Question

The magnitude of the force that a spring exerts (F) when it is stretched a distance x from its unstressed length is governed by Hooke's law, F = kx. (a) What are the dimensions of the force constant, k? (Use the following as necessary: M for mass, T for time, and L for length.)

Answer 1

k = M / T^2

Step-by-step explanation:

Hooke's law states that the lengthening of a spring is directly proportional to the force module applied to it, provided that the spring is not permanently deformed.

F = k * L

So:

k = F / L

Where :

[F] = N (Newton units)

[L] = m (meter)

[k] = N / m

N = ( M * L ) / T^2

[N] = ( kg * m ) / s^2

Finally:

[k] = ( kg * m ) / ( m * s^2 )

[k] = kg / s^2

k = M / T^2