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Acceleration that occurs when a force is applied horizontally to an object on a slope

작성자 Uploader : 황금마차 작성일 Upload Date: 2019-09-18변경일 Update Date: 2019-10-05조회수 View : 242

As shown in the figure, when a force is applied in the horizontal direction to an object on an inclined plane having an angle of θ (deg) with the horizontal plane, the acceleration of the object is obtained as follows.

mass of the object : m (kg)
force applied in the horizontal direction : F(N)
friction coefficient between the inclined surface and the object : μ
gravitational acceleration : g (m/s^2).

The force F applied in the horizontal direction can be divided into the force Fx in the inclined plane direction and the force Fy in the direction perpendicular to the inclined plane.

Fx = F * cosθ
Fy = F * sinθ

The weight of the object can be divided into the force Wx that the object goes down the slope and the force Wy that pushes the slope in a direction perpendicular to the slope.

Wx = m*g*sinθ
Wy = m*g*cosθ

The net force Fp that pushes the object up is given as below in consideration of the frictional force.

Fp = Fx - Wx - μ(Fy+Wy)
   = F*cosθ - m*g*sinθ - μ(F*sinθ+m*g*cosθ)

Therefore, the acceleration a which arises in the object can be calculated by the following formula.

a = Fp / m
  = (F*cosθ - m*g*sinθ - μ(F*sinθ+m*g*cosθ)) / m

*** 참고문헌[References] ***
a = (F*cos(θ) - m*g*sin(θ) - μ*(F*sin(θ)+m*g*cos(θ))) / m
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변수명 Variable 변수값 Value 변 수 설 명 Description of the variable


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