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.)

a) (a) 37.2 lb (b) 1.41 N
b) (a) 37.2 lb (b) 1.41 N
c) (a) 37.2 lb (b) 1.41 N
d) (a) 37.2 lb (b) 1.41 N

Answer 1

The total weight of the bags is 37.2 lb. The force on the wagon, calculated using Newton's second law, is 1.4 N after rounding to the appropriate number of significant figures.

Step-by-step explanation:

The question involves performing calculations with the proper application of significant figures, which is a crucial skill in both mathematics and science, particularly in physics. We have two parts: (a) adding the weights of bags and (b) calculating the force on the wagon.

Part (a): Total Weight Calculation

To find the total weight of the bags, we add the weight of two 13.5 lb bags to the weight of one 10.2 lb bag. The weights need to be added directly since the number of bags (2 and 1) are exact numbers and don't limit the significant figures of the total weight. The total weight is:

13.5 lb + 13.5 lb + 10.2 lb = 37.2 lb

Part (b): Calculating Force on the Wagon

The force on the wagon is found using Newton's second law, F = ma, where m is the mass and a is the acceleration. With a mass (m) of 55 kg and an acceleration (a) of 0.0255 m/s2, the force is:

F = 55 kg × 0.0255 m/s2 = 1.4025 N

We round to two significant digits because the mass given (55 kg) limits the result to two significant figures. Therefore, the correct force on the wagon is:

1.4 N