Calculating speed from tension.

Here’s the question at hand:
A ship is pulled at a constant speed of 2.5ms^-1 by 2 tugs, A and B. Each tug is connected by a cable so that the angle each of the cables make with the direction of travel is 41 degrees. The ship experiences a drag force of 8000v^2 Newtons.
As the tugs attempt to increase the speed of the ship from 2.5ms^-1, tug A breaks down, with its cable becoming slack.
Calculate the speed to which the ship initially decelerates, assuming the tension in the other cable remains constant.

I’m really struggling with this one so any help would be greatly appreciated.

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Reply 1

mqb2766

Original post by Theo298

Have you drawn the two diagrams with two tensions and with one tension?

Reply 2

Theo298

Original post by mqb2766

Have you drawn the two diagrams with two tensions and with one tension?

I have not, no. I do not know how to got about this.

Reply 3

mqb2766

Original post by Theo298

I have not, no. I do not know how to got about this.

Draw the boats, lines, ... and put the tensions, angles, .. on there
If you can't draw the diagrams, Id honestly suggest starting with simpler problems.

Reply 4

Theo298

Original post by mqb2766

Draw the boats, lines, ... and put the tensions, angles, .. on there
If you can't draw the diagrams, Id honestly suggest starting with simpler problems.

I am able to draw diagrams, we were just not supplied with the tensions for the ropes.

Reply 5

the bear

so the key is to realise that with the 2 tugs the net force in the direction of motion is zero newtons. thus the 2 tension components in the forward direction must balance the resistive force in the opposite direction.

you can now work out the individual tensions.

once the cable snaps the only forward force is the tension component from the other tug. this is unchanged, but will not be able to balance the resistive force.

Reply 6

Theo298

Original post by the bear

Thanks this is very helpful. I now have the drag force, 50,000N. Would the tension in the cable be half of the drag force, for there are 2 cables?

Reply 7

mqb2766

Original post by Theo298

Thanks this is very helpful. I now have the drag force, 50,000N. Would the tension in the cable be half of the drag force, for there are 2 cables?

You'd have to resolve forwards and sideways. The tugs are at an angle.

Reply 8

Theo298

Original post by mqb2766

You'd have to resolve forwards and sideways. The tugs are at an angle.

So is the force 25000N?

Reply 9

mqb2766

Original post by Theo298

So is the force 25000N?

Can you post your diagram and explain the figure.
The rope tensions are not 25,000

(edited 4 years ago)

Original post by Theo298

So is the force 25000N?

the forward component of each cable is 25000 N.

Reply 12

mqb2766

Original post by Theo298

When you put the forces / tensions on there you'll see they are not aligned so need to be balanced forwards and sideways

Reply 13

Theo298

Original post by mqb2766

When you put the forces / tensions on there you'll see they are not aligned so need to be balanced forwards and sideways

Okay so I think I have that as 33125.32N.

How would I use that to calculate the original question?

Reply 14

mqb2766

Original post by Theo298

Okay so I think I have that as 33125.32N.

How would I use that to calculate the original question?

Sounds right.
So that should balance the new resistive drag (velocity) which will be aligned with the tension.

(edited 4 years ago)

Reply 15

Theo298

Original post by mqb2766

Sounds right.
So that should balance the new resistive drag (velocity) which will be aligned with the tension.

Would the new drag be 8000v^2 = 33125.32N, as there is only one tug now?

Reply 16

mqb2766

Original post by Theo298

Would the new drag be 8000v^2 = 33125.32N, as there is only one tug now?

Yes, the forces are in the same (opposite) direction.

Do draw the diagrams and put the tensions on there, even if they're unknown. It makes directions / resolving components clear.

Reply 17

Theo298

Original post by mqb2766

Yes, the forces are in the same (opposite) direction.

Do draw the diagrams and put the tensions on there, even if they're unknown. It makes directions / resolving components clear.