Question

to masses 7 kg and 12 KG are connected at the two ends of a light inextensible string that passes over a fictional Pulley using free body diagram method find acceleration of masses and the tension in the string when the masses are released ​

Answer 1

Tension in the string when the masses are released ​is 88.42  N

Acceleration of masses is $\bold{a=2.578 m/sec^2}$

Explanation:  

Given:

Mass ,m1 = 12

Mass , m2 = 7  

g = $9.8m/s^2$

To Find :

Tension  in the string=?

Acceleration of masses=?

Solution:

For mass M_1  

$M_1 a=T-M_1 g$--------------------(1)

For mass M2

$M_2 a=T-M_2 g$---------------------(2)

Adding equation (1) and (2)

$(M_1+M_2)a=(M_2-M_1)g$

Finding Acceleration:

Acceleration is given by

$a=(M_2-M_1 )/(M_1+M_2) g$

Substituting the values,

$a=\frac{(12-7)(9.8)}{(7+12)}$

$a=\frac{(5)(9.8)}{19}$

$a=\frac {49}{19}$

$a=2.578 m/sec^2$

Finding Tension:

From  Equation 1

$M_1 a=T-M_1 g$

Tension can be

$T=M_1 a+M_1 g$

T=(7)(2.578) + 7(9.8)

T=(17.99)+(68.6)

T=86.59 N