Cable connecting the two ships homework

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Homework Help Overview

The problem involves a tugboat pulling a ship, with the goal of determining the tension in the cable connecting the two vessels. The context includes considerations of mass, force, and acceleration, while neglecting water friction.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relevance of gravitational force (g) in the context of horizontal motion and question its influence on the problem. There are attempts to derive expressions for tension (T) based on Newton's second law and the forces acting on the tugboat and ship.

Discussion Status

Participants are actively engaging with the problem, questioning assumptions about the forces involved and sharing their derivations. Some have acknowledged the importance of free body diagrams in their reasoning. There is a recognition of similar results among participants, though no consensus has been reached on the final expression for tension.

Contextual Notes

There is an indication that the problem may be constrained by the assumption of negligible water friction and the focus on horizontal forces. Participants are also reflecting on the necessity of accurately accounting for all forces in their calculations.

Naikon
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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 formula 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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What direction does g apply and what direction are the boats traveling?
 
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:
OK, if g acts down and the boats are traveling in a horizontal direction, what influence does g have on the motion?
 
none , i just edited my previous post. sorry
 
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!
 
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)
 
What, no FBD? Shame of shames... By the way, I got the same answer as you.
 

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