Question 1: Briefly explain what Hooke's Law states about the relationship between force and extension in a spring or elastic object.

Answer: Hooke's Law states that the force needed to extend or compress a spring is directly proportional to the extension or compression, expressed as F = kx.

Question 2: Why is understanding elasticity important in nanotechnology? Provide one example.

Answer: Understanding elasticity is important in nanotechnology because materials behave differently at tiny scales; for example, nanoscale springs used in medical devices rely on elastic properties.

Question 3: What is the symbol 'k' in Hooke's Law, and what does it represent?

Answer: The symbol 'k' represents the spring constant, which measures the stiffness of the spring.

Question 1: Describe how the elastic behavior of materials at the nanoscale can differ from that at the macroscale.

Answer: At the nanoscale, materials may exhibit different elastic properties, such as greater flexibility or stiffness, because atomic bonds and surface effects dominate behavior more than bulk properties.

Question 2: Explain why nanoscale springs are important in the development of medical sensors.

Answer: Nanoscale springs can detect very small forces or deformations, making them ideal for sensitive medical sensors that monitor biological processes at the cellular or molecular level.

Question 1: A nanoscale spring has a spring constant of 50 N/m. What force is needed to extend it by 0.002 meters?

Answer: F = 50 N/m * 0.002 m = 0.1 N

Question 2: If a nanoscale spring is stretched with a force of 0.05 N and has a spring constant of 25 N/m, what is its extension?

Answer: x = F / k = 0.05 N / 25 N/m = 0.002 m

Question 1: Describe a simple theoretical experiment to measure the spring constant of a nanoscale spring. Include variables to control and safety precautions.

Answer: A theoretical experiment involves applying known forces to the nanoscale spring using a controlled device such as an atomic force microscope, measuring the extension at each force, and calculating k from F/x. Variables to control include temperature and environmental vibrations. Safety precautions involve handling equipment carefully to avoid damage and contamination.

Question 1: A nanodevice uses a spring with a spring constant of 100 N/m. When a force of 0.5 N is applied, the spring stretches. Calculate the extension and explain what this implies about the device's sensitivity.

Answer: Extension x = F / k = 0.5 N / 100 N/m = 0.005 m. This small extension indicates the device is highly sensitive, capable of detecting tiny forces.

Question 1: Explain how understanding elasticity at the nanoscale can improve the design of nano-robots used in medicine.

Answer: Understanding nanoscale elasticity allows for designing nano-robots that can flex and respond precisely to biological environments, improving their ability to perform tasks like targeted drug delivery.

Question 2: Identify one challenge scientists face when applying Hooke's Law to nanoscale materials in technological applications.

Answer: One challenge is accurately measuring forces and extensions at the nanoscale due to thermal vibrations and quantum effects.