Minimum Length for Safe 1000kg Plane Landing on 2000kg Barge

In summary, a 1000kg plane is landing on a 2000kg barge in a calm ocean with a frictional force equal to one quarter of the plane's weight. The minimum length of the barge for a safe landing at 50m/s with no water friction is calculated using the equations of conservation of momentum, impulse, and distance. The result is a minimum distance of 510m, but the correctness is uncertain without the correct answer provided. The use of m1 or m1+m1 for the mass in the equation for impulse is also unclear.
  • #1
sean-820
25
0

Homework Statement


1000kg plane lands on a 2000kg barge on in a calm ocean. The only frictional force is equal to one quarter of the planes weight. What must the minimum barge length be to land safely if it hits the deck at 50m/s. Also there is no water friction/resistance.

Homework Equations



mv=mv1+ mv2 (conservation of momentum)

FT=m (v2-v1) (impulse=change in momentum)

distance=VT

The Attempt at a Solution



I think i may have the right answer now, but I am not totally sure.

The momentum of the plane = 1000x50=50000
With twice the planes mass, the 50m/s plane will transfer all of its momentum to pushing the barge back at 25m/s.

Using friction=0.25mg the frictional force =250x9.8=2450N

T=(m(v2-v1))/F
=(1000(-50))/-24500
=20.4seconds

Then using D=VT=25 (20.4) i found the distance traveled must be at least 510m.

What I'm asking does this seem logical and correct? i think it may be, but I'm not totally sure. I wasn't provided the correct answer




Also, is there some way you can go back and read all your own posts?
 
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  • #2
The main thing that I'm not sure on is the impulse = change in momentum. For the mass would i have to do m1 or the total m1+m1 mass?
 

What is the minimum length required for a safe 1000kg plane to land on a 2000kg barge?

The minimum length required for a safe landing of a 1000kg plane on a 2000kg barge depends on several factors such as the wind conditions, the weight distribution of the plane, and the size of the barge. However, a general rule of thumb is that the length of the barge should be at least 1.5 times the length of the plane.

Why is it important to have a minimum length for a safe plane landing on a barge?

The minimum length requirement ensures that the plane has enough space to safely land and come to a complete stop without falling off the barge or colliding with any obstacles. It also allows for any unexpected changes in weather or other conditions that may affect the landing.

What happens if the minimum length requirement is not met?

If the minimum length requirement is not met, it can result in a dangerous landing situation where the plane may not have enough room to stop or may fall off the barge. This can lead to damage to the plane, barge, and potential injuries to the passengers and crew.

Are there any other factors to consider besides the length when determining the safety of a plane landing on a barge?

Yes, besides the length of the barge, other factors such as the weight and distribution of the plane, wind conditions, and the stability of the barge should also be taken into account. It is important to carefully assess all these factors to ensure a safe and successful landing.

Can the minimum length requirement change depending on the type of plane or barge?

Yes, the minimum length requirement may vary for different types of planes and barges. Factors such as the weight, size, and maneuverability of the plane, as well as the strength and stability of the barge, can all affect the minimum length needed for a safe landing. It is crucial to consider these factors and adjust the length accordingly for each specific situation.

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