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A certain computer hard disk drive is rated to withstand an acceleration of 100g without damage. Assuming the drive decelerates through a distance of 2 mm when it hits the ground, from how high can you drop the drive without ruining it?

A  certain  computer   hard  disk  drive  is  rated  to  withstand   an acceleration   of  100g without  damage.  Assuming   the drive decelerates  through  a distance  of 2 mm  when it hits the ground, from how high  can you drop the drive without  ruining  it?

Grade:10

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
From the equation of kinematics, we have
235-164_83.PNG
Where vy represents the final speed of the disk, a is its acceleration, v0y the initial speed and t the time taken by the disk to attain the final speed vy.
From the second equation, the time t is given as:
235-77_84.PNG
Substitute the value in first equation

235-341_85.PNG
Since the disk accelerates under the action of gravity and we take the convention of downward motion to be positive, we can equate a = g in the equation above as:
235-1174_86.PNG
Substitute the given value of v0y to be zero, the above equation can be written as:
235-1023_87.PNG
Assume that the distance travelled by the disk during collision is y’, the speed of the disk just before the contact is v’oy, and the final speed after the collision is v’y , such that the disk experience an acceleration a , then equation (1) can be written as:
235-624_88.PNG
Since the disk will come to rest after colliding, hits final speed v’y is zero. Also the initial speed before collision is equal to vy calculated above.
Given that the disk crushes to a depth of 2 mm, the height y’ can be equated to it.
Substitute the appropriate values in the equation above

235-1828_89.PNG
Therefore if the disk is thrown from height the disk will start to damage, therefore the person can throw the disk from any height which is less than 0.2 m and avoid damaging it.

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