Mary applies a force of 77 N to push a box with an acceleration of 0.45 m/s2. When she increases the pushing force to 82 N, the box's acceleration changes to 0.74 m/s2. There is a constant friction force present between the floor and the box.

(a) What is the mass of the box?

To find the mass of the box, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.

We have two sets of data: when the force is 77 N and the acceleration is 0.45 m/s^2, and when the force is 82 N and the acceleration is 0.74 m/s^2.

Using the first set of data:
Force = 77 N
Acceleration = 0.45 m/s^2

Using Newton's second law, we can write the equation as:
77 N = mass * 0.45 m/s^2

Simplifying the equation:
mass = 77 N / 0.45 m/s^2

mass ≈ 171.11 kg (rounded to two decimal places)

Therefore, the mass of the box is approximately 171.11 kg.

Fap-Fk = m*a

Eq1: 77 - Fk = m*0.45
Eq2: 82 - Fk = m*0.74
Subtract Eq2 from Eq1:
Diff. = -5 = -29m
m = 0.172 kg.