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 700 {\rm kg}, and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 2100N . The tension in the towrope between the transport plane and the first glider is not to exceed 12000 {\rm N}.
and the question? What is the maximum acceleration?
F=ma
12000=(2*700)a
To find the maximum acceleration at which the transport plane can take off without exceeding the tension limit in the towrope, we can use Newton's second law of motion.
First, let's express the forces acting on the gliders and the transport plane:
- The force of gravity on each glider is given by the equation F_gravity = m * g, where m is the mass of the glider and g is the acceleration due to gravity (approximately 9.8 m/s^2).
- The air drag and friction force acting on each glider is given as 2100 N.
- The tension in the towrope between the transport plane and the first glider is not to exceed 12000 N.
Now, let's calculate the net force acting on the gliders:
Net force on the first glider = Tension in the towrope - Drag and friction force - Force of gravity
Net force on the first glider = Tension in the towrope - 2100 N - (700 kg * 9.8 m/s^2)
Since the gliders are in tow, the net force on the first glider is the same as the net force on the transport plane.
Next, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force = mass * acceleration
By equating the net force on the glider to the mass of the glider multiplied by the acceleration, we can find the acceleration:
(Tension in the towrope - 2100 N - (700 kg * 9.8 m/s^2)) = (700 kg + 700 kg) * acceleration
Finally, rearranging the equation to isolate the acceleration, we can solve it:
acceleration = (Tension in the towrope - 2100 N - (700 kg * 9.8 m/s^2)) / (700 kg * 2)
By plugging in the given values, you can calculate the maximum acceleration at which the transport plane can take off without exceeding the tension limit in the towrope.