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An inclined plane makes an angle of 30.0º with the horizontal. 

a) Find the force required to cause a 15 kg box to slide up the plane with an acceleration of 1.2 m/s2. 

b) Find the force required to cause a 15 kg box to slide down the plane with an acceleration of 1.2 m/s2.​

Respuesta :

The force required to push the box upward is 145.3N and the force to pus the box downward is -109.3N

Data given;

  • mass = 15kg
  • angle = 30 degree
  • acceleration = 1.2 m/s^2
  • acceleration due to gravity = 9.8 m/s^2

Force against gravity

To move the plane upward, the box will move against gravity.

[tex]F = F - mgcos X\\ ma = F - mg cosX[/tex]

Let's solve for F

[tex]ma = F - mgcosX\\ 15*1.2 = F - 15*9.8 * cos 30\\ 18 = F - 127.30\\ F = 18 + 127.30\\ F = 145.3N[/tex]

Force towards gravity

When the force pushes the box down the inclined plane, it moves towards gravity.

[tex]F = F + mgcosX\\ ma = F + mgcosX\\ 15*1.2 = F + 15*9.8*cos30\\ F = -109.3N[/tex]

The force required to push the box upward is 145.3N and the force required to push the box downward is -109.3N

Learn more on force across an inclined plane here;

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