Egyptian laborers built the pyramids probably by dragging enormous stone blocks
ID: 1354113 • Letter: E
Question
Egyptian laborers built the pyramids probably by dragging enormous stone blocks up ramps to elevate them to their proper positions. Answer the following questions if a block with a mass of 2000kg is dragged up a 26° ramp with coefficient of friction 0.4 to a final height of 100m. A predrawn Free Body Diagram is provided.
a. Find the required applied force to move this block up the ramp at constant speed.
b. Calculate the work required in moving the block from the ground to its final position. (The pulling distance is not given. Draw a triangle and use some trigonometry to find it.)
c. Calculate the resulting change in potential energy if there is zero starting at the ground.
d. Calculate the %-loss of the total work expended.
e. If using a ramp results in low efficiency, it would seem that the workers are exhausting themselves by wasting a great deal of their energy in elevating the blocks. Why would they use a ramp at all?
FN FA mgi mgi mg 0)Explanation / Answer
If f = F then the object is moving at a constant speed (or is at rest) as the net force on the object is zero.
F = ma = m g cos
= ( 0.4 ) ( 2000 kg ) (9.8 m/s2 ) cos 26o
= 7046. 5 N
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Work done:
W = F .s
= ( 7046. 5 N ) ( 100 m)
= 7.05 x 105 J
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Change in potential energy:
= .mgsin . h - 0
= (0.4 )( 2000 kg ) (9.8 m/s2 ) sin 26o (100 m)
= 7.05 x 105 J
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