Science 122 About Lab 4

Science 122


How To Calculate

To evaluate a relationship such as there are simple rules, and a few easy steps.

Doing calculations only seems difficult. If you break it into small steps you will find that none of the steps requires anything difficult.

The rule is simple: Evaluate anything in parentheses or under square root signs first first. Then 'take' the square root.

Here is a step-by-step guide to evaluation of the relationship for the period of a simple pendulum, as used in lab 5.

When performing any multi-step calculation, write down the appropriate expression at each and every step with the calculated values substituted. It may seem like extra work, but it will keep your thoughts organized. It is easier to enter the numbers into the calculator when they are written down!.

1. Write down the relationship using your measured or given values in place of their symbols.

Suppose your length is L = 48.291 cm. Then your relationship would look like this:

2. Calculate the expression within the square root sign first.

For L = 48.291 cm. it would look like this: .

3. Evaluate the square root:

It would look like this:

The number should already be on the calculator display. If it is, simply press the key on the calculator.

If the number has been erased from the calculator display, reenter it, then press the key.

4. Multiply by 2:

is a number that appears in calculations from time to time. It is the ratio of circumference to diameter of a circle, but it 'pops up' in unexpected places.

There is a key on most calculators. Press the key when you want to enter . If there is not a key, enter the value, 3.14 for .

With the number 0.2219831 still on the calculator display, press the X key, the key, the X key again, then 2, then = .

The result is 1.3947614, which rounds to 1.3948. The unit is seconds.

The calculated result was rounded to the same number of significant figures as the measurement of L. (There are 5 significant figures in 48.291 cm.)

5. The calculated theoretical (standard) period of a simple pendulum of length 48.291 cm. is 1.3948 sec.

T = 1.3948 sec. when L = 48.291 cm

If you followed the instruction in each step you should have arrived at the same result.

If it was difficult, go back and do it again, and again using a different number for L. Soon you will realize that each step is simple and it's only when you try to combine or skip steps that things get complicated.

return to lab 5