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Acceleration when force is applied to two objects connected by pulley

작성자 Uploader : orion 작성일 Upload Date: 2019-11-05변경일 Update Date: 2020-01-13조회수 View : 293

When objects of mass m1 and m2 (kg) are connected with a pulley as shown in the figure, the acceleration a (m/s^2) generated when the force F (N) is applied horizontally and at θ (degrees) to the object m2 can be obtained as follows.

The coefficient of friction between the m2 object and the floor is μ.

The horizontal component force Fx and the vertical component force Fy of the applied force are as follows.

Fx = F*cos(θ)
Fy = F*sin(θ)

The frictional force Ff according to the force applied by m2 to the floor is as follows..

Ff = μ(m2*g - F*sin(θ))

where, g : gravity acceleration (m/s^2)

The net force Ft in the horizontal direction is the force at Fx minus the friction force acting on m1 and the gravity force.

Ft = F*cos(θ) - μ(m2*g - F*sin(θ)) - m1*g

 = F*(cos(θ)+μ*sin(θ)) - g*(m1+μ*m2)

Thus, the acceleration generated 'a' is :

a = (F*(cos(θ)+μ*sin(θ)) - g*(m1+μ*m2))/(m1+m2)


*** 참고문헌[References] ***
a = (F*(cos(θ)+μ*sin(θ)) - g*(m1+μ*m2))/(m1+m2)
변수명 Variable 변수값 Value 변 수 설 명 Description of the variable


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