Tension in the string when the masses are released is 88.42 N
Acceleration of masses is [tex]\bold{a=2.578 m/sec^2}[/tex]
Explanation:
Given:
Mass ,m1 = 12
Mass , m2 = 7
g = [tex]9.8m/s^2[/tex]
To Find :
Tension in the string=?
Acceleration of masses=?
Solution:
For mass M_1
[tex]M_1 a=T-M_1 g[/tex]--------------------(1)
For mass M2
[tex]M_2 a=T-M_2 g[/tex]---------------------(2)
Adding equation (1) and (2)
[tex](M_1+M_2)a=(M_2-M_1)g[/tex]
Finding Acceleration:
Acceleration is given by
[tex]a=(M_2-M_1 )/(M_1+M_2) g[/tex]
Substituting the values,
[tex]a=\frac{(12-7)(9.8)}{(7+12)}[/tex]
[tex]a=\frac{(5)(9.8)}{19}[/tex]
[tex]a=\frac {49}{19}[/tex]
[tex]a=2.578 m/sec^2[/tex]
Finding Tension:
From Equation 1
[tex]M_1 a=T-M_1 g[/tex]
Tension can be
[tex]T=M_1 a+M_1 g[/tex]
T=(7)(2.578) + 7(9.8)
T=(17.99)+(68.6)
T=86.59 N
