Calculating Line Strength to Stop a Salmon

[cd80187]

All right, I am doing my physics homework and I just cannot figure this one out. I have been trying for literally over an hour, so I am running out of ideas. Here it is.

The tension at which a fishing line snaps is commonly called the line's “strength.” What minimum strength is needed for a line that is to stop a salmon of weight 76 N in 13 cm if the fish is initially drifting at 3.1 m/s? Assume a constant deceleration.

All right, so clearly this has to do with force, which is going to end up being the mass of the fish times its decleration. But because they are asking for strength, I am guessing it a magnitude and not a vector. So, I have tried things such as using the velocity over the meters taken to stop the fish, to get time and then apply that to get the acceleration, but that was clearly wrong as the time changes due to the deceleration. I have done all kinds of things, I need help to figure this one out. Thank you

 

[Doc Al]

Use your knowledge of kinematics to find the acceleration. (You are given the initial speed and the distance--that's all you need.) Then use Newton's 2nd law to find the force needed to produce that acceleration. (What's the mass of the fish?)

 

[cd80187]

Thank you so much. I hate those problems that are so simple, yet you overlook. I figured out the answer and it was correct. I used the formula 2a(Change in x) = (final velocity) squared minus (initial velocity) squred. but once again, thank you

 

[mike_24]

another question about the fish problem

I was wondering if someone could explain the fish problem in a bit more detail, I can't seem to get it...

Thanks in advance

 

[Hootenanny]

I was wondering if someone could explain the fish problem in a bit more detail, I can't seem to get it...

Thanks in advance

Welcome to the Forums Mike,

How would you approach the problem yourself? How much do you know about kinematics?

 

[mike_24]

As far as approaching the problem, I am not sure, I was doing a few things with F=ma and replaceing the F with W, but i don't seem to be making a whole lot of progress.

 

[Hootenanny]

As far as approaching the problem, I am not sure, I was doing a few things with F=ma and replaceing the F with W, but i don't seem to be making a whole lot of progress.

Okay, do you know any kinematic equations?

 

[mike_24]

Umm what would be an example of some?

 

[Hootenanny]

Umm what would be an example of some?

Doc Al has authored this rather nice https://www.physicsforums.com/showthread.php?t=110015" in particular deals with basic kinematic equations.

 

[mike_24]

Yes I do know some kinematics

 

[mike_24]

I am familiar with all of those yes

 

[Hootenanny]

Yes I do know some kinematics

Make two list, one with variables you know. The other with variable(s) you wish to find. Which formulae are applicable in your case?

 

[mike_24]

I don't see how the initial speed and the distance can get you the acceleration though.

 

[Hootenanny]

I don't see how the initial speed and the distance can get you the acceleration though.

You also know the final velocity.

 

[mike_24]

For this problem the displacement and velocity equation would be needed i think, and Newtons 2nd law F=ma and maybe W=mg

 

[mike_24]

Ohhh, it would be zero

 

[Hootenanny]

Ohhh, it would be zero

Spot on.

For this problem the displacement and velocity equation would be needed i think,

Good.

and Newtons 2nd law F=ma

Sounds good.

and maybe W=mg

You may want to rethink this. What can you say about the net vertical force is a fish is floating (or swimming) at the same depth?

 

[mike_24]

it would zero if the fish was at the same depth?

 

[Hootenanny]

it would zero if the fish was at the same depth?

Correct, so you don't need to worry about the weight of the fish. However, you do need the weight to calculate the ...

 

[mike_24]

the mass of the fish?

 

[Hootenanny]

the mass of the fish?

Correct. Can you have a go at the question from here?

 

[mike_24]

Yes, i hope so, but one other question, I rearranged the velocity and displacement equation to solve for acceleration and have calculated the mass of the fish, but i get a really large acceleration, is it because i converted the 13cm to m?, isn't that was is always done?, or am I going wrong somewheres else?

 

[Hootenanny]

So, once you re-arrange your equation you should obtain;

$$a = \frac{v_{f}^2}{2\Delta x}$$

Yes, you should always convert your units to S.I. units in this type of problem.

 

[mike_24]

Doing that gives you an acceleration of 36.96m/s^2, just seems like it should be more like 3

 

[mike_24]

Would 36.96 be the correct acceleration?

 

[Doc Al]

Would 36.96 be the correct acceleration?

Yes, that's correct. The units are m/s^2.

 

[Hootenanny]

As Doc Al said, your answer is correct. However, I would be interested to know why you think the acceleration should be around 3m.s^-2?

 

[mike_24]

I had no reason to believe it would be around 3, it was just it seemed 36m/s^2 would be too high of a number. Thanks though for all the help with this problem, I appreciate it.