# what is the si unit of Ks show yor answer in terms of base units using correct symbols.Show how worked it out

Es =1/2 ks X(squared)

Es = potential strain energy

Ks = spring constant

X = compression of spring measured in metres

Relevance

The usual (and clearer) way to write this relation is:

E = 1/2 k x^2

Note that E is energy (and therefore has units of energy), k is the spring constant, and x is a length, as you noted. Using dimensional analysis, we have the following:

Unit of energy in SI: Joules (J) = kg m^2/s^2

Unit of length in SI: meters.

[E] = [k] [x]^2

Where [A] means "dimension of A." [x] = m. [E] = kg m^2/s^2, etc.

kg m^2 /s^2 = [k] m^2

kg /s^2 = [k]

The units of the spring constant are kg /s^2 in the SI system. Since a Newton is a kg m/s^2, we also have that:

[k] = kg /s^2 = kg m/(m s^2) = 1/m (kg m)/s^2 = N/m

This is perhaps more intuitive; it suggests that a certain force is equivalent to a certain length. This is the force required to stretch the spring a particular length.

You can also see this from the Hooke spring law:

F = - kx

Briefly, the lesson here is that dimensions can be treated algebraically; two sides of an equation should have the same dimension. Therefore, I can treat them with the usual algebra rules - if I multiply one side by meters, I should multiply the other side by meters. This ensures the dimension of both sides stays the same.

• Dr W
Lv 7

just substitute the units in and solve for Ks....

Es = 1/2 ks x²

ks = 2 Es / x² = 2 x (potential energy ) / (m)²

but potential energy has units kg m²/s²

so ks = 2 x (kg m²/s²) / m² =2 kg / s²

ie units are kg/s²

or if you prefer....

since 1 N = 1 kg m / s²

ks = 2 x (kg m²/s²) / m² = 2 (kg m/s²) m / m² = 2 (kg m/s²) / m

= 2 N/m

ie units are N/m

so you pick. kg/s² or N/m both are correct.

The units need to be the same on both sides.

Ignore the 1/2, as it doesn't have units, it's just a number.

Rearrange the equation.

E/X^2 = k

The units of k are the same as the units of E/X^2.

The units of X are metres, so the units are whateer the units of E are over metres^2.

• loser
Lv 4