Question 1: Define the spring constant and state its SI unit.

Answer: The spring constant is a measure of the stiffness of a spring, defined as the force required to compress or extend the spring by a unit length. Its SI unit is Newton per meter (N/m).

Question 2: Explain how the spring constant affects the behavior of a spring used in a spacecraft's landing gear.

Answer: A higher spring constant means a stiffer spring, which can absorb more impact energy during landing, providing better shock absorption. Conversely, a lower spring constant results in a softer spring, offering more cushioning but less rigidity.

Question 1: A spacecraft uses a spring with a spring constant of 1500 N/m to deploy solar panels. If the spring is compressed by 0.02 meters during deployment, what force is exerted by the spring?

Answer: Force = spring constant × displacement = 1500 N/m × 0.02 m = 30 N

Question 2: If a spring in a satellite's antenna exerts a force of 45 N when extended by 0.015 meters, what is the spring constant?

Answer: Spring constant = Force / displacement = 45 N / 0.015 m = 3000 N/m

Question 1: Outline the steps to safely measure the spring constant of a spring intended for space use in a laboratory setting.

Answer: First, ensure the spring is free from damage and securely attach it to a testing apparatus. Use a force sensor or weights to apply known forces gradually, measuring the resulting displacement each time. Record the force-displacement data to calculate the spring constant via Hooke's Law. Always wear safety goggles and handle weights carefully to prevent injury or equipment damage. Ensure the setup is stable and free from external vibrations.

Question 1: A spring used in a space probe's docking mechanism exerts 500 N of force when compressed by 0.005 meters. If the spring's spring constant is doubled, what would be the new displacement when the same force is applied?

Answer: Original spring constant, k = 500 N / 0.005 m = 100,000 N/m. New spring constant, 2k = 200,000 N/m. Displacement = Force / spring constant = 500 N / 200,000 N/m = 0.0025 meters.

Question 1: A spacecraft's shock absorber system uses a spring with an unknown spring constant. During testing, a force of 2000 N causes the spring to extend by 0.01 meters. Calculate the spring constant. Then, explain how changing this spring's stiffness could affect the spacecraft's landing performance on a different planet with higher gravity.

Answer: Spring constant, k = Force / displacement = 2000 N / 0.01 m = 200,000 N/m. Increasing the spring's stiffness (higher k) would make it more resistant to compression, which could reduce the impact force during landing but might also transfer more shock to the spacecraft's structure. Conversely, decreasing stiffness would absorb more impact but could lead to excessive compression, affecting the stability of the landing system on planets with higher gravity, where the impact forces are greater.

Question 1: Explain how the spring constant affects the design of landing gear systems in lunar or Martian rovers.

Answer: The spring constant determines how stiff or soft the springs in the landing gear are. Properly calibrated springs absorb shock from landing on rough surfaces, protecting the rover's components. If too stiff, the springs may transmit excessive force; if too soft, the rover may bounce or sink into the surface. Therefore, selecting an appropriate spring constant is essential for safe and effective landings in different planetary environments.