The force exerted by the rope is 132 N.
Explanation:
It is known that the external force applied on any object is directly proportionate to the products of mass of the object and the acceleration attained by the object. So, here, the object is a barrel of mass 12 kg. It is given that barrel is pulled by a rope. So tension force will be acting on the rope during pulling the barrel.
As the barrel is being pulled up with an acceleration of [tex]1.2 \mathrm{m} / \mathrm{s}^{2}[/tex], the force required to attain this acceleration is the net force on the barrel. But there is gravitational force which will also be acting on the barrel in opposing direction to the tension force of the rope.
Thus the net force experienced by the barrel is difference between the tensional force exerted by the rope on the barrel in upward direction and the gravitational force on the barrel in downward direction.
[tex]\text { Net force on the barrel }=\text { Force exerted by the rope - force exerted by gravity }[/tex]
[tex]\text {Force exerted by the rope}=\text {Net force on the barrel }+\text { Force exerted by gravity }[/tex]
As,
[tex]\text { Net force on the barrrel }=\text { Mass } \times \text { Upward acceleration }[/tex]
[tex]\text { Net force acting on the barrrel }=12 \times 1.2=14.4 \mathrm {N}[/tex]
Similarly,
[tex]\text {Force exerted by gravity on barrel}=\text {Mass} \times \text {Acceleration due to gravity}[/tex]
[tex]\text { Net force acting on the barrrel }=12 \times 9.8=117.6 \mathrm{N}[/tex]
Thus, force exerted by the rope=14.4 N + 117.6 N = 132 N
