Final answer:
The tension in the rope connecting a 10 kg block to a 12 kg block on a frictionless surface, both accelerating at 1.25 m/s^2, is 12.5 Newtons.
Step-by-step explanation:
Finding the Tension in the Rope
To find the tension in the rope connecting a 10 kg block and a 12 kg block being pulled on a frictionless horizontal surface, we apply Newton's second law of motion. The force experienced by an object is equal to the mass of the object multiplied by its acceleration (F = m * a). Since the acceleration of both blocks is given as 1.25 m/s2, we can calculate the tension in the rope by considering only the forces acting on the 10 kg block.
The only horizontal force on the 10 kg block is the tension in the rope, as there is no friction. Therefore, the tension (T) is equal to the mass (m) of the 10 kg block times the acceleration (a) of the system:
T = m * a
T = 10 kg * 1.25 m/s2
T = 12.5 N
The tension in the rope is therefore 12.5 Newtons.