The two trees in the figure are 6.5m apart. A back-packer is trying to lift his pack out of the reach of bears.



Calculate the magnitude of the force F→ that he must exert downward to hold a 15-kg backpack so that the rope sags at its midpoint by 1.7m .
Express your answer using two significant figures.

Calculate the magnitude of the force F→ that he must exert downward to hold a 15-kg backpack so that the rope sags at its midpoint by 0.15m .
Express your answer using two significant figures.

Nice tip to whoever can solve this for me.

f = mg = 15 kg(9.8 m/s^2)

I don't think that's right.
Thanks though.

me neither but it's close

You have 2 free body diagrams. One for the person and one for the backpack.

We let downward force to be positive

For the person, you have

Fnet = F-T =0 where T is the tension in the rope and F is the force exerted by the person

For backpack you have

Fnet = mg - 2Tsinx =0 where m is mass of backpack and x is angle between the rope and the horizontal

Now you have two equations and 2 unknowns

You can find x using Pythagorean theorem

This post was edited by 2wo1ne on Oct 29 2014 02:17pm

We know that there are three forces at play, the force of the mass of the bag and gravity pulling it down, as well as the tension of the rope on the bag from either side of the bag attached to either tree. Assuming the rope is massless, the system will be at equilibrium when the backpack sags to the point needed in the problem, and therefore the sum of the forces will be zero.

You start by calculating the force of the bag in the middle of the rope, then divide by twice the angle created when the rope sags in the middle (for each angle formed by the bag sagging).

Good luck.

rofl

Muchas gracias.. I'll send a small fg for helping me set it up. But I need someone to solve it for me!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Should be...

a ) 158.74N (2 sig figs = 160N)
b ) 1596N (2 sig figs = 1600N)

If you need the work let me know.

This post was edited by Dontrunaway on Oct 29 2014 06:36pm