Final answer:
To find the mass of the box, we use Newton's second law, considering the force of friction (15 N) when the box moves at constant velocity and net force (26 N - 15 N) when it accelerates. The mass is calculated as 11 N divided by 4.2 m/s², giving a mass of 2.62 kg.
Step-by-step explanation:
The student is asking how to determine the mass of a box when given two different force scenarios and the resulting motion (constant velocity and acceleration). The first step is to use Newton's second law — force equals mass times acceleration (F=ma) — to find the mass of the box. When the box moves at constant velocity, the net force on it is zero. Therefore, the force of friction is equal to 15 N, the force applied to keep the box moving at a constant velocity. In the second scenario, an applied force of 26 N produces an acceleration of 4.2 m/s². To find the mass, we first need to determine the net force, which is 26 N (applied force) minus 15 N (frictional force), leaving us with a net force of 11 N. Using Newton's second law (F=ma), the mass (m) can be calculated by rearranging the formula to m = F/a. So, the mass of the box is 11 N divided by 4.2 m/s², which is 2.62 kg, rounded to two decimal places.