SUPPLEMENTARY QUESTIONS

MEASUREMENT TECHNIQUES: Uncertainties.

1. Convert the absolute uncertainties in the following measurements into

percentage uncertainties. Restate each measurement in the form:

= %. a. = 1.02 0.01 b. = 20.5 0.2"#$ c. = 100 10%" d. & =20.3 0.2

2. Convert the percentage uncertainties in the following measurements

into absolute uncertainties. Restate each measurement in the form:

= )"*

a. + = 1.1, 10% b. - = 3.55- 2% c. = 9.81"#0 0.5% d. = 20.31% 1%

3. Calculate the percentage uncertainties for the following terms, given

the measurements of the respective variables.

a. 0 given = 1.00 0.01 b. & given & = 20.5 2% c. 2 ( + ) given = 1.25 0.01 and = 2.42 0.01

4. A student measures and states the mass of a trolley as = 1.001% 1%. The student then releases the trolley down a ramp and measures the speed of the trolley at the bottom of the ramp as = 2.50 0.02"#$.

a. Calculate the kinetic energy of the trolley at the bottom of the ramp.

(Use 78 = $0 0) b. What is the percentage uncertainty in the students measurement

of the trolley speed?

c. Hence, calculate the % uncertainty in the students measurement of

the trolleys kinetic energy.

d. How should the student record the kinetic energy of the trolley?

The student must include the absolute uncertainty in the trolleys

kinetic energy.

5. The following are results of a particular experiment relating to the

movement of an object:

Initial velocity = 20.3 m s-1 2%

Final velocity = 10.5 m s-1 2%

Time taken for velocity to change = 5.1 0.1 s

a. What is the uncertainty in the change in velocity, , of the object .

b. Calculate the measured value of the objects acceleration. State your

answer with its absolute uncertainty.

7. The equation that relates the frequency, : of a simple pendulum with its length, is:

: = $0; A student uses a string of length = 0.700 0.001. a. Calculate the frequency.

b. What is the percentage uncertainty in the frequency of the

pendulum?

c. What is the absolute uncertainty in the frequency of the pendulum?