Solution:
Usingthe formulaabove,
Example2:
A librariandisplacesa bookfroman uppershelfto a lowerone. If the verticaldistancebetweenthe two
shelvesis metersand the weightof the bookis Newtons.How muchworkis doneby the librarian?
Solution:
In orderto be able to lift the bookand moveit to its new position,the librarianmustexerta forcethat is at
least equalto the weightof the book.In addition,sincethe displacementis a vectorquantity, then the direction
mustbe takeninto account.So,
meters.
Thus
Herewe say that the workis negativesincethereis a loss of gravitationalpotentialenergyratherthan a
gain in energy. If the bookis liftedto a highershelf,then the workis positive,sincetherewill be a gain in
the gravitationalpotentialenergy.
Example3:
A buckethas an emptyweightof N. It is filled with sandof weight N and attachedto a rope of weight
N/m.Thenit is liftedfrom the floor at a constantrate to a height metersabovethe floor. Whilein
flight,the bucketleakssandgrainsat a constantrate, and by the time it reachesthe top no sandis left in
the bucket.Find the workdone:
- by liftingthe emptybucket;
- by liftingthe sandalone;
- by liftingthe rope alone;
- by the liftingthe bucket,the sand,and the rope together.
Solution:
1.The emptybucket.Sincethe bucket’s weightis constant,the workermustexerta forcethat is equalto
the weightof the emptybucket.Thus