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EASTERN MEDITERRANEAN UNIVERSITY

Department of Physics Lab Final Exam Sample

Duration: 30 minutes You are allowed to use your own calculator.

Name and Surname: Student Number: Group Number: Signature:

Hint: Least square line of 𝑦 with respect to 𝑥 is given by 𝑦 = 𝑚𝑥 + 𝑏 in which 𝑏 = ! !! ! ! !"

! !! ! ! ! and 𝑚 = ! !" ! ! !! !! ! ! ! .

Here 𝑛 is the number of times that the experiment is repeated.

Finding the value of 𝒈 by using the Air Track: In experiment number 4 you measured the time 𝑡 taken by the flag on the glider to pass through the light beam of the optical eye. The following is the table you filled during the experiment: The bold numbers were given.

𝑡(𝑠) 𝐷(𝑚) 𝑣(𝑚/𝑠) =0.10𝑡 𝑣!(

𝑚!

𝑠! ) 0.075 0.40 1.33 1.78 0.068 0.60 1.47 2.16 0.050 0.80 2.00 4.00 0.043 1.00 2.33 5.41 0.046 1.20 2.17 4.73

a) Complete the tables. (1P) b) Find the equation of the least square line 𝑣! with respect to 𝐷. (Please note that 𝐷 is the

variable 𝑥 while 𝑣! is function  𝑦.) (4P) c) Use the relation 𝑣! = 2𝑔𝑠𝑖𝑛𝜃 𝐷 with 𝜃 = 15° to find the experimental value of 𝑔. (3P) d) If the theoretical value of 𝑔 = 9.82𝑚/𝑠! find the percentage error of your experiment.

(2P) Hint: You may use the following table: 𝑥 𝑦 𝑥! 𝑥𝑦

0.40   1.78   0.16   0.71  0.60   2.16   0.36   1.30  0.80   4.00   0.64   3.20  1.00   5.41   1   5.41  1.20   4.73   1.44   5.67  𝑥 =4 𝑦 =18.07  

𝑥! =3.6  

𝑥𝑦 =16.29  

2

𝑚 =𝑛 𝑥𝑦 − 𝑥 𝑦𝑛 𝑥! − 𝑥 ! =  

5   ∙ 16.29− 4 ∙ 18.075 ∙ 3.6− (4)! = 4.59

𝑏 =𝑦 𝑥! − 𝑥 𝑥𝑦𝑛 𝑥! − 𝑥 ! =  

18.07 ∙ 3.6− 4 ∙ 16.295 ∙ 3.6− 4 ! = −0,054  

 

𝑔 =𝑣!

𝐷    1

2 sin𝜃 =𝑚

2 sin𝜃 =4.59

2 sin 15° = 8.87      relative  error  

𝑒𝑟𝑟𝑜𝑟 =8.87− 9.82

9.82 = 0.097 = 9.7%  

   

     

 

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