Question

Hooke's law states that the force, F, in a spring extended by a length x is given by

F=-kx. According to Newton's second law F = ma, where m is the mass and a is
the acceleration. Calculate the dimension of the spring constant k.​

Answer 1

dimensions of k are kg / s^2

Step-by-step explanation:

F=ma (Newton's second law)

F=-kx (Hooke's law)

so equate both

-kx = ma

k = -ma/x

= mass * acceleration / distance (dimensions, -1 has no dimension)

= kg * m/s^2 / m

= kg / s^2