Questions: Read the case study above and answer the following questions.
Divide into pairs and explain Galileo's experiment to your friend.
Write down an aim and a hypothesis for Galileo's experiment.
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:
Determine the time between each picture if the frequency of the exposures were 10 Hz.
Calculate the velocity,
${v}_{2}$ , of the ball between positions 1 and 3.
Calculate the acceleration the ball between positions 2 and 5.
$$a=\frac{{v}_{5}-{v}_{2}}{{t}_{5}-{t}_{2}}$$
Compare your answer to the value for the acceleration due to gravity (
$\mathrm{9,8}\phantom{\rule{2pt}{0ex}}m\xb7$ 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.
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:
Measure the height of a door, from the top of the door to the floor, exactly. Write down the measurement.
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.
The second person watches the floor and starts his stopwatch when the marble hits the floor.
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.
Design a table to show the results of your experiment. Choose appropriate headings and units.
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.
Write a conclusion for your investigation.
Answer the following questions:
Why do you think two stopwatches were used in this investigation?
Compare the value for acceleration obtained in your investigation with the value of acceleration due to gravity (
$\mathrm{9,8}\phantom{\rule{2pt}{0ex}}m\xb7s{}^{-2}$ ). Explain your answer.
A ball is dropped from the balcony of a tall building. The balcony is
$15\phantom{\rule{2pt}{0ex}}m$ above the ground. Assuming gravitational acceleration is
$\mathrm{9,8}\phantom{\rule{2pt}{0ex}}m\xb7s{}^{-2}$ , find:
the time required for the ball to hit the ground, and
the velocity with which it hits the ground.
It always helps to understand the problem if we draw a picture like the one below:
By now you should have seen that free fall motion is just a special case of motion with constant acceleration, and we use the same equations as before. The only difference is that the value for the acceleration,
$a$ , is always equal to the value of gravitational acceleration,
$g$ . In the equations of motion we can replace
$a$ with
$g$ .
Gravitational acceleration
A brick falls from the top of a
$5\phantom{\rule{2pt}{0ex}}m$ high building. Calculate the velocity with which the brick reaches the ground. How long does it take the brick to reach the ground?
A stone is dropped from a window. It takes the stone
$\mathrm{1,5}\phantom{\rule{2pt}{0ex}}s$ to reach the ground. How high above the ground is the window?
An apple falls from a tree from a height of
$\mathrm{1,8}\phantom{\rule{2pt}{0ex}}m$ . What is the velocity of the apple when it reaches the ground?
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
hi vedant can u help me with some assignments
Solomon
find the 15th term of the geometric sequince whose first is 18 and last term of 387
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=