Exercise 1 Solution

¢ A ________________, in the scientific sense, is an analogy or mental image of a phenomena expressed in terms of something else we are\

already familiar
with. It is generally relatively simple and provides a structural similarity
to the phenomena being studied. **model**

¢
A
______________ is more detailed than the above, and can give
quantitatively testable predictions. **theory**

¢ A __________refers to certain concise but general statements about how nature behaves. Sometimes it takes the form of a relationship or

equation between
quantities (such as F = MA). **law**

¢
A
_______________ refers to less general statements than the item in bullet 3
above. **principle**

¢
How many significant
figures are shown in each of the following?

**
**

**
Ø
**
214
________
**
3****
**

**
Ø
**
82.34
________
**4**

**
Ø
**
7.08
________
**3**

**
Ø
**
0.03 ________
**
1
**

**
Ø
**
0.0075
________
**2**

**
Ø
**
1234
________
**4**

**
Ø
**
3600
________
**2 will also accept 2 - see discussion in
text**

¢ Write the following numbers showing all zeros in the space provided.

Ø
1.23
x 10^{5} ______________
**123000**

Ø
12.4 x 10^{-5} ______________
**0.000124
note: first 0 not required-suggested for clarity (to clearly identify the
decimal...)**

¢ What is the percent uncertainty in the following measurement? 1.76 + - 0.25 m?

** **

** Note: as previously
stated, always show your work for a calculation, or show the reasoning
otherwise**

** 0.25/1.76 = 0.1420 which is
stated as 0.14 since the numerator has only 2 significant figures**

** 0.1420x100 = 14.2%
Note that the answer has 3 significant figures. Why?**

^{4} cm?

To find the approximate uncertainty in the area, calculate the area for the specified radius, the minimum radius, and the maximum radius. Subtract the extreme areas. The uncertainty in the area is then half this variation in area.

**Note: Problem not graded** -
requires an assumption (since not given) about uncertainty in the radius.
Assume, for example, that the uncertainty in the radius is 1x10^{4}
cm.

**A**_{specified}**
= ****(r**_{specified})^{2}**
= (3.8x10**^{4}** cm)**^{2}**
= 4.5 x 10**^{9}** cm**^{2}

A_{min}=
_{rmin})^{2}
= (3.7x10^{4} cm)^{2} = 4.3 x 10^{9} cm^{2}

_{max}
= _{rmax})^{2}
= (3.9x10^{4} cm)^{2} = 4.78 x 10^{9} cm^{2}

**D****A****
= ****
0.5(4.78 - 4.30) = 0.24 x **
**10**^{9}**
cm**^{2}

¢
Three students derive the following equations in which x refers to distance
travelled, v the speed, a the acceleration in m/seconds^{2} and t
the time

in seconds, and the subscript 0 means a quantity at time t = 0.

(a) x = vt^{2}
+ 2at**cannot be correct**

(b) x = v_{0}t
+ (1/2)at^{2 }
**can be correct
**

(c) x = v_{o}t
+ 2at^{2}**cannot be correct**

Which of these could possibly be
correct according to a dimensional check?

**
(a)The
quantity vt ^{2}
has units of (m/s) (s^{2})= ms, which do
not match with the units of meters for
x.
The quantity 2at has units **

**
(m/s ^{2})(s)
= m/s, which also do not match with the units of meters for x.
Thus this equation cannot be correct.**

**(****b****)The quantity v**_{0}t**
****has units of (m/s)(s) = m and
(1/2)at**^{2}** and****
****has units of (m/s**^{2}**)(s**^{2}**)
= m.****
****Thus, since each term has units
of **

**
**
**meters, this equation can be correct.**

**
(c)The quantity v _{o}t
has
units of (m/s)(s) = m, and 2at^{2}
has
units of (m/s^{2})(s^{2}) = m.
Thus, since each term has units of meters,
**

**
this equation can be correct.**