How Do You Calculate Tension in a Hanging Mirror?

[Arabell]

Homework Statement

Diagram 4 shows a 2 kg mirror hung on a wall using strings of the same length . The mirror is in equilibrium state.

a) On Diagram 4 , label the force that act on the mirror .

b) Calculate the tension of the string , T that act on the mirror .

c) Suggest a modification to be made so that the string can withstand a larger maximum force .

Homework Equations

The Attempt at a Solution

I had only drawn a free body diagram and I am already stuck and don't know what to do... Help me please , any solution to this question would be greatly aprreciated .

 

[FermionXLR8r]

Solution

First we must take the vertical component of the tension forces acting on the mirror. Let the mass of mirror be m
Then
2TSin45=mg
solve for T by substituting the values.
A modification which can be made is connecting the strings parallely

 

[Arabell]

First we must take the vertical component of the tension forces acting on the mirror. Let the mass of mirror be m
Then
2TSin45=mg
solve for T by substituting the values.
A modification which can be made is

Thanks mate for replying ... In the equation , where does 2 come from , does it come from the mirror which is 2 kg since it is an equilibrium state . Another thing is can you explain why connecting the strings parallely enables it to withstand a larger maximum force

 

[haruspex]

where does 2 come from , does it come from the mirror which is 2 kg since it is an equilibrium state . Another thing is can you explain why connecting the strings parallely enables it to withstand a larger maximum force

The 2 is because there are two strings. If the tension is T, each each string is supplying an upwards force of T sin (45) = T/√2. Since that balances the weight of the mirror, what is T?

If the strings were vertical with tension U, what would the equation be?

 

[Nickie]

a) On Diagram 4, label the force that act on the mirror.
The forces acting on the mirror are the weight of the mirror acting downwards (labeled as Fg), the tension in the string acting upwards (labeled as T), and the normal force from the wall acting inwards (labeled as Fn).

b) Calculate the tension of the string, T that act on the mirror.
To calculate the tension in the string, we can use the equilibrium condition where the sum of all forces acting on the mirror is equal to zero. This can be written as:
Fg + T + Fn = 0
Since the mirror is in equilibrium, the weight and normal forces are equal in magnitude and opposite in direction. Therefore, Fn = -Fg. Substituting this into the equation, we get:
T = Fg = mg = (2 kg)(9.8 m/s^2) = 19.6 N

c) Suggest a modification to be made so that the string can withstand a larger maximum force.
One possible modification could be to use a stronger and thicker string. This would increase the tensile strength of the string and allow it to withstand a larger maximum force without breaking. Additionally, the strings could be attached to the wall at a wider angle, which would distribute the tension force over a larger area and reduce the stress on the string.