Question

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 kg, and the total resistance (air drag plus friction with the runway) on each may be assumed constant and equal to 2900N . The tension in the towrope between the transport plane and the first glider is not to exceed 12000 N.
A- If a speed of 40 m/s is required for takeoff, what minimum length of runway is needed?

B- What is the tension in the towrope between the two gliders while they are accelerating for the takeoff?

Express your answer using two significant figures.

Answer 1

Answer:

a) Δx = 180.59 m

b) T = 6001 N

Explanation:

a)

According to Newton's second law, which says that acceleration is directly proportional to the net force, the equation is equal to:

ΣF = m*a = T-f

Clearing a, and solving:

a = (T-f)/m = (T-f)/2*m = (12000-5800)/(2*700) = 4.43 m/s^2

To evaluate the final speed the following equation will be used:

vf^2 = vi^2 + 2*a*Δx = 0 + 2*a*Δx = 2*a*Δx

Clearing Δx:

Δx = vf^2/2*a = (40 m/s)^2/(2* 4.43 m/s^2) = 180.59 m

b)

The tension is equal to:

T = m*a + f = (700 kg * 4.43 m/s^2) + 2900 N = 6001 N