Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.
Given: The two masses are 8 kg and 12 kg respectively.
The free body diagram for the system is shown below.
The equation of motion can be written as,
T − m 1 g = m 1 a (1)
m 2 g − T = m 2 a (2)
Where, T is the tension in the string and a is the acceleration.
On adding equations (1) and (2), we get
T − m 1 g + m 2 g − T = m 1 a + m 2 a ( m 2 − m 1 ) g = ( m 1 + m 2 ) a a = ( m 1 + m 2 ) ( m 2 − m 1 ) g
By substituting the given values in the above equation, we get
a = 12 − 8 12 + 8 × 10 = 4 20 × 10 = 2 ms − 2
Thus, the acceleration of the masses is 2 ms − 2 .
By substituting the value of a in equation (2), we get
12 × 10 − T = 12 × 2 T = 120 − 24 = 96 N
Thus, the tension in the string is 96 N .
Given: The two masses are
The free body diagram for the system is shown below.
The equation of motion can be written as,
Where,
On adding equations (1) and (2), we get
By substituting the given values in the above equation, we get
Thus, the acceleration of the masses is
By substituting the value of
Thus, the tension in the string is
