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Questions:  Read the case study above and answer the following questions.

  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 = x 3 - x 1 t 3 - t 1
  3. Calculate the velocity, v 5 , of the ball between positions 4 and 6.
    v 5 = x 6 - x 4 t 6 - t 4
  4. Calculate the acceleration the ball between positions 2 and 5.
    a = v 5 - v 2 t 5 - t 2
  5. Compare your answer to the value for the acceleration due to gravity ( 9,8 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.

v i = initial velocity ( m · s - 1 ) at t = 0 s v f = final velocity ( m · s - 1 ) at time t Δ x = displacement ( m ) t = time ( s ) Δ t = time interval ( s ) g = acceleration ( m · s - 2 )
v f = v i + g t
Δ x = ( v i + v f ) 2 t
Δ x = v i t + 1 2 g t 2
v f 2 = v i 2 + 2 g Δ 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.
  8. Answer the following questions:
    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 m · s - 2 ). Explain your answer.

A ball is dropped from the balcony of a tall building. The balcony is 15 m above the ground. Assuming gravitational acceleration is 9,8 m · s - 2 , find:

  1. the time required for the ball to hit the ground, and
  2. the velocity with which it hits the ground.
  1. It always helps to understand the problem if we draw a picture like the one below:

  2. We have these quantities:

    Δ x = 15 m v i = 0 m · s - 1 g = 9 , 8 m · s - 2
  3. Since the ball is falling, we choose down as positive. This means that the values for v i , Δ x and a will be positive.

  4. We can use [link] to find the time: Δ x = v i t + 1 2 g t 2

  5. Δ x = v i t + 1 2 g t 2 15 = ( 0 ) t + 1 2 ( 9 , 8 ) ( t ) 2 15 = 4 , 9 t 2 t 2 = 3 , 0612 . . . t = 1 , 7496 . . . t = 1 , 75 s
  6. Using [link] to find v f :

    v f = v i + g t v f = 0 + ( 9 , 8 ) ( 1 , 7496 . . . ) v f = 17 , 1464 . . .

    Remember to add the direction: v f = 17,15 m · s - 1 downwards.

Got questions? Get instant answers now!

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

  1. A brick falls from the top of a 5 m high building. Calculate the velocity with which the brick reaches the ground. How long does it take the brick to reach the ground?
  2. A stone is dropped from a window. It takes the stone 1,5 s to reach the ground. How high above the ground is the window?
  3. An apple falls from a tree from a height of 1,8 m . What is the velocity of the apple when it reaches the ground?

Questions & Answers

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salma
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ninjadapaul
20/(×-6^2)
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ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
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ninjadapaul
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Commplementary angles
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The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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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
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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.
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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Source:  OpenStax, Siyavula textbooks: grade 10 physical science. OpenStax CNX. Aug 29, 2011 Download for free at http://cnx.org/content/col11245/1.3
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