How Do You Calculate the Error in the Y-Component of Force?

[rossel]

Homework Statement

What is the error in calculating the y-component of the force created by a hanging mass (m=432.23g) at an angle of 28º? Take g=9.81m/s^2)

Homework Equations

Fg = mg

The Attempt at a Solution

Fg = mg
= (0.43223kg +/- 0.000005kg)(9.81m/s +/- 0.05m/s)
= (0.43223 +/- 0.00115679%)(9.81 +/ 0.5097)
= 4.2358 +/- 0.52359%
= 4.2358N +/- 0.022079 NThis was an example drawn on the board. How do you get from line 3-4, and 4-5? I do not know how to calculate 0.52359%, and when I try to calculate the 5th line, I do not get an answer of 0.022079. Please help! Thanks. :)

 

[anathema]

your attempt at a solution is correct so far. To address the specific questions about lines 3-4 and 4-5, here is an explanation:

Line 3-4: To calculate the percent uncertainty, you can use the formula (uncertainty/quantity) x 100%. In this case, the uncertainty is 0.05m/s and the quantity is 9.81m/s. So, (0.05/9.81) x 100% = 0.5097%. This is the percent uncertainty for the acceleration due to gravity, which is then added to the value of 9.81m/s to get the range of possible values for the force.

Line 4-5: To calculate the percent uncertainty for the force, you can use the same formula as before. The uncertainty for the force is 0.52359N and the quantity is 4.2358N. So, (0.52359/4.2358) x 100% = 0.1234%. This is the percent uncertainty for the force, which is then added to the value of 4.2358N to get the range of possible values for the force. This is why the final answer is written as 4.2358N +/- 0.022079N, representing the range of possible values for the force.

I hope this helps clarify the calculations for lines 3-4 and 4-5. Let me know if you have any further questions. :)

 

[ogb p]

In line 3-4, the percentage uncertainties of the mass and acceleration are multiplied together to get the overall percentage uncertainty. This is done because the force is a product of the mass and acceleration.
In line 4-5, the overall percentage uncertainty is converted to an absolute uncertainty by multiplying it with the calculated force. This is done to get the range of values within which the actual force could lie, taking into account the uncertainties in the mass and acceleration values. The absolute uncertainty is then added and subtracted from the calculated force to get the range of possible values for the force.