You pull on a crate with a rope. If the crate moves, the rope's pull on the crate must have been larger than the crate's pull on the rope,
but if the crate does not move, both of these pulls must have been equal.
true or false
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The upward force on the rope is am where a is the acceleration of the rope and crate upwards and m is the mass of the crate (the mass of the rope is negligible).
The downward force on the rope is mg where g is the acceleration due to gravity.
The force T (tension) that the rope exerts equally on the crate and the mass moving the rope is then equal to the sum of the forces acting on it,
T = m(a+g)
The force F that the crate exerts on the rope is equal to mg
If the crate isn't moving, a = 0 and so T = F
If the crate is moving upwwards then a > 0 and T > F
Let the mass of the crate be 'm' then the force on the rope due to gravity due to crate is mg only. If an upward force equal to mg is applied on the rope in the upward direction then the crate will become in equilibrium. An additional force will be required on the rope to move the crate upwards from the ground depending on the acceleration with which the .crate moves upwards. The the upwards pull on the rope has to be larger then the downwards pull due to weight of the crate. The access in force will depend on the acceleration with which the crate is moved upwards. However if the crate is not moved then the upwards pull must be equal to the downwards pull.
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