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A box is hanging from two strings. String #1 pulls up and left, making an angle of 450 with the horizontal on the left, and string #2 pulls up and to the right with a force of 180 N, making an angle of 50 with the horizontal on the right.

Flnd the mass of the box.

Hint: Apply ΣFx-0 and ΣFy 0

Respuesta :

Answer:

The mass of the box is 25.6 kg.

Explanation:

Given that,

Angle = 45°

Force = 180 N

Angle = 50°

We need to calculate the force of left side

Using balance equation

[tex]\sum F_{x}=0[/tex]

[tex]-F_{1}\cos45+180\cos50=0[/tex]

[tex]F_{1}=\dfrac{180\cos50}{\cos45}[/tex]

[tex]F_{1}=163.6\ N[/tex]

We need to calculate the mass of the box

Using balance equation

[tex]\sum F_{y}=0[/tex]

[tex]F_{1}\sin45+180\sin50-mg=0[/tex]

[tex]m=\dfrac{1}{g}(F_{1}\sin45+180\sin50)[/tex]

Put the value into the formula

[tex]m=\dfrac{1}{9.8}\times(163.6\sin45+180\sin50)[/tex]

[tex]m=25.8\ kg[/tex]

Hence, The mass of the box is 25.6 kg.

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