How Do You Calculate Tension in a Rope Pulling Gliders?

[bobber205]

There's a plane pulling two gliders. The first glider is 310 kg while the second glider is 260 kg. The place itself it 2200 kg and is pulling at 1.9 m/s squared.
I need to figure out the tension of the first rope and the second rope. I found the net force on the first plane by taking the total Newton value for both the first glider and the plane and subtracting the mass of the second glider times 1.9

I Thought this would give the tension force of the rope.

Homework Equations

The Attempt at a Solution

What's a good FBD for this?
Here's what I thought it was

<--------- ---> ---->
gliders rope plane

Any help? :)

 

[Redbelly98]

Welcome to PF.

Is this a correct diagram:

G1-----G2-----P →

where
G1 and G2 are the gliders
P is the plane
----- are the ropes
everything is moving to the right (shown by arrow to right of P)


If that diagram is correct, I would draw 3 separate FBD's for each glider and plane and take it from there.

 

[baba89]

I would approach this problem by first setting up a free body diagram for each object involved in the scenario. This would include the two gliders, the rope, and the plane. The forces acting on each object would be the weight force (mg) and the tension force from the rope (T).

Next, I would use Newton's Second Law (F=ma) to calculate the net force acting on each object. For the first glider, the net force would be equal to its mass (310 kg) multiplied by the acceleration (1.9 m/s^2). This would give us a net force of 589 N.

For the second glider, the net force would be equal to its mass (260 kg) multiplied by the acceleration (1.9 m/s^2). This would give us a net force of 494 N.

For the plane, the net force would be equal to its mass (2200 kg) multiplied by the acceleration (1.9 m/s^2) plus the combined net forces of the two gliders (589 N + 494 N). This would give us a net force of 5366 N.

To find the tension in each rope, we can use Newton's Third Law (for every action, there is an equal and opposite reaction) to determine that the tension in each rope is equal to the net force acting on each glider. Therefore, the tension in the first rope would be 589 N and the tension in the second rope would be 494 N.

In summary, the tension in each rope is equal to the net force acting on each glider, which is found by using Newton's Second Law. It is important to set up a free body diagram and carefully consider all forces acting on each object in order to accurately solve this problem.