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
That table is about one and a half football fields long?
anyway
L * 0.000012 ( 40 - 28) = 158 - L
close enough is
158 * 0.000012 ( 40 - 28) = 158 - L
To determine 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 change in length of the meter rule is given by the formula:
ΔL = L * α * ΔT
Where:
ΔL is the change in length
L is the original length of the meter rule
α is the coefficient of linear expansion for steel
ΔT is the change in temperature
In this case, we know the original length of the meter rule (which we'll denote as L_0) at 28 degrees Celsius, the change in temperature (ΔT), and the coefficient of linear expansion (α), but we need to determine the change in length (ΔL) of the meter rule first:
ΔL = L_0 * α * ΔT
Now, we can calculate the change in length of the meter rule:
ΔL = L_0 * α * (40 - 28) = L_0 * α * 12
Next, we need to determine the measured length of the table when using the steel meter rule at 40 degrees Celsius. Let's denote the measured length as L_m.
L_m = 158m
To find the true length of the table, denoted as L_true, we need to subtract the change in length of the meter rule from the measured length:
L_true = L_m - ΔL = L_m - L_0 * α * 12
To complete the calculation, you need to know the original length of the meter rule at 28 degrees Celsius (L_0). Once you have that value, you can substitute it into the equation along with the known values for α, ΔT, and L_m to find the true length of the table.