Boat Tugging a Whale: Solving 2 Unknowns

[Femme_physics]

Am getting stuck with 2 unknowns

Homework Statement

http://img40.imageshack.us/img40/5883/whaltboat.jpg

The 5.5-Mg humpback whale is stuck on the shore due to changes in the tide. In an effort to rescue the whale, a 12-Mg tugboat is used to pull it free using an inextensible rope tied to its tail. To overcome the frictional force of the sand on the whale, the tug backs up so that the rope becomes slack and then the tug proceeds forward at 3 m/s.
If the tug then turns the engines off, determine the average frictional force F on the whale if sliding occurs for 1.5 s before the tug stops after the rope becomes taut. Also, what is the average force on the rope during the tow?

The Attempt at a Solution

As u can see, I get stuck with 1 equation and two unknowns. I was able to solve for N and a (hopefully I did it correctly) though.

http://img121.imageshack.us/img121/3028/19084315.jpg
http://img339.imageshack.us/img339/7913/16323840.jpg

 

[darkxponent]

to find Tension (T)
tension retards the ship
so
T=mass of ship * acc of ship(a)
T= 12000*2
= 24000 N

now u can find Friction usin

m*a = T -F

F = T - m*a
=24000 - 11000
=13000 N

 

[I like Serena]

Hey Fp!

Can you make an FBD of the ship?

Perhaps that will give you an extra equation?

 

[Femme_physics]

Did I make it?!?? I have a strange feeling I did!

http://img11.imageshack.us/img11/6151/boattish.jpg

 

[I like Serena]

Good! :)

Do you have enough information now to find the friction force?

 

[Femme_physics]

I think so!

http://img14.imageshack.us/img14/4449/68659764.jpg

 

[I like Serena]

What?
No victory dance?

 

[Femme_physics]

I got it?!??

w000t! *victory dance!*Wait, let's do it with calculus now!

Give me pointers, I'm sooooooooooo ready!

 

[Femme_physics]

Hmm wait according to the manual

F = 24[kN]
T = 24 [kN]

 

[I like Serena]

Hmm wait according to the manual

F = 24[kN]
T = 24 [kN]

Hmm, if F equals T, then...
The resultant force on the whale is zero...
That doesn't sound right.

I know, I think they made a typo (a copy+paste error)!

I got it?!??

w000t! *victory dance!*


Wait, let's do it with calculus now!

Give me pointers, I'm sooooooooooo ready!

Ah, but then we would need Captain Calculus! Rawwwr!
He got points and angles!

[PLAIN]http://www.cantonschools.org/~lforastiere/00F5BEEB-0075833E.0/Captain%20Calculus.jpg

 

[darkxponent]

Hmm wait according to the manual

F = 24[kN]
T = 24 [kN]

hmmm...sounds right

i got it now: *ques asks for average force...average acceleration is zero so is average net force*

i got the same answer using calculus

 

[I like Serena]

And here's another good pointer:
http://photo.goodreads.com/books/1170573180l/61299.jpg

 

[I like Serena]

hmmm...sounds right

i got it now: *ques asks for average force...average acceleration is zero so is average net force*

i got the same answer using calculus

Nope.
Average acceleration is not zero, since it says in the problem: "sliding occurs for 1.5 s before the tug stops".

 

[darkxponent]

Nope.
Average acceleration is not zero, since it says in the problem: "sliding occurs for 1.5 s before the tug stops".

but it stops after sliding 1.5 s...that means it retards which cancels the intiall acceleration and average becomes zero

 

[Femme_physics]

And here's another good pointer:
http://photo.goodreads.com/books/1170573180l/61299.jpg

Oh now you're just patronizing. Humphffh!

So they're mistaken?

Ah, but then we would need Captain Calculus! Rawwwr!
He got points and angles!

LOL where'd you get that from?!?

Captain Calculus. I'm going to use that haha!

 

[I like Serena]

but it stops after sliding 1.5 s...that means it retards which cancels the intiall acceleration and average becomes zero

The acceleration is never negative, so it can't cancel, nor can its average become zero.

Oh now you're just patronizing. Humphffh!

So they're mistaken?
LOL where'd you get that from?!?

Captain Calculus. I'm going to use that haha!

I believe that they are mistaken.I was googling for funny pointers on calculus when I found the book.
Looking at it I found it *mildly enjoyable* :DAnd errrr... I don't know how to do this problem with calculus...

 

[darkxponent]

If the tug then turns the engines off, determine the average frictional force F on the whale if sliding occurs for 1.5 s before the tug stops after the rope becomes taut. Also, what is the average force on the rope during the tow?

check this

 

[I like Serena]

check this

Check what?

 

[darkxponent]

Check what?

the meanig of the sentence

 

[Femme_physics]

And errrr... I don't know how to do this problem with calculus...

Really? But I thought you studied physics with calculus since you took it at the university

 

[I like Serena]

Really? But I thought you studied physics with calculus since you took it at the university

That's not what I meant. ;)
I could spew a whole lot of calculus formulas here, but it wouldn't be particularly useful for this problem.

 

[Femme_physics]

Well the thing is that I specifically chose this problem because I saw calculus there and I was wondering if I could sort of "pull it off" (excuse the pun), but I've no clue what they did what they did or how they did what they did but...

http://img6.imageshack.us/img6/1403/calculusdolphine.jpg

 

[I like Serena]

Ah, I see.
They used another way to solve the problem.

This is still not really calculus although it looks that way.
They used calculus notation though.

And they used a formula I haven't seen you using yet.
The one about impulse and momentum.
Hold on, I see it now.
Sorry, I made a mistake earlier.

The resultant force on the whale is (T-F), but this force will first accelerate the whale from zero to a certain speed, and after that it will decelerate the whale again, until it is back at zero speed.
This also means that the average acceleration is indeed zero.

On average this means that T and F are equal.
So your answer must indeed be F = 24 kN.
As for the formulas that were used, you have them on your list like this:

If you want, I can explain how they were used.

 

[Femme_physics]

Good morning, captain! And aha! it makes sense, then. Why did they use calculus notation though?

That doesn't really make much sense to me.

 

[I like Serena]

Ahoy ahoy sailor!

The calculus notation comes from the use of "impulse".

Impulse is a varying force that is exerted over a small period of time (the jerking tug in this case).
Typically it is unknown how the force varies exactly.
In cases we would know the varying force F, we would use an integral to sum it up.
That is $J = \int F \cdot dt$.

However, when you work with impulse, you're usually only interested in the total effect, which is the change in momentum. The force F is taken as an average then. Hence the formula $J = F \cdot \Delta t$ on your formula sheet.

Every now and then the calculus notation with an integral is still used to denote the impulse, although there is no intention of actually integrating.

 

[Femme_physics]

Ah, I see gotcha. And thanks for the explanation, cap'n!

I really like the fact you took it out of my formula sheet !

Now where be me rum and me trollops?!? Har!

 

[I like Serena]

Arrr - me crank needs attention.
Set sail for trollopallooza, post haste, matey, or I'll swing ye from the yardarm!

 

[Femme_physics]

(LOL)

Aye aye!

*pulls the anchor and starts calculating the its velocity in various position...*