Question

Perform the following calculations and express your answer using the correct number of significant digits. (a) 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? (b) 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? (The unit of force is called the newton and it is expressed with the symbol N.) i Downloads History Attribution More Information Back Back to Top Next

Answer 1

Answer:

a) 23.7 lb

b) 1.4 N

Explanation:

Part a)

Weight of 1st bag = 13.5 lbs

Weight of 2nd bag = 10.2 lbs

We need to find the total weight of bag keeping in mind the number of significant digits. The total weight will be the sum of two individual weights.

So,

Total weight of bags = 13.5 + 10.2 lbs = 23.7 lbs

In addition and subtraction, we have to look for the least value of decimal places in given numbers i.e. the numbers being added or subtracted. The final answer must have these much decimal places in order to be expressed in significant digits.

The least number of decimal digits in given numbers is 1. In our answer, there is also only 1 decimal digit. So, our answer is already expressed in significant digits. If there would have been more than 1 decimal digits in the final answer, we would have to round it to 1 decimal digit.

So, the answer to this question is 23.7 lbs.

Part b)

Mass of wagon = m = 55 kg

Acceleration = a = 0.0255 m/s²

Force is defined as the product of mass and acceleration. i.e.

F = ma

Using the given values, we get:

F = 55(0.0255) = 1.4025 N

In multiplication and division, in order to express the final answer in significant digits, the number of significant digits must be equal to the least number of significant digits of the given numbers(which are being multiplied or divided)

55 has 2 significant digits.

0.0255 has 3 significant digits. Remember that the 0,s on the right will not be considered significant here.

This means, the final answer can have only 2 significant digits. Rounding the answer to 2 significant digits, we get:

Force = F = 1.4 N