Question #8902
2 forces of 5N and 20N are acting on an object at angle of 120deg. between them find the resultant force and its direction.Find the 3rd force acting in body so that the body will move in x direction of cartesian plane
Expert's answer
The module of the resultant force (using Pythagorean theorem) is
R² = (20 + 5·cos120°)² + (5·sin120°)² = (20 - 5·0.5)² + (5√3/2)² = (20 - 5·0.5)² + (5√3/2)² = 325 ==> R = √325 = 5√13.
The angle between the resultant force and the 20N force (using the law of cosines) is
cosα = ((5√13)² - 20² - 5²) / (-2·20·5) = 1/2 ==> α = 60°.
We can't find the 3rd force acting in body so that the body will move in x direction of cartesian plane cause the angle between the given forces and the x axis isn't assumed.
R² = (20 + 5·cos120°)² + (5·sin120°)² = (20 - 5·0.5)² + (5√3/2)² = (20 - 5·0.5)² + (5√3/2)² = 325 ==> R = √325 = 5√13.
The angle between the resultant force and the 20N force (using the law of cosines) is
cosα = ((5√13)² - 20² - 5²) / (-2·20·5) = 1/2 ==> α = 60°.
We can't find the 3rd force acting in body so that the body will move in x direction of cartesian plane cause the angle between the given forces and the x axis isn't assumed.
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