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An object is being acted upon by three forces and moves with a constant velocity. One force is 60.0 N along the x-axis, the second in 75.0 N along the y-axis. What is the magnitude of the third force?

Respuesta :

asuwafohjames

Answer:

96.05 N

Explanation:

From Vector,

The two forces acting along the x and y axis are perpendicular,

Fr = √(60²+75²) .............. Equation 1

Where Fr is the result of the two forces

Fr = √(3600+5625)

Fr = √(9225)

Fr = 96.05 N.

Note: Since the object moves with a constant velocity when it is acted upon by the three forces, The acceleration is zero and as such the resultant of the forces is equal to zero.

Therefore,

Ft = Fr+F3................... Equation 2

Where Ft = Total resistance of the three forces, F3 = magnitude of the third force.

make F3 the subject of the equation,

F3 = Ft-Fr

Given: Ft = 0 N, Fr = 96.05 N.

Substitute into equation 2

F3 = 0-96.05

F3 = -96.05 N.

Lanuel

Since one force is 60.0 Newton along the x-axis, the second in 75.0 Newton along the y-axis, then the magnitude of the third force is 96.05 Newton.

  • Let the first force be A.
  • Let the second force be B.
  • Let the third force be C.

Given the following data:

  • Force A = 60 Newton.
  • Force B = 75 Newton.

To find the magnitude of the third force, we would apply Pythagorean's theorem since the first force acts along the x-axis while the second force acts along the y-axis.

Mathematically, Pythagorean's theorem is given by the formula:

[tex]C^2 = A^2 + B^2\\\\C^2 = 60^2 + 75^2 \\\\C^2 = 3600 + 5625\\\\C^2 = 9225\\\\C = \sqrt{9225}[/tex]

C = 96.05 Newton.

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