It.is easier to roll a stone up a sloping road than to lift it verticle upwardsbecause???
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If you are lifting a stone on same height then you have to do same amount of work irrespective of any path you follow.
In this case consider that you will take same time for moving the stone at heigh 'h' in both cases .If you are lifting stone vertically upwards then you have to do work against the Gravitational force on stone i.e. 'mg' and displacement will be equal to h. Thefore work done = mg×h (f×s).
Consider 2nd case. Let the slope of road be Q° therefore by considering fbd of stone you have to do work against sine component of Gravitational force i.e. mg sinQ and displacement will be h/sinQ (trignometry)
Thefore work done= mg sin Q ×h/sinQ = mg×h
Note that in first case you need more force than 2nd case since in 2nd force will be divided in 2 components.hence case 1 is difficult than case 2
If you consider frictional force then rolling the stone will require less force than sliding against the frictional force.
In this case consider that you will take same time for moving the stone at heigh 'h' in both cases .If you are lifting stone vertically upwards then you have to do work against the Gravitational force on stone i.e. 'mg' and displacement will be equal to h. Thefore work done = mg×h (f×s).
Consider 2nd case. Let the slope of road be Q° therefore by considering fbd of stone you have to do work against sine component of Gravitational force i.e. mg sinQ and displacement will be h/sinQ (trignometry)
Thefore work done= mg sin Q ×h/sinQ = mg×h
Note that in first case you need more force than 2nd case since in 2nd force will be divided in 2 components.hence case 1 is difficult than case 2
If you consider frictional force then rolling the stone will require less force than sliding against the frictional force.
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