Measure the earth´s gravitational field strength.

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Aim

The aim of my experiment is to measure the earth´s gravitational field strength, which is also the acceleration due to gravity. This involves mass, which is the amount of matter an object contains and weight which is the force of gravity pulling down on a object with a mass. Mass is measured in Kg and weight is measured in Newton´s. Gravity is the weakest of the four fundamental forces, yet it is the dominant force in the universe for shaping the large scale structure of galaxies, stars, etc.

The earth´s gravitational field strength is calculated by the weight (N) / Mass (Kg), therefore the earth´s gravitational field strength (g) is measured in (N/Kg). As an object is in free-fall it accelerates at the rate of g. The gravitational field strength is measured by doing an experiment with a trolley rolling down a tilted runway with the force of g causing it to accelerate down the slope.

Hypothesis

Isaac Newton firstly discovered gravity when an apple fell on his head. He then discovered that every object has a mass and that two masses attract each other. This attraction has a gravitational field strength, Newton wanted to calculate the gravitational field strength of the earth. There is a pendulum that involves g and calculates T the time the pendulum will swing for, the equation is stated below:

T = 2  l/g

Where l is the length of the pendulum. The pendulum is shown in diagram 5. Through this Isaac Newton discovered that g = 9.81 N/Kg. This is now a well now fact and is accepted as the earth´s gravitational field strength.

I will use a different experiment to try and prove that g = 9.81 N/Kg. I predict when I do the experiment as shown in Diagram 2, I will find g = 9.8 N/Kg and if the experiment is accurate and reliable enough I may be able to show g = 9.81 N/Kg but I would be satisfied with the answer accurate to two significant figures.

Referring to the diagram:

ma = mg sin - F

Divided by mass

a = g sin (-F / m)

Then put into the equation of a straight line

y = mx + c

The parts equation represent as follows, y = y axis, x = x axis, m = gradient, c = intercept. When this is put into the equation of a straight line the lines are replaced as follows, a = y, sin = x, g = m, (-F / m) = c. When the results are put into a graph , I can find g by finding the gradient of the line on the graph as shown in Diagram 3.

Definitions

Gravity Force , Fgrav

The force of gravity is the force at which the earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity which is directed "downward" towards the center of the earth. The force of gravity on earth is always equal to the weight of the object as found by the equation:

Fgrav = m * g

where g = 9.8 m/s2 (on Earth)

and m = mass (in kg)

Normal Force, Fnorm

The normal force is the support force exerted upon an object which is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. On occasions, a normal force is exerted horizontally between two objects which are in contact with each other.

Friction Force, Ffrict

The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. The friction force opposes the motion of the object. For example, if a book moves across the surface of a desk, then the desk exerts a friction force in the opposite direction of its motion. Friction results from the two surfaces being pressed together closely, causing intermolecular attractive forces between molecules of different surfaces. As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together.
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Implementation

I will use the following apparatus in my experiment to find "g":

A wooden trolley- the trolley will be able to roll down the runway with a negligible amount of friction acting upon it as it rolls down.

A wooden runway- the runway is wide and long enough to enable the trolley to have a sufficient length run and also be wide enough so the trolley won´t touch the edges.

A light gate and picket fence- the picket fence will pass through the light gate and the velocity at which the picket fence ...

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