Final answer:
The mass of the carriage is found by first calculating the horizontal component of the tension force using the angle of 20 degrees, then applying Newton's second law to find the mass with the given acceleration.
Step-by-step explanation:
To determine the mass of the carriage, we need to analyze the horizontal component of the tension force, which is responsible for the acceleration of the carriage. We start by finding the horizontal component of the tension force using the angle given, which is 20 degrees. The horizontal component (Fhorizontal) is calculated using the cosine function:
Fhorizontal = 600 N * cos(20°)
Once we have Fhorizontal, we can use Newton's second law of motion (F = ma) to find the mass of the carriage. Rearranging the formula to solve for mass gives us:
m = Fhorizontal / a
Substituting the value of Fhorizontal and the acceleration (0.3 m/s²) into the equation, we can calculate the mass of the carriage:
m = (600 N * cos(20°)) / 0.3 m/s²
After completing the calculations, we find that the mass of the carriage falls into one of the options provided.