Revision and Consolidation

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Presentation transcript:

Revision and Consolidation Hooke's Law and Error Estimation 08/09/2002 By Mr. NGAN HON SHING

Hooke’s Law It states that F is proportional to the extension of the spring. i.e.: where F is the stretching force, x is the extension of the spring. It’s also valid when the spring is compressed by a force F and has a compression x. As the spring is compressed, energy is stored in the spring. This energy is called elastic potential energy. 08/09/2002 By Mr. NGAN HON SHING

Error Estimation The maximum probable error in a particular measurement is half of the smallest unit of the measuring instrument. It is also known as the absolute error of the measurement. 08/09/2002 By Mr. NGAN HON SHING

What is the length of the tape? 10 15 cm The measured value is 13cm. We said that the absolute error is 1cm/2 (i.e.: 0.5cm) Absolute error of l,  l = 1cm/2 = 0.5cm l = 13 ± 0.5cm 08/09/2002 By Mr. NGAN HON SHING

More about absolute error(uncertainty) If Y=A+B+C then Y = A+ B+ C If Y=k1A+k2 then Y = k1A If Y=k1A+k2B+k3C then Y = k1A+k2B+k3C Examples: a=5.1±0.1cm; b=3.2 ±0.2m Q=a+b= C=b-a= 3.251 ± 0.201m 3.149 ± 0.201m 08/09/2002 By Mr. NGAN HON SHING

Percentage error i.e.: percentage error in l =(0.5/13)*100%=3.8% If Y=ApBq, then % error in Y = |p|x(%error in A)+|q|x(%error in B) Examples: F=15 ± 0.5N; l=3.0 ± 0.05m; r=(2.3 ± 0.05)x10-4m E=(F x l)/(r2e) Calculate the % error in E. (11.8%) 08/09/2002 By Mr. NGAN HON SHING

Exponential Constant and Exponential Function Exponential Constant, e = 2.7 1828 1828 Exponential Function = ex 08/09/2002 By Mr. NGAN HON SHING

More about exponential fn 08/09/2002 By Mr. NGAN HON SHING

Natural Logarithm Fn (ln x) Common Log Fn: y=log10x ; x=10y Natural Log Fn: y = logex = ln x; x = ey 08/09/2002 By Mr. NGAN HON SHING