Object at rest hanging from two ropes

[mncyapntsi]

Homework Statement

A book is at rest suspending from 2 cords (C1 and C2), and C1 is shorter than C2. The book pulls on the meeting point P of the cords with a force of 10 N. All cords also exerts a force on the Point P. The angle between the strings at P is 90 deg.

True or false:
1- F(C2/P) > F(C1/P) must be true
2- F(C2) > 10 N may be true
3- Vector sum of forces by C1 and C2 is straight up
4- F(C2/P) points downwards to the left
5- The magnitude of the vector sum of the forces exerted by C1 and C2 is greater than 10 N

Relevant Equations

NetF = ma

Here is where I am at :
1- F(C2/P) > F(C1/P) must be true I believe this is false, considering the angle separating C1 from the 'ceiling' is bigger
2- F(C2) > 10 N may be true I believe this is true because F(C2) could be broken down into vector components which may go above 10 N
3- Vector sum of forces by C1 and C2 is straight up True because the book is resting
4- F(C2/P) points downwards to the left False because it points up to the right ?
5- The magnitude of the vector sum of the forces exerted by C1 and C2 is greater than 10 N False because it must be equal to 10 N if the book is at rest?

Please help!

 

[mncyapntsi]

Here is a little diagram if it helps clarify some things :

Thank you for any help!

 

[kuruman]

Answers 3-5 are correct for the reasons you give. To verify your answers for 1 & 2 consider this: If you do a geometric addition of the three vectors, you will see that they form a closed triangle because their sum is zero. What kind of relations must the sides of a triangle obey?

 

[mncyapntsi]

Answers 3-5 are correct for the reasons you give. To verify your answers for 1 & 2 consider this: If you do a geometric addition of the three vectors, you will see that they form a closed triangle because their sum is zero. What kind of relations must the sides of a triangle obey?

Well, then C2 can't be larger than 20 N because it isn't a hypothenuse. But what is the third vector you are talking about, just so I don't confuse myself?

 

[Father_Ing]

But what is the third vector you are talking about, just so I don't confuse myself?

The weight

 

[mncyapntsi]

The weight

Alright I've tried :
1 - False
1- True
1- True
1- False
1- False
Yet this has been marked as incorrect by my professor. I am to find which one(s) are incorrect...I really don't see it.

 

[Father_Ing]

Well, then C2 can't be larger than 20 N

Hm.I don't think this is correct. Try to make free body diagram

 

[mncyapntsi]

Hm.I don't think this is correct. Try to make free body diagram

Yes, by intuition I wrote True on that - It can be larger than 20N because it is the hypothenuse. However, the pattern
1- True
2- True
3- True
4- False
5- False
Has also been marked as wrong by my professor...

 

[Rikudo]

As what @Father_Ing said, try to make the free body and calculate the forces in x and y direction using F = ma.
You will find the value of both tensions

 

[kuruman]

Yes, by intuition I wrote True on that - It can be larger than 20N because it is the hypothenuse. However, the pattern
1- True
2- True
3- True
4- False
5- False
Has also been marked as wrong by my professor...

Intuition can be faulty. Try reasoning. Draw the right triangle, label the sides and provide reasons for your answers. That's the short way. The long way is to draw a free body diagram, find the tensions and use the fact that β > α.

 

[Lnewqban]

Yes, by intuition I wrote True on that - It can be larger than 20N because it is the hypothenuse. However, the pattern
1- True
2- True
3- True
4- False
5- False
Has also been marked as wrong by my professor...

You need to understand this simple problem before you advance to more complicated ones.
See figure 6.3 in this link:
https://courses.lumenlearning.com/s...apter/6-1-solving-problems-with-Newtons-laws/

Start by re-arranging the cords and angles in such a way that the set up is symmetrical.
Then, make α=90° and β=90°, so C1 and C2 become both vertical:
F_y_C1=F_y_C2=0.5gm_B

Then, make α=45° and β=45°, so C1 and C2 become perpendicular to each other:
F_y_C1+F_y_C2=gm_B
Because of the above, the magnitudes of F_C1 and F_y_C2 must be greater.

Lastly, break the symmetry and make α=30° and β=60°, so C1 and C2 remain perpendicular to each other, as your problem states.
Now, being in lateral balance, the system must comply with
F_x_C1=F_x_C2

In order for that to happen, how F_y_C1, F_y_C2, F_C1 and F_C2 must naturally re-adjust their magnitudes to keep a vertical balance of forces?

 

[mncyapntsi]

Intuition can be faulty. Try reasoning. Draw the right triangle, label the sides and provide reasons for your answers. That's the short way. The long way is to draw a free body diagram, find the tensions and use the fact that β > α.

I am so sorry, I got mixed up : by intuition I got that 2 - False!
1- True
2- False
3- True
4- False
5- False
I drew out the vectors and their x and y components, and found all this above
However---This has been marked incorrect... I really don't understand

 

[kuruman]

I am so sorry, I got mixed up : by intuition I got that 2 - False!
1- True
2- False
3- True
4- False
5- False
I drew out the vectors and their x and y components, and found all this above
However---This has been marked incorrect... I really don't understand

Please show your drawing. It should be a right triangle with sides C1, C2 and angles α and β labeled. Then provide reasons why you answered the first two items the way you did on the basis of what you see in this triangle. It may be that you drew the wrong triangle.