Physics – SpaceThe Earth has a gravitational field that exerts a force on objects both on it and around it.

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

Weight can be defined as the force on a mass due to the gravitational field of a large celestial body, such as the Earth. It is a force measured in Newtons which can be derived from Newtons Second Law of motion F=ma, where we arrive with F=mg where ‘m’ is the mass and ‘g’ is the gravitational force.

Mass: quantity of matter in a substance. Unit: kgWeight: force which acts on a mass within a gravitational field. Weight is directly proportional to the strength of the gravitational field (as mass remains constant).

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

GPE is the energy that a mass possesses due to its position within a gravitational field. Gravitation is a force of attraction, and if an object in the Earth’s gravitational field is moved further away from the centre of the Earth, work must be done on the object.

- An object gains gravitational potential energy as it moves against the field. - When an object moves closer to the centre of the Earth, its GPE is changed into kinetic energy. In such a

case, work is done by the object instead of on the object.

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. Ep=−Gm1m2r

Gravitational potential energy is the energy of a mass due to its position within a gravitational field. Any mass within a gravitational field has GPE. Due to the inverse square relationship in the Law of Universal Gravitation, the force of attraction between a planet and an object will become only zero only at an infinite distance away from the planet.

- Because work is done on an object, when it is moved to infinity, as the infinity mark is equivalent to zero by definition, all objects within a gravitational field is counted from this mark and hence has a negative GPE.

On Earth, EP = W =Fs = mgh. When an object falls from ‘h’, then its EP is converted into kinetic energy. On Earth, we

take the ground as being zero as mentioned earlier. Ep=−Gm1m2r

Change in GPE:

∆ E p=GmM ( 1r2− 1r 1 )Perform an investigation and gather information to determine a value for acceleration due to gravity using pendulum motion or computer assisted technology and identify reason for possible variations from the value 9.8ms -

2.When a pendulum swings with a small angle, the mass on the end undergoes a motion called simple harmonic motion. The period of the pendulum is given by

Rearranging this equation gives an expression that can be used to calculate g.

The period of the pendulum – the time taken to complete a single back-and-forth swing, depends upon just two variables: the length of the string and the rate of the acceleration due to gravity.

Aim: to determine the rate of acceleration due to the gravity using the motion of a pendulum.

Equipment: Retort stand, boss head and clamp, 1 metre of string, 50gram mass carrier, stopwatch, metre ruler.

Method:1. Set up retort stand and clamp on the edge of the table. 2. Tie on the string and adjust its length.3. Add on the mass carrier on the bottom of the string. This becomes your pendulum. 4. Measure the length of the pendulum from the knot at its top to the base of the mass carrier. Record this

length. 5. Adjust the pendulum to swing at a 30⁰ maximum deviation from the vertical and use stopwatch to time 10

complete back and forth swings. Start the stopwatch at extreme start and stops to get the most accurate period of the pendulum results.

6. Repeat and adjust length of string in any increments four- five times.

As you gather information during your investigation, you may need to carry out repeat trials to confirm the reliability of your results. Also, you may want to use other, more accurate, timing devices or procedures to minimise the effect of random errors.

You need to be able to identify reasons for possible variations from the value 9.8 ms-2. Variations can be as a result of two general factors; either from experimental errors or from actual variations in the value of acceleration due to

gravity as an effect of local variations in the nature of the Earth’s crust.

Experimental errors might occur as a result of things like the accuracy of equipment and human reaction time in the use of equipment.

Gravitational force and its variations:

The acceleration of an object at the Earth’s surface is determined by the distance of the object from the centre of the Earth. This means the gravitational force on Earth isn’t always the constant of 9.8m/s2.

g=GM E

(Re+altitude)2

Where G= Newton’s gravitational constant = 6.67 x 10-11 Nm2kg-2

Me= mass of Earth = 6 x 1024 kg Re = 6.4 x 106 m

Variations in ‘g’:- The Earth’s crust varies in thickness and density because of such things as tectonic plate boundaries and

different dense mineral deposits. This can cause localised variations in g- The Earth is flatter at the poles, so the surface is closer to the centre of the Earth than that at the equator,

so g will be greater at the poles and less at the equator. - The centrifuge effect created by the spin of the Earth reduces the value of g. This is the greatest at the

equator. Acceleration due to gravity at sea level varies from 9.782m/s2 at the equator to 9.832m/s2 at the poles.

- Another factor is height above sea level. Altitude increases the distance from the centre of the Earth. The formula takes this into consideration.

Gather secondary information to predict the value of acceleration due to gravity on other planets./ Analyse information using the expression: F=mg to determine the weight force for a body on Earth and for the same body on other planets.

By using the formula above that determines the gravity on other planets, the weight force for a body can be also determined on other planets. As mass remains constant, by calculating the gravity on other planets, the weight force can be also be determined.

e.g. A man having a mass of 76kg on Earth. He has a weight force of 76 x 9.8 on Earth, whereas, Mercury having a gravitational acceleration of 4.01 gives this man a weight force of 76 x 4.01 on Mercury’s surface.