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

2. 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

3. 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

4. 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

5. 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

6. 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

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

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

9. 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