HOOKE'S LAW Introduction In physics, Hooke's Law is one of the fundamental principles governing how objects deform under external forces . Named after the 17th-century British physicist Robert Hooke, this law provides a crucial understanding of the behavior of elastic materials, such as springs and rubber bands. Whether stretching a rubber band or compressing a spring, Hooke's Law helps explain what happens when forces act on these materials. What is Hooke's Law: Hooke's Law states that the force F needed to extend or compress a spring by some distance x is proportional to that distance. Mathematically, it is expressed as: F= -kx Here k represents the spring constant, which is the measure of the stiffness of the spring, and x is the displacement from the displacement position. The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement. Understanding the Spring Constant: The spring constant k is a critical co
SIGNIFICANT FIGURES
The value of a physical quantity is expressed by a
number followed by some suitable unit. Every
measurement of a quantity is an attempt to find its true
value. The accuracy in measuring a physical quantity
depends upon various factors:
+ the quality of the measuring instrument
+ the skill of the observer
+ the number of observations made
For example, a student measures the length of
a book as 18 cm using a measuring tape. The
numbers of significant figures in his/her measured value are two. The left digit 1 is the accurately known digit.
While the digit 8 is the doubtful digit for which the student may
not be sure.
Another student measures the same book using a
ruler and claims its length to be 18.4 cm. In this case all the
three figures are significant. The two left digits 1 and 8 are
accurately known digits. Next digit 4 is the doubtful digit for
which the student may not be sure.
A third student records the length of the book as
18.425 cm. Interestingly, the measurement is made using the
same ruler. The numbers of significant figures is again three;
consisting of two accurately known digits 1, 8 and the first
doubtful digit 4. The digits 2 and 5 are not significant. It is
because the reading of these last digits cannot be justified
using a ruler. Measurement upto third or even second decimal
place is beyond the limit of the measuring instrument.
The significant figures are all the digits that
are known accurately and the one estimated digit. More
significant figure means greater precision.
Rules for Finding Significant Figures:
SIGNIFICANT
FIGURES
1.
All
Non-zero digits are called as Significant Figures
a.
123 has 3 SF
b.
56788367 has 8 SF
c.
654 has 3 SF
2.
Zeros
that are locating between non-zero digits are called Significant Figures.
a.
2705 has 4 SF
b.
280635 has 6 SF
3.
Final
zeros or zero after decimal point are significant.
a.
275.00
has 5 SF
4.
Zeros
that are used for spacing the decimal point are not significant figures (OR)
Zeros that are locating left side of the decimal point are not significant
figures.
a.
0.03 has 1 SF
b.
0.0027 has 2 SF
c.
0.002070 has 4 SF
5.
Zeros
that are locating right of the whole number which do not contain any decimal
point are not significant figures.
a.
500 has 1 SF
b.
0.500 has 3 SF
Exercise:
Which of the following are significant Figures.
a. 100.8
b. 0.00580km
c. 210.0
(a) All the four digits are significant. The zeros between the two significant figures 1 and 8 are significant. To write the quantity in scientific notation, we move the decimal point two places to the left, thus 2 100.8 s = 1.008 x10 s
(b) The first two zeros are not significant. They are used to space the decimal point. The digit 5,8 and the final zero are significant. Thus there are three significant figures. In scientific notation, it can be -3 written as 5.80x10 km.
(c) The final zero is significant since it comes after the decimal point. The zero between last zero and 1 is also significant because it comes between the significant figures. Thus the number of significant figures in this case is four. In scientific notation, it can be written as 2 210.0 g = 2.100 x 10
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