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Questions regarding a workman's toolbox

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A workman carries a sheet of metal up to the roof of a skyscraper by transporting it in the building's elevator. Inside the elevator, the metal sits at an angle of 26o from the horizontal. The workman absentmindedly places his toolbox on the smooth metal surface, and it begins to slide with negligible friction.

a. Draw a free-body diagram for the toolbox.
b. Before the elevator starts to move, what is the acceleration of the toolbox along the
metal surface?
c. When the elevator is accelerating upward at 0.40 g (that is, at 40% of the acceleration due to gravity), the toolbox feels a normal force of 130 N. What is the mass of the toolbox?
d. If the toolbox feels a normal force of 80 N, find the acceleration of the elevator.
e. Could the elevator accelerate in such a way that the toolbox will not accelerate along the metal surface at all? If so, find the acceleration of the elevator; if not, explain why not.

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This solution helps answer various questions regarding a workman's toolbox. Free body diagrams for the toolbox are given.

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A workman carries a sheet of metal up to the roof of a skyscraper by transporting it in the building's elevator. Inside the elevator, the metal sits at an angle of 26O from the horizontal. The workman absentmindedly places his toolbox on the smooth metal surface, and it begins to slide with negligible friction.
a. Draw a free-body diagram for the toolbox.
b. Before the elevator starts to move, what is the acceleration of the toolbox along the
metal surface?
c. When the elevator is accelerating upward at 0.40 g (that is, at 40% of the acceleration due to gravity), the toolbox feels a normal force of 130 N. What is the mass of the toolbox?
d. If the toolbox feels a normal force of 80 N, find the acceleration of the elevator.
e. Could the elevator accelerate in such a way that the toolbox will not ...

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