Question

A plane takes off a level runaway with two gliders in tow, one behind the other. The first Glider has a mass of 1600kg and the second 800kg. The frictional drag may be assumed constant and equal to 2000 N on each glider. The towrope between the first and the plane can withstand a tension of 10 000 N.

a) If a velocity of 40m/s is required for takeoff, how long a runway is needed?
b) How strong must the towrope between the two gliders be?

Answer 1

More third law, I see!

I was wondering, how can we find the length of the runway needed?
Since there is a limited amount of tension we can have, there is a limited propelling force, so a limited acceleration.

If we know this acceleration, we can look to the kinematic equation that has acceleration, distance, and velocity.

Answer 2

yea, we know force of drag to be constant 2000 N. So can we figure out the acceleration in the horizontal component?

Answer 3

Right. We'll use the tension that you labeled. The tension cannot be greater, so that is our maximum. All that matters is that the greatest force (and so acceleration) we can have must put only 10,000N of tension on that rope.

Answer 4

Fnet x= Ft-Fd
FNet x= 10000 - 2000
Fnetx=8000N [F]

Fnetx=ma m=1600+800=2400kg
8000/2400=a
a=3.3m/s/s? is that right so far or have i made a mistake

Answer 5

I guess we should dig into this problem...
What are you looking at the net force on? Now it's important to consider these things.

Answer 6

Net Force in the horizontal component.

Answer 7

Net force on the system of all three? Or is that the net force on the two gliders? Or on one glider? Or on just the plane?1. I like the plane you drew.
2. Each box that I put on there contains a "system" - by which I mean a collection of objects.

Now, which system are you looking at?