Question

Two masses mA 1.0 kg and m 12.0 kg are connected by a rope as shown in the figure. The coefficient of kinetic friction between each of the masses is and the inclined plane is μk 0.25. Determine the acceleration of the system.

Dos masas mA = 1.0 kg y m la figura. El coeficiente de fricción cinética entre cada una de las masas y el plano inclinado es με = 12.0 kg están conectadas por una cuerda según se muestra en (10 puntos) 4. 0.25. Determine la aceleración del sistema. 21

Answer 1

Let the mass m_B has an acceleration a towards the direction of velocity. So, the all system will have same acceleration as both masses are connected by a mass - less string.

The force of friction is defined as

Where, N is normal force

i.e.   

and

From the free body diagram , we can write

   (g = 9.8 m/s² is acceleration due to gravity) ..............................(1)

   . .........................(2)

BmBg cos 21°

.........................(3)

.............................(4)

Now we can write equation (3) and (4) as :

............................(5)

and ...........................(6)

Adding equation (5) and (6), we get

Putting all the given values, we get

  

or,

or,

For any doubt please comment and please give an up vote. Thank you.