Why does a tight hammock pull so hard on the trees?

Quick guess

You pull the hammock ropes tighter, so they hang flatter. The pull in each rope…

Make your guess to see the idea.

02

Play with it

Pull the ropes tighter

Same person, same rope. Only the angle changes.

Try this · 0/3Make each rope pull exactly your weightMake it pull more than 4 times your weightSnap the rope

03

The rule

Two up-parts carry the weight

Up and down balance

2\,\force{T}\sin\theta = \force{W}

Pull in each rope

\force{T} = \dfrac{\force{W}}{2\sin\theta}

At 30°, $\sin 30^\circ = 0.5$ , so each rope pulls exactly $\force{W}$ . Flatter than that, each rope pulls more than the whole weight. It's the same idea as splitting a force into two parts.

04

Real world

Where engineers use this

Crane slings. Riggers keep sling legs steep. Below 30° to the horizontal, each leg carries more than the whole load.
Power lines. They sag on purpose. Pulled straight, the pull would break the wire or the pylons.
Suspension bridges. The main cables hang deep for the same reason, and the towers are tall to let them.

05

Your turn

Prove it

= Solve1/3

How hard does each rope pull?

To do

A person weighing $\force{0.8}\,\mathrm{kN}$ lies in a hammock. Both ropes rise at 30° above the horizontal. What is the pull in each rope?

A person weighing $\force{180}\,\mathrm{lb}$ lies in a hammock. Both ropes rise at 30° above the horizontal. What is the pull in each rope?

= Solve2/3

How hard is each sling pulled?

To do

A crane lifts a $\force{20}\,\mathrm{kN}$ pallet on two slings. Each sling leg is at 45° to the horizontal. What is the pull in each leg?

A crane lifts a $\force{4{,}000}\,\mathrm{lb}$ pallet on two slings. Each sling leg is at 45° to the horizontal. What is the pull in each leg?

◆ Pick3/3

Why do power lines sag between pylons?

To do

06 · Takeaway

Flatter rope, bigger pull.

\force{T} = \dfrac{\force{W}}{2\sin\theta}

Related: how to split one force into two · why bridges are made of triangles.