Please answer this Its a question related to pulleys, NLM and constraints i guess
Answers
Answer:
sorry I didn't know this answer
Method 1: (Ground frame):
Let acceleration of block m
1
with respect to pulley to a upward and the acceleration of m
2
w.r.t. pulley is a (downward)
Equation of motion for
′
m
1
′
T−m
1
g=m
1
a
1
..........(i)
T−m
2
g=m
2
a
2
..........(ii)
a
1
=
a
1.p
+
a
p
=a+a
0
..........(iii)
a
2
=
a
2.p
+
a
p
=−a+a
0
.........(iv)
Substituting a
1
from (iii) in (i),
T−m
1
g=m
1
(a+a
0
)........(v)
Substituting a
2
from (iv) in (ii)
T−m
2
g=m
2
(−a+a
0
).......(vi)
Solving (v) and (iv),
T=
m
1
+m
2
2m
1
m
2
(g+
)
and a=
m
1
+m
2
m
2
−m
1
(g+a
0
)
Method 2 : Solving problem from non-inertial frame of reference
Let us build the equations by using Newton's second law sitting on the accelerating pulley. Hence, we impose pseudo force m
1
a
0
↓ and m
2
a
0
↓ on both m
1
and m
2
, respectively, in addition to the upward tension and their weights m
1
g↓m
2
g↓, respectively, If m
1
accelerates up relative to the pulley, m
2
must accelerate down relative to the pulley with acceleration a.
Force equation :
For m
1
:T−m
1
g−m
1
a
0
=m
1
a........(i)
For m
2
:Tm
2
g+m
2
a
0
−T=m
2
a........(ii)
Solving (i) and(ii), we have
a=
m
1
+m
2
m
2
−m
1
(g+a
0
)