Question

Problem 8.1. We experience the pull of gravity as constant and not dependent on position. How does it come to be inter- preted as exerting a spring force that is linearly propor- tional to position? (Hint: Think about the equation of motion in which the relevant term appears.) Identify the fundamental physical dimensions of the spring stiffness, k, and the mass, m, and use them to determine the physical dimensions of wo for a spring, mass oscillator. Problem 8.2.

Answer 1

8.1) In many aspects the two forces gravitational force and spring force can be interpreted alike as both are conservative forces , a particular potential energy is defined for both the forces as gravitational potential energy and spring potential energy .

8.2) From the spring force equation,

F = KX

dimension of force is [MLT*-2] and dimension of X is [L] , dimension of K will be [ MT*-2]

since , w = √(K/m) ,where m is mass

So , dimension of w = [√([MT*-2]/ [M])]

[√T*-2] = [T*-1]