# Essay about Special Relativity and Earth

Submitted By a5997284
Words: 4408
Pages: 18

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1.1 The Earth has a gravitational field that exerts a force on objects both on it and around it
1.1.1 Define weight as the force on an object due to a gravitational field
Weight is the force applied to an object by a gravitational field. It is defined by the equation Fw=mg and is measured in Newtons (N).
1.1.2 Explain that a change in gravitational potential energy is related to work done
The gravitational potential energy (GPE) of an object at height h is equal to the work done in raising it to that height.
EP =work done=FΔh=(mg)Δh
EP =mgΔh
1.1.3 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= -(Gm1m2)/r
This equation holds true where zero is defined as a point infinitely far away from the centre of the Earth. The formula is negative for objects below the point zero because an object further away from the earth has a higher GPE than one closer to it. mg= (Gm1m2)/d2 Δh=d

EP = -mgΔh
EP = -[(Gm1m2)/d2]*d
EP = -(Gm1m2)/d
1.1.P1 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 9.8ms-2
Aim
To determine a value for gravity based on the motion of a pendulum]
Method
1.The experiment was set up as shown below

2. The pendulum was raised to a height (into the page as seen from the diagram), it was released and allowed to complete one oscillation, and then it was timed how long it took to complete three further oscillations. This time was recorded in a table.
3. Step 2 was repeated twice
4. Steps 2 and 3 were repeated for string lengths 45cm, 60cm, 75cm and 90cm
Results and Conclusion
The results were put into a table and the average time for one oscillation at each string length was determined. Each of these averages was substituted into the formula g=(4πℓ)/T2 and an average value of g was determined for all lengths of string. The value determined for gravity was 9.92. Possible reasons for deviation from the accepted value of 9.8 may include human error in timing the oscillations, the string length may not have been exact, the fact that the base of the retort stand rocked while the pendulum was swinging and that the string is not weightless or inflexible. Ways to improve these results would be to repeat the experiment, get a retort stand with a heavier base, replace the string with an inflexible rod and make the mass on the end heavier
1.1.P2 Gather secondary information to predict the acceleration due to gravity on other planets
Planet
Mass (kg)
Gravity (ms-2)
Mercury
3.30e23
2439000
3.7
Venus
4.87e24
6052000
8.9
Mars
6.42e23
3398000
3.7
Jupiter
1.90e27
71492000
24.8
Saturn
5.69e26
60268000
10.5
Uranus
8.69e25
25559000
8.9
Neptune
1.02e26
24764000
11.1
Pluto
1.32e22
1160000
0.7
The values for mass and radius were taken and substituted into g= Gmplanet/rplanet2
1.1.P3 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 A man has a mass of 85kg, find his weight:
a) on Earth
b) on Mars

a) Fw =mg gEarth=9.8ms-2 Fw = 9.8*85 m=85kg Fw = 833N

b) Fw=mg gMars=3.7ms-2 Fw=3.7*85 m=85kg Fw=314.5N
1.2 Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth
1.2.1 Describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and