Firing a Margarine Tub

Tubby The Tub Practical

Results:

Stretching Distance of the Elastic Band (x) / m Ѓ} 0.005 Distance Travelled by the Tub (from the Original Position) Average Distance Travelled by the Tub (s) / m Uncertainty in Average Distance Travelled by the Tub / m

Trail 1 / m Ѓ} 0.005 Trail 2 / m Ѓ} 0.005 Trail 3 / m Ѓ} 0.005

0.100 0.092 0.104 0.082 0.09 0.02

0.150 0.356 0.344 0.326 0.34 0.02

0.200 0.552 0.544 0.612 0.57 0.04

0.250 0.856 0.966 0.978 0.93 0.07

0.300 1.480 1.678 1.662 1.6 0.1

0.350 2.756 2.266 2.732 2.6 0.3

Log x / m Uncertainty in Log x / m Log s / m Uncertainty in Log s / m

-1.00 0.02 -1.0 0.1

-0.82 0.01 -0.47 0.03

-0.70 0.01 -0.24 0.03

-0.602 0.009 -0.03 0.03

-0.523 0.007 0.21 0.03

-0.456 0.006 0.41 0.05

Data Processing

Uncertainty in average distance traveled by the tub:

To find the uncertainty in the average distance traveled by the tub, find the maximum and minimum values from the three trails of the distance traveled by the tub, take the difference, and divide by two.

e.g. for stretching distance = 0.100 Ѓ} 0.002 m,

(Distance Traveled)max = 0.104 + 0.002 m = 0.106 m

(Distance Traveled)min = 0.082 – 0.002 m = 0.080 m

So Ñ"Ñž(Average Distance Traveled) = (0.106 – 0.080 m)/2

= 0.013 m

≈ 0.01 m (to 1 sig. fig.)

Uncertainty in Log x:

To find the uncertainty in log x, find the maximum and minimum values of log x, take the difference, and divide by two.

e.g. for log x = -1.00 m,

(log x)max = log (0.100 + 0.005 m) = -0.9788 m

(log x)min = log (0.100 – 0.005 m) = -1.0223 m

So Ñ"Ñž(log x) = (-0.9788 – -1.0223 m)/2 = 0.02175 m ≈ 0.02 m (to 1 sig. fig.)

Uncertainty in Log s:

To find the uncertainty in log s, find the maximum and minimum values of log x, take the difference, and divide by two.

e.g. for log s = -1.0 m,

(log s)max = log (0.09 + 0.02 m) = -0.9586 m

(log s)min = log (0.09 – 0.02 m) = -1.1549 m

So Ñ"Ñž(log s) = (-0.9586 – -1.1549 m)/2 = 0.09815 m ≈ 0.1 m (to 1 sig. fig.)

Plotting the Log Graph:

A relationship in the form s = kxn is suspected, where

s = Average Distance Traveled by the Tub

x = Stretching Distance of the Elastic Band

k = constant of proportional

n = the power of x (any number)

Logarithmic Graphs can be used to calculate k and n. (REFER TO THE GRAPH PAGE)

Start with s = kxn

=> log s = log (kxn)

=> log s = log k + log (xn)

=> log s = log k + n log x

=> log s = n log x + log k

This equation is of the form y = mx + c where m is the gradient and log k is the y-intercept.

From the Log Graph:

The gradient, m = 2.5454

mmax = 3.0832

mmin = 2.272

Ñ"Ñžm = (3.0832 - 2.272)/2 = 0.4056 = 0.4 (to 1 sig. fig.)

 n = 2.5 Ѓ} 0.4