Assuming there is no friction, which orientation requires more force to pull?

When a rope is pulled at an angle to the table, the force required to pull it is affected by the angle's geometric relationship with the horizontal plane. This angle can lead to a component of the pulling force acting vertically, influencing the frictional resistance that could be encountered if friction were present. However, since the question specifies that there is no friction, we focus purely on the forces involved in the pulling action.

When pulling the rope at an angle, some of the force exerted is directed upward rather than solely horizontal. This upward force reduces the normal force exerted by the rope on the table, which, if there was friction, would decrease the frictional resistance. But for this specific scenario of a frictionless environment, we encounter an important aspect: since the pulling force is not entirely horizontal, more effort is needed to achieve the same horizontal movement compared to pulling the rope parallel to the table.

In contrast, when the rope is pulled parallel to the table, all the force is focused on moving the object horizontally with no vertical component affecting the dynamics. Therefore, pulling parallel requires less force to maintain the same movement compared to pulling at an angle. As a result, pulling with the rope at an angle requires more force to obtain the same movement