# Gravity and Gravitational Fields

## Define weight as the force on an object due to a gravitational field

Weight is the force experienced by an object due to a gravitational field. It is directly related to the strength of the gravitational field at the point where the object is located, and is equal to the force which the field is exerting on the object.

Remember- Weight is the force on an object due to a gravitational field.

## Explain that a change in gravitational potential energy is related to work done

This section will be hard to answer if you don’t fully understand how potential energy works. If this here isn’t enough, make sure you read through the various textbooks and look for other resources to make sure you understand potential energy properly.

Work done is the measure of how much energy was used to displace an object a specified distance. W = Fs where s is displacement. When an object is moved away from a gravitational field, it gains energy. This is because by raising it up from the field’s origin, work is done. If a 1kg stone was raised 100m, then work done would be 980J. However, conservation of energy states that this energy cannot be destroyed. The 980J is now 980J of gravitational potential energy, because if the stone was dropped from 100m then it would regain 980J in the form of kinetic energy due to the gravitational field. Gravitational potential energy is the potential to do work, and is related to work done.

Remember- Potential energy is the work done to raise an object in a gravitational field.

## Perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion or computer-assisted technology and identify reasons for possible variations from the value 9.8 $m/s^2$.

This experiment will definitely give you a value that differs from 9.8 $m/s^2$, so make sure you know both experimental reasons for your error, as well as the factors affecting gravity itself.

In our investigation we used a pendulum consisting of a weight attached to a thick, non-elastic string that was tied to a clamp on a retort stand. We set the pendulum in motion by swinging it, being careful to ensure that the pendulum was deflected no more than 30◦ at maximum deflection, to minimise errors caused by tension in the string (because the string will lose tension at angles greater than 30◦). We timed the pendulum over 10 complete cycles (time taken to return to its point of origin) in order to minimise timing errors and random factors affecting individual swings. We then used the formula $T=2\pi \sqrt{\frac{l}{g}}$ where $T$ is the period (time taken for one complete cycle), $l$ is the length of the string (measured from the knot on the clamp to the centre of gravity of the weight) and $g$ is gravitational acceleration, in order to calculate a value for $g$.

There are numerous factors affecting the strength of gravity on Earth (aside from experimental errors producing a result different to 9.8 $m/s^2%$).

Firstly, as the Earth spins it bulges at the equator, flattening at the poles. This causes the poles to be closer to the centre of the Earth than the equator. According to the formula for gravitational force, the force experienced depends on the distance from the centre of the field. This means that Earth’s gravitational field is stronger at the poles than at the Equator.

Secondly, the field of the Earth varies with the density of nearby geography. Places where the lithosphere is thick, or where there are dense mineral deposits or nearby mountains experience greater gravitational force compared to places over less dense rock or water.

Thirdly, as gravitational force depends on altitude, places with greater elevation such as mountain ranges experience less gravitational force, compared to areas at or below sea level.

Remember- Pendulum experiment, errors in the experiment, factors affecting the strength of Earth’s gravity.

## Gather secondary information to predict the value of acceleration due to gravity on other planets

Just pick and choose a few values to memorise. If they give you a question in the exam regarding the different accelerations they’ll most likely give you a table of values and ask you to do calculations with it. Don’t spend long on this point. Also, Pluto is no longer officially a planet.

 Planet Gravitational Acceleration ($m/s^2%$) Mercury 4.07 Venus 8.90 Earth 9.80 Mars 3.84 Jupiter 24.83 Saturn 10.50 Uranus 8.45 Neptune 11.20

## Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field

Again, you need to understand this section. A question may focus on why potential energy takes a negative value, and you need to be able to comprehensively explain and justify why. The reason the dotpoint is defined as a very large distance away is because this is equivalent to a point outside the field. Gravitational fields, like many fields, have no theoretical maximum range and theoretically exist at an infinite distance away from an object. In practice, because gravitational fields obey inverse square law and decrease in strength rapidly as distance increases, at large distances the field is for all intents and purposes nonexistent. Regardless, there is technically no point in the universe outside a gravitational field, hence a very large distance away is used.

Gravitational potential energy is defined as the work done to move an object from a point a very large distance to a specified point in the gravitational field. The work done is the energy input provided by the gravitational field to the object as it falls to that particular distance. $E_p = -\frac{Gm_1m_2}{r}$ is a more accurate definition because it takes into account the weakening of gravitational fields at a distance, and also results in objects far away out of the field having no energy, rather than the simpler definition $E_p = mgh$ where at an infinite distance, there is infinite potential energy.

Remember- Potential energy is negative, and is the work done in moving an object from an infinite distance to a point within the field.