1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
GalinKa [24]
3 years ago
12

A heavy mirror that has a width of 2 m is to be hung on a wall as shown in the figure below. The mirror weighs 700 N and the wir

e used to hang it will break if the tension exceeds 700 N (breaking strength). What is the shortest length of wire L that can be used to hang the mirror without the wire breaking? (Ignore any friction forces between the mirror and the wall.)

Physics
2 answers:
loris [4]3 years ago
7 0

The translational equilibrium condition allows finding that the response for cable length with a maximum tension is

      L = 2.56 m

Newton's second law says that the force is proportional to the mass and the acceleration of the body, in the special case that the acceleration is zero, the relationship is called the translational equilibrium condition.

              ∑ F = 0

 

Where the bold indicates vectors, F is the force and the sum is for all external forces.

The reference systems are coordinate systems with respect to which the decomposition of the vectors is carried out and the measurements are made, in this case we will use a system with the horizontal x axis and the vertical y axis.

In the attachment we can see a free body diagram of the system, let's write the equilibrium condition for each axis.

x-axis  

         Tₓ -Tₓ = 0

y-axis

         T_y + T_y - W =0

         2T_y - W = 0

Let's use trigonometry to decompose the tension, we can see from the graph and the adjoint that each string is half the length, let's call the angle θ

          cos θ = \frac{T_x}{T}

          sin θ = \frac{T_y} { T}

          Tₓ = T cos θ

          T_y = T sin θ

We substitute

          2 T sin θ = W          (1)

The text indicates that the length of the block is 2 m, so the distance to the midpoint is

        x = 1 m

Let's use the Pythagoras' Theorem            

            H² = CA² + CO²

           CO = \sqrt{H^2 - CA^2}

           CA = x

           CO = \sqrt{(\frac{L}{2} )^2  - 1 }

Where CO is the opposite leg,  CA is the adjacent leg and H is the hypotenuse indicating H = L / 2,

Let's write the trigonometry functions

           sin θ = \frac{CO}{H}

Let's substitute        

            sin θ = \frac{2 \sqrt{\frac{L^2}{4} -1 } }{L}

Let's subtitute in the equation  1

          2 T  ( \frac{2 \sqrt{\frac{L^2}{4} -1 } }{L}   ) = W

          \sqrt{\frac{L^2}{4}-1  }  = \frac{1}{4}  \ \frac{W}{T} \ L

Let's solve by squaring

         \frac{L^2}{4}  -1 = \frac{1}{4} \ (\frac{W}{T} )^2 \ \frac{L^2}{4}  

         \frac{L^2}{4} ( 1 - \frac{1}{4} (\frac{W}{T})^2  ) -1 =0

They indicate that the maximum tension of the cable is T = 700N and the weight is worth W = 700N, we substitute the values

        \frac{L^2}{4} ( 1- \frac{1}{4}) - 1 =0 \\\frac{3 L^2}{16} = 1 \\ L^2 = \frac{16}{3} \\L = \sqrt{\frac{16}{3} }

        L =   2.31 m    

In conclusion using the translational equilibrium condition we can find that the response for cable length with maximum tension is

      L = 2.31 m

Learn more about translational equilibrium here:

brainly.com/question/12966823

vfiekz [6]3 years ago
6 0

Answer:

2tsin(theta)-700=0

2(700)sin(theta)=700

sin (theta=(700/1400)

theta =30 degrees

cos (theta)=1/2L

L=2/cos (theta)

L=2.31m

Explanation:

You might be interested in
Which types of muscle enables your stomach to produce a churning sound
SVETLANKA909090 [29]
In voluntay smoth tissue muscles
6 0
3 years ago
Which use combustion to release thermal energy?
julia-pushkina [17]
Heat of combustion.<span> The calorific value is the total energy released as heat when a substance undergoes complete combustion with oxygen under standard conditions. The chemical reaction is typically a hydrocarbon or other organic molecule reacting with oxygen to form carbon dioxide and water and release heat.</span>
8 0
3 years ago
Read 2 more answers
What happens in the process of gravitational condensation?
marissa [1.9K]

Answer:

An object decreases in size due to the collision of materials. An object increases in size due to the addition of materials. Gas particles are formed from solar nebula materials.

6 0
3 years ago
Read 2 more answers
Newtons first law stateS that object will move With a constant velocity if nothing acts on it. Does our every day experience con
bazaltina [42]

Answer:

hi

Explanation:

hi

4 0
2 years ago
Choose the correct answer from the given alternatives
Black_prince [1.1K]

Answer:

d

Explanation:

cggbhhgffffggdfvvcdfh

8 0
3 years ago
Other questions:
  • A gas cylinder contains argon atoms (m=40.0 u). The temperature is increased from 286 K (13°C) to 362 K (89°C) (a) What is the c
    8·1 answer
  • Lemaitre (based on Hubble's observations) was the first to suggest the _____.
    14·1 answer
  • Which are ways to build self esteem?
    10·1 answer
  • What fundimental force is responsible for the repulsion between two positively charged particles?
    5·1 answer
  • A tumbleweed is moving with a velocity of 5.4 m/s westward. A sudden gust of wind blows for 1.5 seconds and reduces its velocity
    15·1 answer
  • A person bounces up and down on a trampoline, while always staying in contact with it. The motion is simple harmonic motion, and
    15·1 answer
  • 1-A boy rolls a toy car across a floor with a velocity of 3.21 m/s. How long does it take the car to travel a distance of 4.50 m
    11·1 answer
  • How would the atmosphere of earth differ if the earth was much larger
    9·2 answers
  • Water is considered to be
    5·1 answer
  • I know the acceleration due to gravity (ie 9.8 m/s2) will have a negative sign when falling down, a positive one when going up.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!