Solving Tug of War Physics: Who Wins?

  • Thread starter iampaul
  • Start date
  • Tags
    Physics
In summary: I just remembered that the mass of the rope is irrelevant to the tension in the rope: I'm sorry. The tension in the rope is the same everywhere, regardless of the mass of the rope. This is because the tension in the rope is the force that the rope exerts on the boys, and Newtons Third Law tells us that the force on the boy from the rope is equal to the force on the rope from the boy.
  • #1
iampaul
93
0

Homework Statement


Two boys play tug of war.If according to Newton's third law, for every force a there is a reaction b with the same magnitude but opposite direction. What determines who wins?
Our professor gave a hint that it has something to do with the ground.

Homework Equations


f=ma and Newtons 3rd law

The Attempt at a Solution


I have identified these forces:
A= force exerted by boy1 to the rope
A'=reaction to A ,force exerted by the rope to boy1
B=force exerted by boy1 to the rope
B'=reaction to B ,force exerted by the rope to boy2
Fa=Friction exerted at boy1
Fb=Friction exerted at boy2
Our professor said that no one wins if the ground is frictionless but i can't see why.
thanks!

 
Physics news on Phys.org
  • #2
iampaul said:
Our professor said that no one wins if the ground is frictionless but i can't see why.
thanks!

Actually the heavier person will win for frictionless ground.

Here's how to think about it: What is external force on the system? Where is the center of mass? Does it move? Where will the two players meet if they keep pulling?
 
Last edited:
  • #3
iampaul said:

Homework Statement


Two boys play tug of war.If according to Newton's third law, for every force a there is a reaction b with the same magnitude but opposite direction. What determines who wins?
Our professor gave a hint that it has something to do with the ground.

Homework Equations


f=ma and Newtons 3rd law

The Attempt at a Solution


I have identified these forces:
A = force exerted by boy1 to the rope
A'=reaction to A ,force exerted by the rope to boy1
B=force exerted by boy1 to the rope
B'=reaction to B ,force exerted by the rope to boy2
Fa=Friction exerted at boy1
Fb=Friction exerted at boy2
Our professor said that no one wins if the ground is frictionless but i can't see why.
thanks!
You started out listing some great 3rd law couples:
Boy 1 pulls the rope, the rope pulls Boy 1
Boy 2 pulls the rope, the rope pulls Boy 2

You then degenerated into some general descriptions
Fa=Friction exerted at boy1
Fb=Friction exerted at boy2

You must express those forces, that you just called Friction, as 3rd law Couples.

Do that and I will get back to you if that doesn't already answer your problem.
 
  • #4
boy2 pushes the ground,ground pushes boy2 ??
boy1 pushes the ground, ground pushes boy1 ??

The forces acting on boy1 are A' and the force from the ground.
The forces acting on boy2 are B' and the force from the ground.
The forces acting on the rope are A and B
 
  • #5
iampaul said:
boy2 pushes on ground,ground pushes on boy2 ??
boy1 pushes on ground, ground pushes on boy1 ??

??

Great.
That is a total of 8 forces, drouped according to Newtons 3rd Law couple.

Now group the forces according to which body they act on: boy 1, boy 2, the rope and the ground

eg
Rope: Boy 1 pulls rope, Boy 2 pulls rope

Now You -

Boy 1:
Boy 2:
Ground:

Then look at the sizes of the pair of forces grouped this way.

NB: Newtons Third law says that the pair of forces : Boy 1 pulls Rope, Rope pulls Boy 1 are equal in size, but Newtons law does not compare the force of the Rope pulling Boy 1 to the force of Boy 2 pushing the Ground
 
  • #6
Boy1: Ground pushes boy1(Fa), rope pulls boy1(A')
Boy2: Ground pushes boy2(Fb), rope pulls boy2(B')
Rope:Boy1 and boy2 pull on rope(A and B)
A=-B if the rope is in equilibrium or if the rope is massless
I don't know what's next!
Should i treat the rope massless?
 
  • #7
The system moves to the side of boy 1 if fa>A'=A>B=B'>Fb?
Fa>fb
 
  • #8
iampaul said:
Boy1: Ground pushes boy1(Fa), rope pulls boy1(A')
Boy2: Ground pushes boy2(Fb), rope pulls boy2(B')
Rope:Boy1 and boy2 pull on rope(A and B)
A=-B if the rope is in equilibrium or if the rope is massless
I don't know what's next!
Should i treat the rope massless?

The tension in the rope ensures that all forces involving the rope have the same size.

Now to the boys: The size with which the rope pulls them is equal, so it is the one who is pushed more strongly by the ground that wins.

And of course Newtons Third Law tells us that the ground pushes most strongly on the boy that pushes most strongly on the ground.
So he who pushes the ground the hardest wins.
 
Last edited:
  • #9
thanks a lot!
 
Last edited:
  • #10
"The tension in the rope ensures that all forces involving the rope have the same size."

Wouldn't that happen only if the rope is in equilibrium or if the rope is massless?
Please reply! Last question =)
 
  • #11
iampaul said:
"The tension in the rope ensures that all forces involving the rope have the same size."

Wouldn't that happen only if the rope is in equilibrium or if the rope is massless?
Please reply! Last question =)

The boys would simply not be able to accelerate at the rate required to vary the tension in the rope - especially since the rope has a much lower mass than each of the boys. In fact in a tug of war, motion is generally very slow

If the rope was as heavy as the boys [50+ kg] and one of them took off faster than an olympic sprinter you might notice something.

We can demonstrate by changing the situation to a mass-less rope with a 2kg mass in the middle [so two ropes actually] and the boys having mass 49 kg. [this is to mimic a rope of mass 2kg]

suppose Boy 1 wins, by pushing on the ground with a force 20N more than Boy 2. The net force on the system is thus 20N so the 100 kg system will accelerate at 0.2 m/s^2.

Individually, the 2 kg mass has an unbalanced force of 0.4N acting [it is accelerating at 0.2 m/s^2 also remember]

That would mean the tension in the rope from Boy 1 to the mass is 0.4N more than the tension in the rope from the mass to boy 2.

Now to accelerate at 0.2 m/s is an extremely high rate of acceleration - not the sort of acceleration one associates with a tug of war, so the effects are probably much less than this, indicating that the tension will be pretty well constant even with a real rope.
 
  • #12
Thanks! Now i get it!=)
 

1. How does the weight of the players affect the outcome of a tug of war?

The weight of the players is a major factor in determining the outcome of a tug of war. The heavier team will have a greater force pulling on the rope, giving them an advantage. However, the distribution of weight among the players and their positioning can also play a role in the outcome.

2. Why is it easier for a taller team to win a tug of war?

Taller players have a longer reach and can therefore apply more force to the rope. This gives them an advantage over a shorter team. However, the strength and technique of the players are also important factors in determining the winner.

3. How does friction affect the outcome of a tug of war?

Friction between the rope and the ground can help or hinder the teams. If the ground is rough and provides good traction, it can help the teams maintain their positions and pull harder. On the other hand, a slippery or smooth surface may make it more difficult for the teams to gain traction and could potentially lead to a tie.

4. Is there a limit to how many people can participate in a tug of war?

The number of people participating in a tug of war can vary depending on the length and strength of the rope. However, there is a limit to the number of people on each team that can effectively pull on the rope without getting in each other's way. Generally, a maximum of 8-10 players per team is recommended.

5. How can one team gain an advantage in a tug of war?

Aside from having heavier and taller players, other factors that can give a team an advantage in a tug of war include proper technique, teamwork, and strategy. For example, using a lower stance and pulling from a lower angle can provide a stronger force. Also, having a clear leader and effective communication among team members can make a difference in the outcome.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
7K
  • Introductory Physics Homework Help
Replies
5
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
20
Views
2K
  • Classical Physics
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
3K
  • Introductory Physics Homework Help
Replies
2
Views
5K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
2
Replies
35
Views
2K
Back
Top