How gravity is measured?

When it comes to the issue of how to measure the magnitude of acceleration due to gravity (g), it leaves some gaps among others. Okay! Today I want to let you know through this post the basic concept on how this gravity is measured.

Keep reading.!

There are common two (2) methods that are frequently utilized in measuring acceleration due to gravity in geophysics.

How can you measure gravity?

1: Absolute gravity Method

This method involves measuring gravity at only one point. This method gives true gravity.

i/ Pendulum Method

When it comes to simple Pendulum, it consists of a string which is attached to a small mass metal object known as Pendulum Bob. This system is displaced at a small angle less than 15° and allowed to move freely in a simple harmonic motion provided that the effect due to air resistance is neglected see Figure 1 below.

Figure 1: Simple Pendulum and its resolved forces.

When the Pendulum execute Simple Harmonic Motion (S.H.M), force components become in equilibrium states

String Tension (T) = mgcosθ...............(i)

Restoring Force (F) = - mgsinθ ............(ii)

But, Also F = - Kx

Then, mgsinθ = - Kx.................(iii)

Since θ is small, sinθ ~ θ

Then, mgθ = - Kx .................(iv)

From Figure 1, the arc x is directly proportional to θ

Then, x = Lθ Since L is constant.

Substitute x above into equation (iv) and simplify

Then, mg = - KL..................(v)

Divide by m throughout and simplify, Put K/m = w2

But w = 2π/T, Then w2 = 4π2/T2

Then, from (v), g = w2L

g = 4π2L/T2...................(vi)

Rearrange equation (vi), and make T the subject to give Period of a Pendulum (T) = 2π√(L/g)

Period (T) = 2π√(L/g)

Then Acceleration due to gravity (g) can be computed from that formula, when Length (L) of a string and Period time (T) are known.

If we plot the Graph of Length (L) against the square of time (T2), as shown in the figure 2 below.

Figure 2: The graph of Length (L) against Time (T2).

Recall, T = 2π√(L/g), and make L the subject L = gT2/4π2, Then compare this equation with y = mx + c.

If y - axis = L and x - axis = T2, and Slope (m) = g/4π2,

Then g = 4π2 × slope (m)

ii/ Free Fall body method

When the body is released from a height above the ground and made to fall freely under the influence of force of gravity only, it is said to move under Free Fall Motion.

From second equation of rectilinear motion, s = ut + at2/2

For free fall motion, a = g > 0 for down direction, s = H, u = 0, t - time for body to reach the ground.

Then equation above simplifies to, H = gt2/2

When H varies and t will vary for different measurements.

We can plot the graph of H (m) versus square of time (t2). The graph will have the straight (Linear) nature. with the slope (m) = g/2

Then we can compute the value of g = 2 × Slope .

2: Relative gravity Method

This measures the difference in gravitational acceleration at two different adjacent stations.

i/ Mass and Spring Method

This is a commonly used method in most gravimeters used in exploration surveys based on a simple mass-spring system.

Since, As weight increases with increases in spring length

w is directly proportional to spring length (x), according to Hooke's law

w = Kx

Since w = mg

Then , mg = Kx

Then g = Kx/m

Where, K - Spring constant (Stiffness), x - extension (Spring length)

What is a gravimeter (Gravity meter)?

Gravimeter is an instrument designed to measure (detect) spatial variation of gravitational acceleration (force of gravity). It is also known as Gravity Meter.

Gravity meter can be categorized into two (2) types, based on their working principle,

i/ Stable Gravimeter

It applies the mass spring effect (proportional). Such that spring length increases with change in mass. Refer to Hooke's Law.

ii/ Unstable Gravimeter.

This applies to the negative restoring force effect. Such that the spring length varies as a result of negative restoring force.

Example : Wooden and Lacoste Gravimeter.

I hope now you have a concept on how acceleration due to gravity (gravity) is measured.

Thanks for reading this!

Follow and Join this blog on Telegram group to gain more benefits.

Is the content useful and helpful to you? Want to support the Effort! You can support the Effort via >"Support the Effort Page"<

A simple checklist of equipment and tools that can suit your Electrical Resistivity Project! Have it Now!

BASIC RESISTIVITY EQUIPMENTS and TOOLS