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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? Write your answer in the space provided.

    

    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 105  ______________  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?

 

¢  What is the area, and its approximate uncertainty, of a circle of radius 3.8 x 104 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 1x104 cm.

Aspecified = (rspecified)2 = (3.8x104 cm)2 = 4.5 x 109 cm2

 

Amin= (rmin)2 = (3.7x104 cm)2 = 4.3 x 109 cm2

Amax = (rmax)2 = (3.9x104 cm)2 = 4.78 x 109 cm2

DA = 0.5(4.78 - 4.30) = 0.24 x 109 cm2

 

¢  Three students derive the following equations in which x refers to distance travelled, v the speed, a the acceleration in m/seconds2 and t the time

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

 

     (a) x = vt2 + 2at                        cannot be correct

     (b) x = v0t + (1/2)at2                 can be correct

     (c) x = vot + 2at2                      cannot be correct

Which of these could possibly be correct according to a dimensional check? Circle the correct answer(s).

(a)The quantity vt2  has units of (m/s) (s2)= ms, which do not match with the units of meters for x.  The quantity 2at has units

    (m/s2)(s) = m/s, which also do not match with the units of meters for x.  Thus this equation cannot be correct.

 

(b)The quantity v0t  has units of (m/s)(s) = m and (1/2)at2 and  has units of (m/s2)(s2) = m.  Thus, since each term has units of

     meters, this equation can be correct.

 

(c)The quantity vot  has units of (m/s)(s) = m, and 2at2  has units of (m/s2)(s2) = m.  Thus, since each term has units of meters,

     this equation can be correct.

 

 

 

 

 

 

Exercise 2

 

Exercise 3