Video Transcript
Three objects have masses of three plus or minus 0.1 kilograms, seven plus or minus 0.1 kilograms, and four plus or minus 0.05 kilograms. What is the uncertainty in the total mass of the three objects?
Here, we have three objects with masses we’ll call 𝑚 one, 𝑚 two, and 𝑚 three. And we want to solve for the uncertainty in the total mass of these objects. That total mass, we’ll call it capital 𝑀, equals 𝑚 one plus 𝑚 two plus 𝑚 three, which can also be written like this, with our three mass values substituted in.
We can see that the total mass capital 𝑀 will equal three plus seven plus four kilograms. That’s 14 kilograms. But we also know that there will be an uncertainty associated with this mass. Whenever we add together values, each of which has an uncertainty associated with it, as we’re doing here, the total uncertainty is equal to the sum of the individual uncertainties. The total uncertainty in the overall mass then is equal to 0.1 plus 0.1 plus 0.05. These three numbers add up to 0.25.
Our question asks us only for the uncertainty in the total mass of the three objects. Our final answer, then, is that the uncertainty in the total mass of these three objects is 0.25 kilograms.
