# 0.3 Gravity and mechanical energy

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1. Divide into pairs and explain Galileo's experiment to your friend.
2. Write down an aim and a hypothesis for Galileo's experiment.
3. Write down the result and conclusion for Galileo's experiment.

## Research project : experimental design

Design an experiment similar to the one done by Galileo to prove that the acceleration due to gravity of an object is independent of the object's mass. The investigation must be such that you can perform it at home or at school. Bring your apparatus to school and perform the experiment. Write it up and hand it in for assessment.

## Case study : determining the acceleration due to gravity 1

Study the set of photographs alongside showing the position of a ball being dropped from a height at constant time intervals. The distance of the ball from the starting point in each consecutive image is observed to be: ${x}_{1}=0$  cm, ${x}_{2}=4,9$  cm, ${x}_{3}=19,6$  cm, ${x}_{4}=44,1$  cm, ${x}_{5}=78,4$  cm and ${x}_{6}=122,5$  cm. Answer the following questions:

1. Determine the time between each picture if the frequency of the exposures were 10 Hz.
2. Calculate the velocity, ${v}_{2}$ , of the ball between positions 1 and 3.
${v}_{2}=\frac{{x}_{3}-{x}_{1}}{{t}_{3}-{t}_{1}}$
3. Calculate the velocity, ${v}_{5}$ , of the ball between positions 4 and 6.
${v}_{5}=\frac{{x}_{6}-{x}_{4}}{{t}_{6}-{t}_{4}}$
4. Calculate the acceleration the ball between positions 2 and 5.
$a=\frac{{v}_{5}-{v}_{2}}{{t}_{5}-{t}_{2}}$
5. Compare your answer to the value for the acceleration due to gravity ( $9,8\phantom{\rule{2pt}{0ex}}m·$ s ${}^{-2}$ ).

The acceleration due to gravity is constant. This means we can use the equations of motion under constant acceleration that we derived in  motion in one dimension to describe the motion of an object in free fall. The equations are repeated here for ease of use.

$\begin{array}{ccc}\hfill {v}_{i}& =& \mathrm{initial velocity}\left(\mathrm{m}·{\mathrm{s}}^{-1}\right)\mathrm{at}\phantom{\rule{2pt}{0ex}}\mathrm{t}=0\mathrm{s}\hfill \\ \hfill {v}_{f}& =& \mathrm{final velocity}\left(\mathrm{m}·{\mathrm{s}}^{-1}\right)\mathrm{at time}\phantom{\rule{2pt}{0ex}}\mathrm{t}\hfill \\ \hfill \Delta x& =& \mathrm{displacement}\left(\mathrm{m}\right)\hfill \\ \hfill t& =& \mathrm{time}\left(\mathrm{s}\right)\hfill \\ \hfill \Delta t& =& \mathrm{time interval}\left(\mathrm{s}\right)\hfill \\ \hfill g& =& \mathrm{acceleration}\left(\mathrm{m}·{\mathrm{s}}^{-2}\right)\hfill \end{array}$
${v}_{f}={v}_{i}+gt$
$\Delta x=\frac{\left({v}_{i}+{v}_{f}\right)}{2}t$
$\Delta x={v}_{i}t+\frac{1}{2}g{t}^{2}$
${v}_{f}^{2}={v}_{i}^{2}+2g\Delta x$

## Experiment : determining the acceleration due to gravity 2

Work in groups of at least two people.

Aim:  To determine the acceleration of an object in freefall.

Apparatus:  Large marble, two stopwatches, measuring tape.

Method:

1. Measure the height of a door, from the top of the door to the floor, exactly. Write down the measurement.
2. One person must hold the marble at the top of the door. Drop the marble to the floor at the same time as he/she starts the first stopwatch.
3. The second person watches the floor and starts his stopwatch when the marble hits the floor.
4. The two stopwatches are stopped together and the two times substracted. The difference in time will give the time taken for the marble to fall from the top of the door to the floor.
5. Design a table to show the results of your experiment. Choose appropriate headings and units.
6. Choose an appropriate equation of motion to calculate the acceleration of the marble. Remember that the marble starts from rest and that it's displacement was determined in the first step.
7. Write a conclusion for your investigation.
1. Why do you think two stopwatches were used in this investigation?
2. Compare the value for acceleration obtained in your investigation with the value of acceleration due to gravity ( $9,8\phantom{\rule{2pt}{0ex}}m·s{}^{-2}$ ). Explain your answer.

so some one know about replacing silicon atom with phosphorous in semiconductors device?
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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