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 the value of "a" using the given measured quantities, we need to substitute the values of v1 and d2 into the formula a = 4v1^2 / d2. Since we also have uncertainties associated with v1 and d2, we need to propagate the uncertainties to calculate the uncertainty in "a."
Let's start by substituting the values:
v1 = 1.55 m/s
d2 = 1.753 m
Now, let's calculate the value of "a":
a = 4 * (1.55 m/s)^2 / 1.753 m
Calculating this, we get:
a = 4 * 2.4025 m^2/s^2 / 1.753 m
a = 9.61 m^2/s^2 / 1.753 m
a ≈ 5.485 m/s^2
Now, let's calculate the uncertainty in "a" using the given uncertainties:
∆v1 = 0.15 m/s (uncertainty in v1)
∆d2 = 0.001 m (uncertainty in d2)
To propagate the uncertainties, we can use the formula:
∆a = |a| * √((∆v1 / v1)^2 + (∆d2 / d2)^2)
Substituting the values:
∆a = 5.485 m/s^2 * √((0.15 m/s / 1.55 m/s)^2 + (0.001 m / 1.753 m)^2)
∆a ≈ 5.485 m/s^2 * √(0.09677419 + 5.703227 × 10^-7)
Calculating this, we get:
∆a ≈ 5.485 m/s^2 * √0.096774196
∆a ≈ 5.485 m/s^2 * 0.31
∆a ≈ 1.70 m/s^2
Therefore, the calculated value of "a" is approximately 5.485 m/s², with an uncertainty of 1.70 m/s².