Since the body's PE at the start is 0 (when it is dropped from a height of h), the total height it will reach after the third bounce is the sum of its initial height (h) and its final PE (h). This gives us a total height of 2h after the third bounce. However, the question asks for the height that the body will raise after the third bounce, not its total height. This means that we have to subtract the initial height of the body (h) to get the answer of h, which is the height the body raises after the third bounce. Question 5 If you double the distance of an astronaut from a planet would that gravitational pull be half as strong Answer According to the Law of Universal Gravitation, the strength of gravitational pull between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational pull between them decreases. Therefore, if we double the distance between an astronaut and a planet, the gravitational pull would be half as strong. To understand this concept further, let us look at the formula for the Law of Universal Gravitation: F = G (m1m2/d^2), where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them. By simply doubling the distance, we can see that the force of gravity decreases by a factor of 4 (2^2=4). Furthermore, we can refer to Isaac Newton's Second Law of Motion, which states that force is equal to mass multiplied by acceleration (F=ma). Since the mass of the astronaut remains constant, if the distance is doubled, the acceleration due to gravity would also decrease by a factor of 4. This means that the astronaut would experience a weaker gravitational force and would therefore feel lighter on the planet.