Can the max friction be determined in B-ii?

[phys_student2018]

This question is on our worksheet for this week. Part A and B-i I'm fine with.

Part B-ii I'm confused by. I've asked my physics lecturer and he implied there is a way of finding fs,max using part B-i. My class tutor was a bit confused by the wording of the question and tried to break part of it down but I think I'm still missing something. My math tutor said we can't determine fs,mas as there is no coefficient of friction or other information to determine that.An eagle with a mass of 5.0 kg is hunting when it sees a rabbit on the ground below. After catching it, the eagle returns to its nest carrying the 1.5 kg rabbit and flying at a constant horizontal velocity. You may ignore air resistance.

(A) What must the lift force acting on the eagle be, if it is to maintain constant velocity? 5.0 + 1.5 x 9.8 = 63.7N

(B) The eagle’s nest sits on the surface of a rock inclined at 30◦ above the horizontal. While landing, the eagle can exert a maximum force of 87 N downwards on the rock.
NB: it is assumed the eagle is still carrying the rabbit in parts B-i and B-ii.
i) What is the frictional force required to stop the eagle sliding down the rock when it has landed (IE standing still)? 63.7sin30 = fs31.85
ii) Can the eagle land on the rock without sliding down it? You will need to consider the maximum force that the eagle exerts on the rock when landing.

Here's what I have so far:
87sin30 = 43.5N
The eagle landing with a force of 87N requires a frictional force of 43.5N to stop it from sliding, if the frictional force is less than 43.5N the eagle will slide. As we do not know fs,max or μsN, we cannot determine the maximum static friction.
If assumed the the maximum friction is equal to 31.85N (answer to B-i) then the eagle would slide as 43.5N > 31.85N

So, is it possible to determine the maximum friction from the information provided? And if so, how is this determined please?

 

[haruspex]

can exert

Can or will?

If assumed the the maximum friction is equal to 31.85N

I see no basis for such an assumption.
Your math tutor is correct.

 

[phys_student2018]

Can or will?

I see no basis for such an assumption.
Your math tutor is correct.

My tutor made that assumption about the maximum friction being 31.85N...

And yes 'can exert' - it's copied directly from the question

 

[CWatters]

My class tutor was a bit confused by the wording of the question and tried to break part of it down but I think I'm still missing something. My math tutor said we can't determine fs,mas as there is no coefficient of friction or other information to determine that.

I agree with your maths tutor.

There isn't enough information to give an answer. If the rock was covered in ice the coefficient of friction would be low or zero. No amount of downward force will stop the eagle sliding off (unless it hovers, but that doesn't really count as landing).

Were you given the weight of the empty nest?

Edit: ignore this post. See below.

 

[CWatters]

Actually ignore my post above. I don't think you need the weight of the nest...

If the nest doesn't slide off you know the coefficient of friction is at least tan(angle).

So your physics lecturer is correct, I think it can be solved.

 

[haruspex]

And yes 'can exert' - it's copied directly from the question

That is the first error in the question. "Can exert" says the eagle is capable of exerting such a force, not that it necessarily does.
A second error is that it says nothing about horizontal force. As the eagle, if there were a risk of the nest's sliding, I would land with a horizontal component opposing the slope.

My tutor made that assumption about the maximum friction being 31.85N...

That's the third and worst error. There is no basis for that assumption.
We are taught that maximum frictional force is proportional to normal force. If, strangely, there is a maximum independent of normal force then the question must state that.

 

[phys_student2018]

Actually ignore my post above. I don't think you need the weight of the nest...

If the nest doesn't slide off you know the coefficient of friction is at least tan(angle).

So your physics lecturer is correct, I think it can be solved.

Could you explain the use of tanθ here please? I used sinθ in my other calculations, is tanθ instead of sin or are you referring to a separate equation that I haven't worked out yet?

 

[haruspex]

Could you explain the use of tanθ here please? I used sinθ in my other calculations, is tanθ instead of sin or are you referring to a separate equation that I haven't worked out yet?

It is sin if you are comparing the downslope component of the applied force with a given frictional force. But CWatters is assuming that the limit comes from the coefficient of friction, making the maximum frictional proportional to the normal force. That brings a cos into the equation, which reduces the sin to a tan.
Note that this assumption is different from that you say your tutor is making. But it is a more reasonable assumption, so there is reason to question what your tutor said/meant.

 

[CWatters]

One way to measure the coefficient of friction of a surface is to increase the angle until an object on it just starts to slide. If you work the numbers mg cancels leaving u=tan(theta).

So I'm thinking that if the nest on its own doesn't slide off then u must be >tan(theta) so in this case u>tan(30) or >0.58.

My guess is that this is what your physics tutor was referring to and your maths tutor missed it.

 

[haruspex]

My guess is that this is what your physics tutor was referring to and your maths tutor missed it.

The maths tutor missed nothing!
Part Bi asks what frictional force is necessary to stop the nest sliding off. Nowhere does it indicate whether the actual force is equal to that, or more, or less.
Further, though this may have lost something in the translation, post #3 says that the physics tutor assumed the max frictional force was the value found in part Bi, not the coefficient of friction.

 

[CWatters]

Perhaps I'm getting confused with which of the three tutors said what.

Anyway I agree with the answer for part I)..

i) What is the frictional force required to stop the eagle sliding down the rock when it has landed (IE standing still)? 63.7sin30 = fs31.85

As for part ii)...

ii) Can the eagle land on the rock without sliding down it? You will need to consider the maximum force that the eagle exerts on the rock when landing.

(B) The eagle’s nest sits on the surface of a rock inclined at 30◦ above the horizontal. While landing, the eagle can exert a maximum force of 87 N downwards on the rock.

The maximum force the eagle can exert down the slope is:

87*Sin(30) = 43.5N

Since the nest on it's own doesn't slide then μ > tan(30).
The available friction force up the slope (when the eagle exerts the maximum of 87N downwards) is:

> tan(30)*87*Cos(30)
> 0.86*87*Cos(30)
> 64.8N

64.8N > 43.4N

So my answer for Bii) would be yes the eagle can land without sliding down the slope.

However since both equations contain the downward force term (87N) the actual downward force the eagle exerts is irrelevant. The available friction force will always be greater than the force down the slope.

I guess the fact that the value 87N isn't need is an argument against my approach but that's the answer I'd give.