Final answer:
The tension at the midpoint of the rope pulling a 10 kg block on a smooth surface with a force of 36 N at the end is approximately 36 N, calculated using Newton's second law.
Step-by-step explanation:
The question concerns a scenario in which a 10 kg block is on a smooth surface and is being pulled by a rope with a mass of 2 kg. A force of 36 N is applied at the end of the rope. To find the tension at the midpoint of the rope, we should consider Newton's second law, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration (F=ma).
In this case, the entire system (block plus half of the rope's mass) being considered for the tension at the midpoint would have a mass of 11 kg (10 kg for the block and 1 kg for half the rope's mass). The force applied (36 N) would accelerate this system. Thus, the acceleration can be calculated as:
a = F / m = 36 N / 11 kg = 3.27 m/s2
The tension at the midpoint is then the force required to accelerate half the system (block plus half of the rope), which is the mass times the acceleration (T = ma).
T = 11 kg * 3.27 m/s2 = 35.97 N
Since the tension must be equal throughout the rope (assuming it's massless), we'll round this to the nearest whole number which suggests the tension at the midpoint of the rope is approximately 36 N, implying that the rope's mass doesn't significantly affect the tension in this context.