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Let the mass of the concrete bucket bucket be m then the force due to gravity on the bucket is mg only. If an upward force equal to mg is applied on the bucket then the bucket will become in equilibrium. An additional force will be required to move the bucket upwards from the ground depending on the acceleration with which the bucket moves upwards and that is why one may feel that one has to pull up harder than the bucket pulls down on you. Otherwise is the acceleration is negligible, and that is generally the case, then the upwards force is almost equal to the downwards pull.
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