Does anyone know how to find the propogation error for this equation?
K_i = 1⁄2 m_b v_i^2
= ½ (.069g)(6.49m/s)²
= 1.45(kgm²)/s²
Thank you so much!
To find the propagation error for an equation, you need to know the uncertainties associated with each variable in the equation. In this case, let's assume you have uncertainties for the mass (m_b) and velocity (v_i) terms.
To calculate the propagation error, you can use the formula for calculating the uncertainty of a product:
δQ/Q = √[(δA/A)² + (δB/B)² + ...]
Where:
δQ is the uncertainty in the result (K_i),
Q is the result (K_i),
δA is the uncertainty in the first variable (m_b),
A is the first variable (m_b),
δB is the uncertainty in the second variable (v_i),
B is the second variable (v_i), and so on.
In your case, we'll assume a relative uncertainty for both m_b and v_i, represented as δA/A and δB/B, respectively.
Let's say the relative uncertainty for m_b is 10% (0.1) and for v_i it is 5% (0.05).
Using the given values:
m_b = 0.069g (converted to kg) = 0.069 * 0.001 kg = 0.069 * 10^-3 kg,
v_i = 6.49m/s,
We can calculate the propagation error as follows:
δK_i/K_i = √[(δm_b/m_b)² + (δv_i/v_i)²]
= √[(0.1)² + (0.05)²]
= √[0.01 + 0.0025]
= √[0.0125]
= 0.1118
Now, we can find the propagation error in K_i:
δK_i = (0.1118) * K_i
= (0.1118) * 1.45(kgm²)/s²
= 0.162 kgm²/s²
Therefore, the propagation error in K_i is 0.162 kgm²/s².
Please note that the uncertainty calculations assume that the uncertainties in m_b and v_i are independent and have a symmetric distribution.