Question Video: Applying Appropriate Precisions to Calculations of Forces

Perform the following calculations and express your answer using the correct number of significant digits. A woman has two bags weighing 13.5 lb and one bag with a weight of 10.2 lb. What is the total weight of the bags? The force 𝐹 on an object is equal to its mass 𝑚 multiplied by its acceleration 𝑎. If a wagon with mass 55 kg accelerates at a rate of 0.0255 m/s², what is the force on the wagon?

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Video Transcript

Perform the following calculations and express your answer using the correct number of significant digits. A woman has two bags weighing 13.5 pounds and one bag with a weight of 10.2 pounds. What is the total weight of the bags? The force 𝐹 on an object is equal to its mass 𝑚 multiplied by its acceleration 𝑎. If a wagon with mass 55 kilograms accelerates at a rate of 0.0255 meters per second squared, what is the force on the wagon?

Let’s begin by highlighting the important information given in the statement. In part one, we’re told that there are two bags weighing 13.5 pounds and one bag weighing 10.2 pounds. In part two, we’re told of a wagon with a mass 55 kilograms, which accelerates at a rate of 0.0255 meters per second squared. Let’s call the total weight of the bags in part one capital 𝑊, and we’ll call the force on the wagon in part two capital 𝐹.

We’ll start with part one, the total weight of the bags. In part one, we’re told we have two bags, each with a weight of 13.5 pounds, equaling a combined weight of 27.0 pounds. In this multiplication, we’re able to keep all three of the original significant figures of the weight of the bags because we’re multiplying them by an exact number, two. So just as our given values had three significant figures, so does our intermediate answer of 27.0 pounds.

Now let’s take that result and add the weight of the third bag, which is 10.2 pounds. This results in a total weight of 37.2 pounds. Our final answer has three significant digits because all of the given information for this part of our problem also gave us three.

Now let’s move to part two, where we solve for the force applied to a wagon. We’re told that the wagon has a mass we’ll call 𝑚 of 55 kilograms and an acceleration we’ll call 𝑎 of 0.0255 meters per second squared. We’re told further that the force on an object in general is equal to the mass of that object times its acceleration.

By the way, this relationship has a name; it’s Newton’s second law. As we apply this second law to our scenario, we can insert the given values for 𝑚 and 𝑎. As we look at this value, we see that 𝑚 has two significant figures and that 𝑎, the acceleration, has four.

The rule for calculations that have values with different numbers of significant figures is to give our answer in terms of the fewest numbers of significant figures of any of the values involved. In this case, that fewest number of significant figures is two, the number of significant figures given in the mass.

When we multiply these numbers together, we find a force of 1.4 newtons. Our answer has two significant figures because that is the fewest number of significant figures of any of the values involved in our calculation.

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