Cable connecting the two ships homework

In summary, the discussion focused on determining the tension, T, in the cable connecting a tugboat and a ship being pulled. Through the use of Newton's second law and considering the horizontal forces acting on the objects, the formula T = FM/(M+m) was derived. The importance of creating a force body diagram was also emphasized.
  • #1
Naikon
4
0

Homework Statement



A tugboat of mass m pulls a ship of mass M, accelerating it. Assume that water friction on the two vessels' is negligible.

If the force acting on the tug's propellar is F, what is the tension, T, in the cable connecting the two ships

(Variables: F, M, m)


Homework Equations



F=ma


The Attempt at a Solution



to get T I thought I would use the equation,

a= (T-mg)/m & a= -(T-Mg)/M

However, I cannot figure out how to derive a forumla for T that only involves F, M, and m.

I can derive:

T= (2gMm)/(M+m)

I'm stuck can anyone help?
 
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  • #2
Welcome to the forums.

What direction does g apply and what direction are the boats traveling?
 
  • #3
hotvette said:
What direction does g apply and what direction are the boats traveling?


I guess g is irrelevant in this question, the boat would be traveling the same direction as the tugboat as it is being pulled so I would only need to consider the horiztonal forces acting on the objects?
 
Last edited:
  • #4
OK, if g acts down and the boats are traveling in a horizontal direction, what influence does g have on the motion?
 
  • #5
none , i just edited my previous post. sorry
 
  • #6
Naikon said:
I guess g is irrelevant in this question, the boat would be traveling the same direction as the tugboat as it is being pulled so I would only need to consider the horiztonal forces acting on the objects?

Correct!
 
  • #7
Ok so I completely forgot to add up my forces for Newton's second law, thank you. I guess now I realize the importance of a force body diagram.

I derived:

(T+F/m) = a

(T/M) = a

Resulting in : -FM/(M+m)
 
  • #8
What, no FBD? Shame of shames... By the way, I got the same answer as you.
 

Related to Cable connecting the two ships homework

1. What is the purpose of connecting two ships with a cable?

The purpose of connecting two ships with a cable is to allow them to transfer goods, materials, or people between each other while at sea. This can also be used in emergency situations to tow a disabled ship or to provide additional stability during rough seas.

2. How is the cable connected between the two ships?

The cable is typically secured to both ships using heavy-duty clamps or shackles. It is important to ensure that the connection is strong and secure to prevent any accidents or damage to the ships.

3. What type of cable is used for connecting two ships?

The type of cable used for connecting two ships is typically a heavy-duty steel wire rope. These ropes are specifically designed to withstand the harsh conditions of the ocean, including strong winds and waves, and have a high breaking strength to support the weight of the connected ships.

4. How long can the cable connecting two ships be?

The length of the cable connecting two ships can vary depending on the specific needs of the ships. However, most cables used for this purpose are typically several hundred feet long to allow for flexibility and movement between the two ships.

5. What are the safety precautions when using a cable to connect two ships?

Some of the safety precautions when using a cable to connect two ships include regular inspections for any wear or damage, using appropriate personal protective equipment when handling the cable, and having a designated crew member to monitor the connection and handle any issues that may arise.

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