Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

Two blocks of 7 kg and 5 kg are connected by a heavy rope of mass 4 kg. An upward force of 200N is applied as shown in the diagram. The tension at the midpoint of heavy rope is:
seo images

Answer
VerifiedVerified
495.3k+ views
1 likes
like imagedislike image
Hint: Remember force is a vector quantity and so its direction is also to be taken into account. We need to find the total forces acting on the system and then find the net force in order to find the acceleration of the system.

Complete step by step answer:
Let us take the value of g = 10m/s2
The blocks and the rope both have mass. So, total mass of the system is 7+4+5= 16 kg
Force of gravity acts on the system and it always acts downwards, so the force is 16g=160N
Tension is 200 N and it acts in the upward direction, since upward force is greater in magnitude than the downward force, thus the system moves upwards. Applying Newton’s second law here,
F=ma
200160=16a
a=2.5m/s2
So, the value of acceleration is 2.5 m/s2and is moving upwards.
Now to find the tension at the midpoint of the heavy rope, the mass is uniformly distributed of the rope so at midpoint, 2 kg is upside and 2 kg is downside.
T=(7+2)(g+a)
T=9×12.5
T=112.5N
Thus, the tension at the midpoint of heavy rope is 112.5 N

Note: Such problems can be briskly solved using Newton’s equations of motions. we are given the question that the rope is homogeneous which means mass is uniform throughout. Also, we have taken the value of g = 10m/s2.