Question:
a block of metal is lying on the floor of a bus.the maximum acceleration which can be given to the bus so the block remains at rest will be
Answer:
As the box lies on the floor of the bus, there is frictional force. We know that the static friction fs <= µs N where µs is the coefficient of static friction and N is the normal reaction (which is mg if m is the mass of the box)
This static frictional force should be balanced with the external force applied to the bus. Let this force be represented by F which is ma, product of mass and acceleration
Hence, F = fs
<= µs N
ma <= µs (mg)
a <= µs g
Maximum value of acceleration occurs at equal to condition. Hence, amax = µs g gives the maximum acceleration which can be given to the bus so that the block remains at rest.
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