Finding Force for Backpacker in Bear Sling Equilibrium

  • Thread starter Thread starter Lightsout565
  • Start date Start date
  • Tags Tags
    Equilibrium
Click For Summary
SUMMARY

The discussion focuses on calculating the force a backpacker must exert to hold a 16-kg backpack suspended between two trees 7.6 meters apart, with the rope sagging at its midpoint by 1.5 meters and 0.15 meters. The initial calculation yielded a force of 57.6N, which was incorrect. The correct approach involves using trigonometric relationships to find the tension in the rope, leading to a final force of 427N for the sag of 1.5 meters. Participants emphasized the importance of understanding the distribution of weight and the tension in the rope, clarifying that the force exerted is the sum of the tensions on both sides of the backpack.

PREREQUISITES
  • Understanding of basic physics concepts, particularly forces and tension.
  • Familiarity with trigonometric functions and their application in physics.
  • Knowledge of free body diagrams and Newton's laws of motion.
  • Ability to perform calculations involving weight and force components.
NEXT STEPS
  • Study the principles of tension in ropes and pulleys in physics.
  • Learn how to draw and interpret free body diagrams for complex systems.
  • Explore trigonometric applications in physics problems, particularly in force calculations.
  • Investigate the effects of different sag angles on tension and force exerted in similar scenarios.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the mechanics of forces in static systems, particularly in outdoor scenarios involving weight distribution and tension management.

Lightsout565
Messages
4
Reaction score
0

Homework Statement


Two trees are 7.6m apart. Calculate the magnitude of force a backpacker must exert to hold a 16-kg backpack so that the rope sags at its midpoint by (a) 1.5m, (b) 0.15m.

http://2.bp.blogspot.com/_qDvB7jRAneY/SrLIlGBVq1I/AAAAAAAAAVA/J8UdxspkfSk/s1600-h/bear+sling.bmp"


Homework Equations


\SigmaFy = 0


The Attempt at a Solution


I tried to figure the angle measure and get a component of the force but I think that's totally wrong. For part a I ended up getting 57.6N
 
Last edited by a moderator:
Physics news on Phys.org
Lightsout565 said:

Homework Statement


Two trees are 7.6m apart. Calculate the magnitude of force a backpacker must exert to hold a 16-kg backpack so that the rope sags at its midpoint by (a) 1.5m, (b) 0.15m.

http://2.bp.blogspot.com/_qDvB7jRAneY/SrLIlGBVq1I/AAAAAAAAAVA/J8UdxspkfSk/s1600-h/bear+sling.bmp"


Homework Equations


\SigmaFy = 0


The Attempt at a Solution


I tried to figure the angle measure and get a component of the force but I think that's totally wrong. For part a I ended up getting 57.6N
That's not right, please show your work in determining the angle and tension in the wire. Note that the weight of the 16 kg backpack is vertically distributed equally to the rope section on each side of it. The rope tension can then be calculated using simple trig.
 
Last edited by a moderator:
(a)
(3.8m)2 + (1.5m)2 = x2
x = 4.085m

Fg = Ftsin\theta
(16kg)(9.8 m/s2) = Ft(1.5/4.085)
F = 427N

Correct?
 
Lightsout565 said:
(a)
(3.8m)2 + (1.5m)2 = x2
x = 4.085ml
yes, good
Fg = Ftsin\theta
(16kg)(9.8 m/s2) = Ft(1.5/4.085)
F = 427N

Correct?
No, the backpack weight splits vertically 1/2Fg to each side. Draw a free body diagram of the rope joint to prove this using Newton 1. Your result is off by a factor of 2.
 
But the questions asks "Calculate the magnitude of force a backpacker must exert", which is the sum of the two tensions forces. So wouldn't my answer be correct?
 
Lightsout565 said:
But the questions asks "Calculate the magnitude of force a backpacker must exert", which is the sum of the two tensions forces. So wouldn't my answer be correct?
Why would you sum them? The rope tension around an ideal pulley is the same on both sides of the pulley. Would you say that the rope tension at the right hand tree is 427 N or 213.5 N? Draw a free body diagram of the rope at the tree connection.
 

Similar threads

Replies
1
Views
2K
Replies
17
Views
3K
Replies
4
Views
5K
  • · Replies 1 ·
Replies
1
Views
13K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 6 ·
Replies
6
Views
13K
  • · Replies 2 ·
Replies
2
Views
4K