Net Force on Rope in Tug of War?

[timseb]

Homework Statement

In a tug of war two boys exert an equal force of 30N. What is the nett force on the rope?

Homework Equations

The Attempt at a Solution

Since there is a tensile force on the rope will it be 30 N?

(When a spring replaces the rope it will elongate by 'x'. So the force will be kx
where k is the spring constant)

 

[astrorob]

The net force on the rope is calculated by summing the forces on it. Remember though, force is a vector (it has direction).

 

[HallsofIvy]

Be careful. Understand exactly what astrorob said: there are two boys pulling on the rope with equal "force"- but in opposite directions. What will the net force on the rope be? Another way of looking at is this: F= ma. What is the 'acceleration' of this rope? So what is the net force on it?

 

[Sheneron]

sorry to interject, but if it said find the total tension what would that be?

 

[Doc Al]

sorry to interject, but if it said find the total tension what would that be?

It would be meaningless. Asking for the tension in the rope makes sense, but "total" tension would not. A tension is created by two forces pulling in opposite directions.

 

[Sheneron]

so would the tension be 60N?

 

[Doc Al]

so would the tension be 60N?

No, just 30 N. To create a tension of 30 N requires the ends to be pulled apart by 30 N forces. The tension force is just the force that the rope exerts which must be equal and opposite to the forces that the boys exert.