a steel meter rule has correct lenght at 28 degree celcius on the day the temparature is 40 degree celicius,it measures the lenght of a table at 158m .what is the true lenght of the table.alpha=0.000012 raise up to power one per kelvin.
40 - 28 = 12 degrees higher so measured length is longer than true length (The ruler expanded)
error in length / length = 1.2 *10^-5 * 12 deg
error in length = 158 meters (but I think that is a typo)*1.2*10^-5
= 189.6 * 10^-5 meters
= 0.001896 meters
(it is probably centimeters :)
so
158.000000 - .001896
whoops, forgot the 12 degrees, multiply change in length by 12 !!!!
To find the true length of the table, we need to account for the expansion of the steel meter rule due to the change in temperature.
The formula for linear expansion is given by:
ΔL = α * L * ΔT
Where:
ΔL = change in length
α = coefficient of linear expansion
L = initial length
ΔT = change in temperature
Given:
L = 1 meter (initial length of the rule)
ΔT = (40 - 28) = 12°C (change in temperature)
α = 0.000012 K^(-1) (coefficient of linear expansion)
Substituting the values into the formula, we can calculate the change in length:
ΔL = (0.000012 K^(-1)) * (1 meter) * (12 °C)
ΔL ≈ 0.000144 meters
Now, to find the true length of the table, we need to subtract the change in length from the measured length.
True Length = Measured Length - ΔL
= 158 meters - 0.000144 meters
= 157.999856 meters
Therefore, the true length of the table is approximately 157.999856 meters.
To find the true length of the table at 40 degrees Celsius, we can use the concept of thermal expansion.
The thermal expansion coefficient (alpha) is a measure of how much a material expands or contracts with a change in temperature. In this case, alpha is given as 0.000012 per kelvin.
First, we need to calculate the change in temperature from 28 degrees Celsius to 40 degrees Celsius:
Change in temperature = final temperature - initial temperature
Change in temperature = 40°C - 28°C
Change in temperature = 12°C
Next, we'll calculate the expansion factor, which is given by:
Expansion factor = alpha * change in temperature
Expansion factor = 0.000012 * 12°C
Expansion factor = 0.000144
The expansion factor represents the fractional increase in length due to the change in temperature. Since the original length of the meter rule at 28°C is correct, we need to increase the measured length of the table by the expansion factor:
True length of the table = measured length * (1 + expansion factor)
True length of the table = 158m * (1 + 0.000144)
Now, we can calculate the true length of the table:
True length of the table = 158m * 1.000144
True length of the table = 158.227872m
Therefore, the true length of the table at 40 degrees Celsius is approximately 158.23 meters.