d1 = 2.53 cm +/- .05 cm
d2 = 1.753 m +/- .001 m
0 = 23.5 degrees +/- .5 degrees
v1 = 1.55 m/s +/- .15 m/s
Using the measured quantities above, calculate the following. Express the uncertainty calculated value.
a = 4 v1^2 / d2
To calculate 'a' using the measured quantities, we can follow these steps:
1. Evaluate the individual measurements first.
- d1 = 2.53 cm +/- 0.05 cm
- d2 = 1.753 m +/- 0.001 m
- 0 = 23.5 degrees +/- 0.5 degrees
- v1 = 1.55 m/s +/- 0.15 m/s
2. Calculate the value of 'a' using the formula:
a = 4 * v1^2 / d2
Now, let's calculate each part step-by-step:
Step 1: Evaluate individual measurements
For d1 = 2.53 cm +/- 0.05 cm, we have the value of d1 as 2.53 cm, and the uncertainty as +/- 0.05 cm.
For d2 = 1.753 m +/- 0.001 m, we have the value of d2 as 1.753 m, and the uncertainty as +/- 0.001 m.
For 0 = 23.5 degrees +/- 0.5 degrees, we have the value of 0 as 23.5 degrees, and the uncertainty as +/- 0.5 degrees.
For v1 = 1.55 m/s +/- 0.15 m/s, we have the value of v1 as 1.55 m/s, and the uncertainty as +/- 0.15 m/s.
Step 2: Calculate 'a' using the formula
Now, let's substitute the measured quantities into the formula:
a = 4 * v1^2 / d2
= 4 * (1.55 m/s)^2 / 1.753 m
To account for the uncertainties, we need to use the concept of propagation of errors. When dividing or multiplying measured quantities, we add the relative uncertainties.
Relative uncertainty of (v1^2 / d2) = (2 * relative uncertainty of v1) + (relative uncertainty of d2)
Substituting the respective relative uncertainties into the formula, we get:
Relative uncertainty of (v1^2 / d2) = (2 * (0.15 m/s) / 1.55 m/s) + (0.001 m / 1.753 m)
Now, we can calculate the value of 'a' with the propagated uncertainty:
a = (4 * (1.55 m/s)^2 / 1.753 m) +/- [4 * (2 * (0.15 m/s) / 1.55 m/s) + (0.001 m / 1.753 m)]
Calculating the above expression, we get the final result for 'a' with its uncertainty.