half report for experiment 1

Experiment 1: Motion a in Viscous Medium

1. Aims

The aim of this experiment is to observed and explain the physical force shown on the electronic balance with respect to the bead and its position. From there we explained the relationship of

beads motion in viscous medium - detergent. mg−kv−B=mdVdt

- eq(1). From eq(1), we will

derive a new equation V T=mgk

− Bk

- eq(2), where it show the relationship of beads movement at

terminal velocity. We will get the measurement of the VT from displacement-time graph and from eq(2), we will determine the value of detergent viscosity, η.

2. Objectives of the Experiment

The objective of the experiment is to record down the physical force of R1, R2 and R3 and observed the reading of electronic balance at R4 and R5 of the experiment. After that discuss about the reading above. Another objective is to determine the terminal velocity of each bead size VT and calculate the viscosity η of the detergent when using different bead size using eq(2), k = 6 πηr -eq(3). and buoyancy force, B = ρl gvb -eq(4).

where :m = mass of bead (g)g = force of gravity, 981(cm/sec2)η = viscosity of liquid (cps or gcm-1sec-1-)r = radius of bead (cm)vb = volume of bead (cm3)ρl= density of liquid (gcm-3)

3. Data Analysis and Result Discussion3.1 Preliminary Observation of Beads Position had on Physical Force shown in Electronic Balance.

R1, when bead is immersed in liquid hold by a stringbalance show a force of 0.716g. Force R1 actually is the Newton third-law pair of the buoyancy force of bead acting on liquid. Although bead is not in direct contact with the electronic balance, but the balance is in contact with the beaker and the beaker is with contact with the liquid. Therefore R1 = Bbead on liquid = -Bliquid on bead.

R2, when bead is at the bottom touching the beaker.balance show a force of 0.953g. R2 is the force mg of bead on beaker.

R2 = (mg)bead on beaker = - (mg)bead on beaker (mg)balance on beaker = - (mg)beaker on balance

Therefore R2 = (mg)bead on balance

PH1198 Physics Laboratory


R3, when bead is raise to the position of R1 from R2 using a stringbalance show a force of 0.628g. R3 is the force of Bbead on liquid - fbead on liquid where f is the fluid resistance force. Therefore it also correspond to fliquid on bead - Bliquid on bead.

R4, when bead is drop to R2 and pull up quickly using the stringthe reading R4 was observed to be decreasing as the bead move up from the beaker. The value R4

was actually observed to went over to -ve reading of physical force. This might due to the fact that external force is introduced to the system, when a positive external force is applied on the bead, the bead move up which result in a negative acceleration as downward motion is define to be positive force and upward motion is define to be negative.

When Fexternal > mg - f + B, R4 = -ve

R5, when bead allowed to drop freely into viscous medium without being hold by stringWhen bead is allowed to drop feely into beaker filled with detergent, R5 is expected to be observe to be steadily increase in physical force. At time = 0, instantaneous, R5 = R1. As the Bead drop further down in the viscous medium, at time = x, R5 = mg - f - b. Since bead is in downward motion, mg > f + B. At t = tfinal R5 is equal to R2 when the bead reached the bottom. Since mg > f + B, mg is > B. Therefore the value of R5 at to < tx < tfinal. The physical force reading increases as time increase when the bead continue to falls.

3.2 Measurement of Terminal velocity and Determination of the viscosity of Mama Lemon Dishwashing Liquid

From the Experiment, the raw data of three different bead size displacement-time data is processed and ploted:

Figure.1 Plot of Displacement(cm) against Time(sec) Graph of Three Different Bead Size



From the Figure.1, we can derive the VT of each bead size using the gradient of linear plot of each bead size final 5 value. The final 5 Value is used as the bead most likely had reached VT. If further prove is required, a velocity - time graph can be plotted. In the velocity - time graph, the point where the graph is join with a straight horizontal line, with gradient = 1, the y-intercept will be the VT which correspond to the gradient of linear line of displacement-time graph.

Therefore from figure.1:VT for small beads = 0.143 cm/secVT for medium beads = 0.251 cm/secVT for large beads = 0.471 cm/sec

It is observed that as the size of the bead get bigger, the terminal velocity of the bead also get larger. As the beads travels down the column of viscous liquid, both different beads actually experience similar fluid resistance force. However as larger bead has a larger mass as compare to the smaller bead, it experiences a greater downward force of gravity. The large bead accelerate for a longer period of time before reaching the sufficient upward fluid resistance requires to balance the downward force of gravity. Therefore the larger bead actually reached the terminal velocity later thus it had a greater magnitude of terminal velocity.

From the Raw and Processed Data:Small Bead Medium Bead Large Bead Unit

Terminal Velocity, VT 0.143 0.251 0.471 cmsec-1

Mass, m 0.069 0.178 0.945 gRadius, r 0.227 0.315 0.550 cm

Volume, vb 0.0490 0.131 0.697 cm3

Buoyancy, B 58.0153 155.0231 825.1881 g cm sec-2

mg, 67.68900 174.61800 927.04500 g cm sec-2

k 67.65 78.07 216.26 g sec

Using eq(2),(3) and (4):

V T=mgk

− Bk

- eq(2).

k = 6 πηr - eq(3).

B = ρl gvb - eq(4).

η= g6 π V T r

(m−4 π3

ρl r3) ------eq(5)

Substitute the values into eq(5), we will get:Viscosity, η for small beads = 15.8 gcm-1sec-1

Viscosity, η for medium beads = 13.1 gcm-1sec-1

Viscosity, η for large beads = 20.9 gcm-1sec-1



Therefore, viscosity in terms of cps:Viscosity, η for small beads = 1580 cpsViscosity, η for medium beads = 1310 cpsViscosity, η for large beads = 2090 cps

Comparing calculated viscosity to reference value of 1410cps,

%Error of Results from Reference Values = Results−Referece

Referencex 100%

Therefore %Error of Viscosity, η:%Error for small beads = 12% %Error for medium beads = -7%%Error for large beads = 48%

Therefore from the result we can see that the as the for the small and medium bead, the %Error is still somewhere "acceptable", ±12%. But for the large bead, the %Error is actually approximate 48%. This show using f = kv (drag force) to calculate viscosity is ineffective for bead that is larger than certain size as VT is larger den certain values.

When an object move through a fluid, the frictional force is either viscous (drag) or turbulent drag. A larger objects or object that have faster motion actually favors the turbulent drag in comparison to a smaller object that move slower which favors viscous drag. For this experiment, we actually make use of eq(1), where f = kv. This equation will become inaccurate when the object is travelling above certain velocity.

Once the object reached the certain velocity, the frictional force might get more complicate as there is overlapped between the two types of drag - viscous and turbulent. Therefore to calculate viscosity using large beads, Reynolds number had to be introduced to the equation for the fluid resistance force. Reynolds number is a constant that represent an ratio of inertial forces against viscous forces which can be used to compute for both the situation above.



4. Error AnalysisThe measurement error of time is taken from average delayed human reaction which is assume to be ±0.2sec + the precision error of the stopwatch which is (±20/100)sec, therefore equate to ±0.4sec. The diameter error of the bead is taken from the precision error of the vernier caliper, ± 0.002cm.The displacement error is taken from the radius of the bead with error + error from the ruler reading. Therefore for a large bead of diameter 11.00mm, the max displacement error will

be 1.102

2 + 0.05 ≈ 0.6cm (round off to nearest instrument precision). The measurement error of

the electronic balance is taken to be the fluctuation of the reading ± 0.001g.

For the displacement error, the measurement error is ≈ ±0.6cm. However the std error computed is found to be larger compared to measurement error. Example for large bead, at t = 135sec, the standard error is found to be 3.4cm as compare to measurement error to 0.6cm of measurement. Therefore the std error is used in computing the errors bar for the displacement-time graph, figure.1.

5. ConclusionIn conclusion, this experiment had helps us to visually the physical force of how bead motion had on the liquid medium. It also help us to explain the relation between mg, B and f from observation of reading R1 R2 R3 and R5. In addition, we had calculate the viscosity of detergent using VT with three different bead sizes. Although equation 2 is not accurate for computing the viscosity for large bead as the results deviation from references viscosity greatly, it had shown us that we can get the approximate viscosity of the detergent using the small bead and medium bead, in another words, when velocity is below certain limits. Therefore this experiment had proved that f = kv is true at low speed

6. Reference(s)

[1] The University of Arizona, (N.D). Terminal Velocity. Retrieved from the University of Arizona Website: http://www.physics.arizona.edu/physics/gdresources/documents/06_Terminal_Velocity.pdf.


half report for experiment 1

Documents