Tension in a rope in an accelerating towplane (AP French 7-1)

In summary, the problem involves two identical gliders being towed in tandem by a plane initially traveling at a constant speed. The tension in the tow rope A is T(sub0) and the gliders are experiencing a retarding force from drag. When the plane starts to accelerate, the tensions in the ropes A and B are calculated to be T(sub0) + 2ma and .5*T(sub0) + ma, respectively. The retarding force from drag remains constant throughout the situation.
  • #1
TimSon
9
0

Homework Statement


AP French Mechanics Problem 7-1

Two identical gliders, each of mass m, are being towed through the air in tandem. Initially they are traveling at a constant speed and the tension in the tow rope A is T(sub0). The tow plane then begins to accelerate with an acceleration A. What are the tensions in A and B immediately after this acceleration begins?

Crude Drawing

Glider2 (Mass m) ---- rope B ----- Glider1 (Mass m) ----- rope A ------ Tow Plane (Initially at Rest then accelerating)

Homework Equations

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The Attempt at a Solution

[/B]

This is what I tried:

Initially at constant velocity:

Forces on Glider1: T(rope A) - T(rope B) = 0

Since T(ropeA) == T(sub0),
then T(ropeB) == T(sub0)

When Tow Plane Starts to Accelerate:

1) I assumed that entire system accelerated the same

Forces on Glider1:
T(ropeA) - T(ropeB) = m * a (1) (where m is mass of Glider 1)

Forces on Glider2:
T(ropeB) = m* a (2) (where m is mass of Glider2)

Therefore,

substituting, equation (2) into equation (1),

T(ropeA) = 2*m*a.

However, in the back of the book the answer states:

T(ropeA) = T(sub0) + 2ma
T(ropeB) = .5 * T(sub0) + ma

I just want to know why the initial condition of T(sub0) is included, though I assume it is because of the constant velocity at the beginning and the plane accelerating in relation to that initial velocity, Also, if it would helpful if someone could point out flaws in my logic.

Thanks.
 
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  • #2
If the plane and gliders are initially traveling at constant speed, with tensions in the ropes pulling the gliders forward, there must be an equal force pushing them back. Where does that force come from and what is it called? Does that retarding force disappear when the plane starts to accelerate?

What does the force in the ropes have to be in order to (1) overcome the retarding force and (2) provide the acceleration.
 
  • #3
andrewkirk said:
If the plane and gliders are initially traveling at constant speed, with tensions in the ropes pulling the gliders forward, there must be an equal force pushing them back. Where does that force come from and what is it called? Does that retarding force disappear when the plane starts to accelerate?

What does the force in the ropes have to be in order to (1) overcome the retarding force and (2) provide the acceleration.

I would think the force would come from Drag and that it would equivalent to T(sub0) since the forces must balance out. When the plane accelerates this force does not disappear.

Therefore initial situation (constant v):

Forces on Glider 1:

T(ropeA) - (TropeB) - Force(drag) = 0 (1)

Forces on Glider 2:

T(ropeB) - Force(drag) = 0 (2), therefore Force(drag) = T(ropeB)

Substituting (2) into (1) and substituting T(sub0) for T(ropeA):

T(sub0) = 2 F(drag)

F(drag) = .5 * T(sub0)

Accelerating situation:

Glider 2)

T(ropeB) - F(drag) = ma - > T(ropeB) = ma + .5 *T

Glider 1)

T(ropeA) - T(ropeB) - F(drag) = ma

-> T(ropeA) = T(sub0) + 2ma

Thanks for the help.

From now on, ill work applicable constant velocity problems in the same way.
 

1. What is tension in a rope?

Tension in a rope is the force applied to the rope in order to keep it taut. It is the force that is transmitted through the rope as a result of external forces acting on either end of the rope.

2. How does tension change in a rope when a towplane accelerates?

As a towplane accelerates, the tension in the rope will increase. This is because the force of the acceleration is transmitted through the rope, causing it to stretch and become taut. The greater the acceleration, the higher the tension in the rope will be.

3. What factors affect the tension in a rope in an accelerating towplane?

The tension in a rope in an accelerating towplane is affected by several factors, including the mass of the towplane, the force of the acceleration, the length and thickness of the rope, and the angle at which the rope is attached to the towplane.

4. How is tension in a rope related to the speed of a towplane?

The tension in a rope is directly related to the speed of a towplane. As the towplane's speed increases, the tension in the rope will also increase. This is because the force of the towplane's motion is transmitted through the rope, causing it to stretch and become more taut.

5. What happens to the tension in a rope when a towplane decelerates?

When a towplane decelerates, the tension in the rope will decrease. This is because the force of the deceleration is transmitted through the rope, causing it to relax and become less taut. The greater the deceleration, the lower the tension in the rope will be.

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