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Two identical strings making an angle of 0= 26.3 degree with respect to the vertical support a block of mass m=13.7 Kg what is the tension in each of the strings ?

Two Identical Strings Making An Angle Of 0 263 Degree With Respect To The Vertical Support A Block Of Mass M137 Kg What Is The Tension In Each Of The Strings class=

Sagot :

The free-body diagram of the configuration shown is the following:

Now, we add the forces in the vertical direction:

[tex]\Sigma F_v=T_y+T_y-mg[/tex]

Since the system is in equilibrium the sum of forces in the vertical direction is zero:

[tex]T_y+T_y-mg=0[/tex]

Now, we add like terms:

[tex]2T_y-mg=0[/tex]

Now, the y-component of the tension is determined using the following right triangle:

Now, we use the trigonometric function cosine:

[tex]cos(26.3)=\frac{T_y}{T}[/tex]

Now, we multiply both sides by "T":

[tex]Tcos(26.3)=T_y[/tex]

Now, we substitute in the sum of vertical forces:

[tex]2Tcos(26.3)-mg=0[/tex]

Now, we solve for "T". First, we add "mg" to both sides:

[tex]2Tcos(26.3)=mg[/tex]

Now, we divide both sides by "2cos(26.3)":

[tex]T=\frac{mg}{2cos(26.3)}[/tex]

Now, we plug in the values of mass and the acceleration of gravity:

[tex]T=\frac{(13.7kg)(9.8\frac{m}{s^2})}{2cos(26.3)}[/tex]

Now, we solve the operations:

[tex]T=74.88N[/tex]

Therefore, the tension is 74.88 Newton

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View image TremonG78141
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