What is the tension in the rope that the father is pulling in the following case?
The father exerts force F that makes an angle of 30 degrees with the horizontal and that leads to an acceleration of two sleds. The mass of each sled with each twin is m. Assume no friction.
In the question, the father pulls a rope with a force F. The rope makes an angle of 30 degrees with the horizontal and is attached to a series of sleds on which his twins with a mass m are seated. The sleds are accelerated due to the force exerted by the father.
The tension in the rope that is pulled by the father is equal to F. The other details do not have any affect on this. The fact that the rope is at an incline to the horizontal will only reduce the acceleration of the sleds being pulled. It does not change the tension in the rope being pulled by the father.
The tension in the rope being pulled by the father is always equal to the force exerted by him, which is F.