A transport plane takes off from a level landing field with two gliders in tow, one behind the other. The mass of each glider is 700n , and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 2600n . The tension in the towrope between the transport plane and the first glider is not to exceed 12000 .

a.) find the minimum length of the runway, if a speed of 40m/s is needed to takeoff.

b.)tension between 2 gliders while they are accelerating for takeoff

448000000

To find the minimum length of the runway, we need to consider the forces acting on the transport plane and the gliders.

Let's start by analyzing the forces acting on the transport plane:

1. Thrust force (T): This is the force generated by the engines of the transport plane pushing it forward.
2. Air drag force (D): This is the resistance force due to air resistance acting in the opposite direction to the motion.
3. Tension force (FTP): This is the force exerted by the towrope between the transport plane and the first glider.
4. Friction force (Frp): This is the force between the transport plane and the runway, opposing the motion.

Now, let's analyze the forces acting on the gliders:

1. Tension force (FTG): This is the force exerted by the towrope between the gliders.
2. Air drag force (DG): This is the resistance force due to air resistance acting in the opposite direction to the motion.
3. Friction force (Frg): This is the force between the gliders and the runway, opposing the motion.

To determine the minimum length of the runway, we need to consider the forces acting on the transport plane and the gliders when the speed is 40 m/s.

a.) To calculate the minimum length of the runway, we need to ensure that the net force acting on the transport plane and the gliders is sufficient to accelerate them to a speed of 40 m/s. The net force is given by:

Net Force (Fnet) = Total force - Resistance force

For the transport plane:
Fnet = T - D - FTP - Frp

For the gliders:
Fnet = FTG - DG - Frg

At the minimum length of the runway, the net force for the transport plane and the gliders should be zero, as there will be no acceleration. Set the Fnet equations equal to zero:

For the transport plane:
T - D - FTP - Frp = 0

For the gliders:
FTG - DG - Frg = 0

We can rearrange the equations as follows:

T = D + FTP + Frp
FTG = DG + Frg

Now, let's calculate the tension between the transport plane and the first glider:

Given:
Maximum tension (FTP) = 12000 N
Mass of each glider (m) = 700 kg
Air drag plus friction on each glider (DG + Frg) = 2600 N
Acceleration (a) = 0 m/s^2 (due to zero net force)

Using Newton's second law (F = ma), we can calculate the tension (FTP):

FTP = m * a + DG + Frg
12000 = (2 * 700) * 0 + 2600
12000 = 2600

Since the maximum tension is less than the calculated tension, we can conclude that the gliders will not accelerate during takeoff. Therefore, the tension between the two gliders will be zero.

To summarize:

a.) The minimum length of the runway is undefined because the gliders will not accelerate.
b.) The tension between the two gliders is zero as they will not accelerate during takeoff.