Two masses 8kg and 12kg are connected at the two ends of a light inextensible string that goes over a light and frictionless pulley. find the acceleration of the masses and the tension in the string when the masses are released. (g=10 m/s^2)
Answers
Explanation:
m= 8 kgM= 12 kgg(acceleration due to gravity)=10 m/ s2
The system of masses and pulley has one smaller mass,’m’ and one larger mass, ‘M’.
‘T’ is the tension in the strings,
‘a’ is the acceleration of the masses.
The larger mass, ‘M’ moves downward with supposed acceleration ‘a’ and thus mass, ‘m’ moves upward.
According to the Newton’s second law of motion, we get equation of motion for each masses,
For mass m:
T – mg = ma …..(i)
For mass M:
Mg - T = Ma ……(ii)
We add both of the equation(i) and (ii), to get:
(M – m)g = (M+m)a
⇒
……(iii)
putting
⇒
= 2 m/s2
The acceleration of the masses is 2 m/s2
To find tension, We substitute the value of a from eq(iii) in eq(ii), we get:
⇒ T=96 N
The tension in the string when the masses are released is 96 N.
Answer:
a=2 m/s²
T=96 N
Explanation:
Take 12 kg as m1 and 8 kg as m2 and g=10
Acceleration
a= (m2-m1)g÷m2+m1
using this we get
a= (12-8)10 divided by 12+8
=40÷20
=2 m/s²
Tension
T= (2×m1×m2)g÷m1+m2
using this we get
T=(2×12×8)10÷12+8
=192×10÷20
=192÷2
=96 N