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.

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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,

ie

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

**answer: true**