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a 8.0 kg object is sliding down s frictionless inclined ramp at an acceleration of 2.6/s/s. what is the angle of the inclined plane​

a 80 kg object is sliding down s frictionless inclined ramp at an acceleration of 26ss what is the angle of the inclined plane class=

Respuesta :

Answer:

[tex]15.4^{\circ}[/tex]

Explanation:

There is only one force acting along the direction parallel to the plane: the component of the weight parallel to the incline, which is given by

[tex]mg sin \theta[/tex]

where

m = 8.0 kg is the mass of the object

[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity

[tex]\theta[/tex] is the angle of the incline

Therefore, the equation of motion along this direction is

[tex]ma=mgsin \theta[/tex]

where

[tex]a=2.6 m/s^2[/tex] is the acceleration of the object

Re-arranging the equation, we can solve to find the angle of the incline:

[tex]sin \theta = \frac{a}{g}=\frac{2.6}{9.8}=0.265\\\theta = sin ^{-1} (0.265)=15.4^{\circ}[/tex]

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