Work Done by Tension in Cable: More Than Gravity?

[rootX]

This questions asks what is the work done by the tension in the cable. And, the book answered that it is equal to the work done by the gravity.
But shouldn't it be more than the work done by the gravity? (because there is also a horizontal displacement)
see the attached image

 

[Andrew Mason]

I can't see your attachment yet, what is the direction of the force? So what is $\vec{F} \cdot \vec{d}$ ?

AM

 

[m2003]

The work done by the tension in the cable is a result of both the vertical and horizontal components of the force acting on the cable. While the work done by gravity is only in the vertical direction, the tension in the cable also contributes to the horizontal displacement of the object. Therefore, the work done by tension will be greater than the work done by gravity alone. This can be seen by considering the total work done on the object, which is equal to the change in its kinetic energy. If the object is moving both vertically and horizontally, the total work done will be the sum of the work done by both gravity and tension. So while the work done by gravity may be equal to the work done by tension in the vertical direction, the total work done by tension will be greater due to its contribution to the horizontal displacement of the object. It is important to consider all components of the forces acting on an object in order to accurately calculate the work done.