Answer:
The total resistance is 5000 N. So the net force left for acceleration is 7 000 N (12 000 - 5 000).
7000 N applied to 2x700 kg gives a maximum acceleration of
a = F/m = 7000/1400kg = 5 m/s^2
At 5m/s^2, it will take 8 s to reach 40 m/s. In 8 second the distance covered will be
d = 1/2 at^2 = 1/2 x 5 x 8^2 = 160 m
Because each glider has the same drag and inertia, the tension in the rope between the gliders will be exactly half of the tension between plane and the two gliders:
12 000/2 = 6 000N.
The second law of Newton and kinematics allows to find the answers for the distance and tension are:
A) The distance traveled is 127.2 m
B) The tension in the second glider is 6003 N
Kinematics studies the movement of bodies establishing relationships between the position, velocity and acceleration of bodies
v² = [tex]v_o^2 + 2 a x[/tex]
Where v is the velocity, v₀ the initial velocity, a the acceleration and x the distance traveled
Newton's second law states that the net force is proportional to the mass and the acceleration of the body
F = m a
Where the bold letters indicate vectors, F is the force, m the mass and the acceleration of the body
A) Ask the length needed for takes off
We look for the acceleration that the system has using Newton's second law,
The free body diagram is a representation of the system without the details of the bodies, in the adjoint we can see a free body diagram of the forces, let's write Newton's second law for each axis
Glider 1
x-axis
T₁ - T₂ -fr = m a
y-axis
N₁ - W = 0
N₁ = W
Glider 2
x-axis
T₂ -fr = m a
y-axis
N₂ - W =
N₂ = W
We write the system of equations
T₁ - T₂ -fr = m a
T₂ - fr = m a
We solve the system
T₁ - 2 fr = 2 m a
a = [tex]\frac{T_1 - 2 fr}{2m}[/tex]
Indicates that the friction force for each glider is 1600 N
Calculate
a = [tex]\frac{12000 - 2 \ 1600}{2 \ 700}[/tex]
a = 6.29 m / s²
Taking the acceleration we can use the kinematics relationship to find the distance traveled
v² = [tex]v_o^2+2ax[/tex]
As part of rest the initial velocity is zero
v² = 0 + 2 ax
x = [tex]\frac{v^2}{2a}[/tex]v² / 2 a
indicate that the speed of 40 { m/s} is required for takeoff
x = [tex]\frac{40^2}{2 \ 6.29}[/tex]
x = 127.2 m
B) The tension (T2) between the two gliders is requested
We write the second Newton law for the second glider, see attached
T₂ - fr = m a
T₂ = m a + fr
T₂ = 700 6.29 + 1600
T₂ = 6003 N
In conclusion using Newton's second law and kinematics we can find the answers for the distance and tension are;
A) The distance traveled is 127.2 m
B) The tension in the second glider is 6003 N
Learn more about Newton's second law and kinematics here:
https://brainly.com/question/13016721
