Lab #2 - Measurements

Physics 4A Lab #2: Measurements Lab Group Members: 1. _________________________ 2. _________________________ 3. _________________________ Type all responses, including equations

LAB #2: MEASUREMENTS THEORY The density of an object is defined to be the ratio of its mass and volume. An equation, this variable can be expressed as ࠵? = ࠵? ࠵? When considering a cube, the equation for its volume is defined to be ࠵? = ࠵?࠵?ℎ where ࠵? is the cube’s length, ࠵? is the cube’s width, and ℎ is the cube’s height. When considering the volume of a solid cylinder, the equation for its volume is defined to be ࠵? = ࠵?࠵? ! ℎ 4 where ࠵? is the solid cylinder’s diameter and ℎ is the solid cylinder’s height. When considering the volume of a hollow cylinder, the equation for its volume is defined to be ࠵? = ࠵?(࠵? " ! − ࠵? # ! )ℎ 4 where ࠵? " is the hollow cylinder’s outer diameter, ࠵? # is the hollow cylinder’s inner diameter, and ℎ is the hollow cylinder’s height. When considering the volume of a solid sphere, the equation for its volume is defined to be ࠵? = ࠵?࠵? $ 6 where ࠵? is the solid sphere’s diameter. A ruler can measure in both inches and centimeters, but we will use exclusively use its centimeters. The smallest scale division on the ruler is one-tenth of a centimeter, such that, the whole number of tenths may be accurately read, or resolved, directly from the ruler. However, it is possible to estimate the fraction of this smallest scale division. The uncertainty involved this estimation is quantified by “splitting the difference” in its resolution. As seen below in FIGURE 1 , the black-colored object’s length is formally expressed as (41.64 ± 0.05) ࠵?࠵? . The digits 41.6 are directly resolved from the ruler, while the 4 in the hundredths place is an estimate by the experimenter since it is not directly read from the ruler’s scale. The ± 0.05 portion of the measurement represents the uncertainty in the estimation from this ruler.

LAB #2: MEASUREMENTS FIGURE 3 – A sample measurement using the Vernier Caliper, in both inches and millimeters. PROCEDURE 1. Record the mass of all four objects . a. Properly zero the mass scale before taking measurements. 2. Record the following measurements for the specified object: a. Cube • Ruler o Length o Width o Height • Vernier Caliper o Length o Width o Height b. Solid cylinder • Ruler o Diameter o Height • Vernier Caliper o Diameter o Height c. Hollow cylinder • Ruler o Outer diameter o Inner diameter

LAB #2: MEASUREMENTS o Height • Vernier Caliper o Outer diameter o Inner diameter o Height d. Sphere • Ruler o Diameter • Vernier Caliper o Diameter DATA ANALYSIS • Show the following calculations for the specified object: o Cube i. Ruler data § Density § Density Percent Error o Solid Cylinder ii. Ruler data § Density o Hollow Cylinder iii. Ruler data § Density o Sphere iv. Ruler data § Density

LAB #2: MEASUREMENTS DATA TABLE: HOLLOW CYLINDER MEASUREMENTS MASS ࠵? ± ࠵?࠵? ( ࠵? ) ± OUTER DIAMETER ࠵? " ± ࠵?࠵? " ( ࠵?࠵? ) INNER DIAMETER ࠵? # ± ࠵?࠵? # ( ࠵?࠵? ) HEIGHT ℎ ± ࠵?ℎ ( ࠵?࠵? ) RULER ± ± ± VERNIER CALIPER ± ± ± DATA TABLE: SPHERE MEASUREMENTS MASS ࠵? ± ࠵?࠵? ( ࠵? ) ± DIAMETER ࠵? ± ࠵?࠵? ( ࠵?࠵? ) RULER ± VERNIER CALIPER ±

LAB #2: MEASUREMENTS Cube – Ruler Data Density: ࠵? = ࠵? ࠵?࠵?ℎ ࠵? = ( )( )( ) ࠵? = Density Percent Error: ࠵?࠵? = |࠵? − ࠵? % | ࠵? % × 100% ࠵?࠵? = | | × 100% ࠵?࠵? = Solid Cylinder – Ruler Data Density: ࠵? = 4࠵? ࠵?࠵? ! ℎ ࠵? = 4( ) ࠵?( ) ! ( ) ࠵? = Density Percent Error: ࠵?࠵? = |࠵? − ࠵? % | ࠵? % × 100% ࠵?࠵? = | | × 100% ࠵?࠵? =

LAB #2: MEASUREMENTS TABLE OF RESULTS OBJECT AND MEASUREMENT DEVICE EXPERIMENTAL DENSITY ࠵? ( ࠵? ࠵?࠵? $ ⁄ ) ACCEPTED DENSITY ࠵? % ( ࠵? ࠵?࠵? $ ⁄ ) PERCENT ERROR ࠵?࠵? ( % ) Cube Ruler Data 8.52 Vernier Data Solid Cylinder Ruler Data 2.60 Vernier Data Hollow Cylinder Ruler Data 7.30 Vernier Data Sphere Ruler Data 11.34 Vernier Data

LAB #2: MEASUREMENTS Answer the following questions below using complete sentences: 1. In the context of physics measurements, what is parallax? 2. What is the resolution of the ruler, the Vernier Caliper, and the mass scale? Include units in your answers. 3. Based on your results, which object (i.e., cube, solid cylinder, hollow cylinder, or sphere) had the most accurate density? 4. Overall, did the ruler or Vernier Caliper produce the most accurate densities? Justify your answer. 5. Overall, were your densities accurate or inaccurate? Justify your answer.