Mechanics 1 Help: Solve Questions on Bead Equilibrium

[CathyLou]

[SOLVED] Mechanics 1 help

Hi.

Could someone please help me with the following M1 level questions?

A smooth bead B is threaded on a light inextensible string. The ends of the string are attached to two fixed points A and C on the same horizontal level. The bead is held in equilibrium by a horizontal force of magnitude 6 N acting parallel to AC. The bead B is vertically below C and angle BAC = x. tan x = 3/4.

(a) Find the tension in the string.

I drew a diagram and wrote down:

Resolving horizontally:

6 - Tsinx = 0

sin x = 3/5 so T = 10 N.

However, the answer should be 7.5 N. This means that I should be using cos x but I do not understand why this is the case.

(b) Find the weight of the bead.

Would I need to resolve vertically here? If yes, could someone please help me to form the resulting equation.

I would really appreciate any help as I am really stuck at the moment.

Thank you.

Cathy

 

[Hootenanny]

For part (a), I'm assuming that you've either drawn or are given a diagram. If your diagram is set up correctly, the tension should be acting along the hypotenuse (BA) of a right angled triangle from B to A and the angle x should be the angle between the hypotenuse and the side AC. Now, you need to find the horizontal component of the tension, and this component acts parallel to the line CA which is adjacent to the angle x.

Does that make sense?

 

[CathyLou]

For part (a), I'm assuming that you've either drawn or are given a diagram. If your diagram is set up correctly, the tension should be acting along the hypotenuse (BA) of a right angled triangle from B to A and the angle x should be the angle between the hypotenuse and the side AC. Now, you need to find the horizontal component of the tension, and this component acts parallel to the line CA which is adjacent to the angle x.

Does that make sense?

Hi.

Thank you for your help! I understand how to do part (a) now.

Could you please help with (b) also?

Cathy

 

[Hootenanny]

Hi.

Thank you for your help! I understand how to do part (a) now.

Could you please help with (b) also?

Cathy

For (b), yes you have to resolve the forces vertically and you know that since the bead is in equilibrium the sum of these forces must be zero. So, what forces are acting on the bead? (Be careful with the tension)

 

[CathyLou]

For (b), yes you have to resolve the forces vertically and you know that since the bead is in equilibrium the sum of these forces must be zero. So, what forces are acting on the bead? (Be careful with the tension)

I have worked out the correct answer now. Thank you so much for your help!

Cathy

 

[Hootenanny]

I have worked out the correct answer now. Thank you so much for your help!

Cathy

A pleasure