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Two ropes in a vertical plane exert equal-magnitude forces on a hanging weight but pull with an angle of 72.0掳 between them. What pull does each rope exert if their resultant pull is 372 N directly upward?

Short Answer

Expert verified

The pull exerted by each rope is230N.

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The angle at which ropes are pulled is, =72.
  • The resultant pull exerted is,F=372N.
02

Significance of the force

Force is equal to the rate of momentum change with respect to time in any given situation, which facilitates the acceleration of an object

03

Determination of pull exerted by the ropes

The magnitude of resultant of the components of two vectors in the y-direction is given by,

Cy=Ay+By

Here, Ayis the magnitude of y-component of force A鈬赌, Byis the magnitude of y-component of force B鈬赌
and Cyis the magnitude of resultant of forces,A鈬赌and B鈬赌.

Assuming y-axis lies along the north, the three vectors, their magnitudes and their direction areshown in the diagram given below,

The magnitude of the two vectors is equal. and they make equal angle with the y-axis.

Therefore,

Ay=By=Acos=Acos36

Substitute values in the equation of resultant force, the value of A is given by,

A肠辞蝉胃+B肠辞蝉胃=CyAcos36+Acos36=3722Acos36=372A=230N

Thus, the pull exerted by each rope is 230N.

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