Question

Can you explain me the reasoning behind this statement: "A box suspended by a rope is pulled to one side by a horizontal force. The tension in the rope is greater than before."

Answer 1

the horizontal force will move the block tangentially,

and this can be considered tangent to a circular path,

hence it can be said that the object goes ina pseudo circular path,

hence tension is greater,
bcoz of circular path, mv^2/r

force will also be there

Answer 2

A rope, chain, etc. transmits the applied force (in this case, pull) via electromagnetic interactions between the atoms. The displaced atoms pull on the atoms behind them, and so on until the force is communicated to the object, and thus the rope is stretched.

Answer 3

Then Newton's second law states the net force on a particle is equal to the time rate of change of its linear momentum p in an inertial reference frame:
\[F=\frac{dp}{dt}=\dfrac{mv}{dt}\]
where, since the law is valid only for constant-mass systems, the mass can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus
\[F=m\frac{dv}{dt}=ma\]
where F is the net force applied, m is the mass of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it.
Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems.

Answer 4

@trex

but the applied force is horizontal, and hence it produces acceleration in horizontal direction,

whicjh is not the cause of increase in tension,

Answer 5

Consider an object hanging freely
The magnitude of the force of tension in the rope is equal and opposite the force of gravity. Let's label the up direction positive y and the right direction positive x.\[|\overrightarrow{F_g}|=|\overrightarrow{T}|=mg\overrightarrow{y}\]