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.
d1 (tan (0))
To calculate the value of d1(tan(θ)), we need to first find the value of tan(θ) and then multiply it by d1.
Given:
d1 = 2.53 cm +/- 0.05 cm
θ = 23.5 degrees +/- 0.5 degrees
Step 1: Calculate the value of tan(θ).
tan(θ) = tan(23.5 degrees)
You can use a scientific calculator or the trigonometric functions on your computer or smartphone to find the tangent of an angle. If you're using a scientific calculator, follow these steps:
1. Make sure your calculator is in "degree" mode.
2. Enter the angle, 23.5.
3. Press the "tan" or "tangent" function key.
For example, if you calculate tan(23.5 degrees) and get 0.4284.
Step 2: Calculate the value of d1(tan(θ)).
d1(tan(θ)) = d1 * tan(θ)
d1(tan(θ)) = 2.53 cm * 0.4284
Multiply the value of d1 by the value of tan(θ) to get the result. In this case, the result is approximately 1.083 cm.
Step 3: Determine the uncertainty in the calculated value.
To calculate the uncertainty in the final result, we need to consider the uncertainties in both d1 and θ.
To find the uncertainty in d1(tan(θ)), we can use the following formula:
uncertainty in d1(tan(θ)) = |d1(tan(θ))| * √((uncertainty in d1/d1)^2 + (uncertainty in tan(θ)/tan(θ))^2)
Substituting the values:
uncertainty in d1(tan(θ)) = 1.083 cm * √((0.05 cm / 2.53 cm)^2 + (0.4284 / 0.4284)^2)
Perform the calculations to find the uncertainty in the final result. In this case, the uncertainty is approximately 0.057 cm.
Therefore, the calculated value of d1(tan(θ)) is approximately 1.083 cm with an uncertainty of 0.057 cm.