Final answer:
To find the tension in rope 1 (r1) connecting the 3.0-kg and 1.0-kg blocks, you need to calculate the weight of each block. Then, using Newton's second law, set up equations to find the tension. Solving these equations will give you the tension in rope 1 (r1). The tension in rope 1 (r1) is 29.4 N.
Step-by-step explanation:
To find the tension in the rope, we first need to calculate the weight of both blocks. The weight of an object can be calculated using the formula weight = mass × gravitational acceleration. In this case, the gravitational acceleration is approximately 9.8 m/s². The weight of the 3.0-kg block is 3.0 kg × 9.8 m/s² = 29.4 N. The weight of the 1.0-kg block is 1.0 kg × 9.8 m/s² = 9.8 N.
Since the rope is not massless, the tension in rope 1 (r1) will be different for each block. The tension in rope 1 (r1) connecting the 3.0-kg and 1.0-kg blocks can be found using Newton's second law, which states that the net force acting on an object is equal to the mass of that object multiplied by its acceleration. In this case, the acceleration of the system is the same for both blocks because they are connected by a rope. Therefore, the net force acting on the 3.0-kg block is Tension - Weight1 = 3.0 kg × acceleration, where Tension is the tension in rope 1 (r1) and Weight1 is the weight of the 3.0-kg block. Similarly, the net force acting on the 1.0-kg block is Tension - Weight2 = 1.0 kg × acceleration, where Weight2 is the weight of the 1.0-kg block.
Solving these two equations simultaneously, we can find the tension in rope 1 (r1). Let's assume that the acceleration of the system is a.
Tension - 29.4 N = 3.0 kg × a
Tension - 9.8 N = 1.0 kg × a
Subtracting the second equation from the first equation, we get:
Tension - 29.4 N - (Tension - 9.8 N) = 3.0 kg × a - 1.0 kg × a
19.6 N = 2.0 kg × a
Dividing both sides by 2.0 kg, we find that the acceleration of the system is 9.8 m/s². Substituting this value back into one of the original equations, we can find the tension in rope 1 (r1).
Tension - 29.4 N = 3.0 kg × 9.8 m/s²
Tension - 29.4 N = 29.4 N
Subtracting 29.4 N from both sides, we find that the tension in rope 1 (r1) is 29.4 N.