Final answer:
The tension force in each rope of the pulley system is calculated using Newton's second law, accounting for both gravitational force and the upward acceleration of the object. For an object with a mass of 10 kg and an upward acceleration of 2 m/s², the tension is approximately 60 N per rope, which is closest to option (c).
Step-by-step explanation:
To solve for the tension force in each rope of the pulley system with an object of mass 10 kg accelerating upward at 2 m/s², we use Newton's second law of motion (F=ma) and account for the gravitational force (mg) acting on the object. The equation is:
T - mg = ma
First, we calculate the gravitational force (mg) which equals 10 kg × 9.8 m/s² = 98 N. Then we add this to the product of the mass and the acceleration (10 kg × 2 m/s² = 20 N) for the total tension:
T = mg + ma = 98 N + 20 N = 118 N
However, in a simple pulley system, the tension in the rope is distributed evenly between two segments of rope. Therefore, the tension in each rope is half of the total:
T per rope = 118 N / 2 = 59 N
However, none of the provided options (a) 20 N, (b) 40 N, (c) 60 N, (d) 80 N exactly match this result, but the closest answer is (c) 60 N.