Work Step by Step
To hold the backpack up, the rope exerts a vertical upward force that balances the pack’s weight. The force exerted by the rope on the pack is directed along the rope itself. For each side, the vertical component of this force is $F sin \theta$, where $\theta$ is the small angle between the rope and the horizontal. The higher the pack rises, the smaller the angle, and the larger the force F must become to balance the pack against gravity. The rope can never be perfectly horizontal because there must be an upward component of force on the pack.