[physical]

HI
At time t = 0 a block rests on a plate as shown, and the spring is unstretched. The initial position of the plate is s = 0. If the plate moves according to the equation shown, find the s coordinate at the moment when the block slips with respect to the plate.

In the equation, s is in metres and t is in seconds.





Note that the equation fully describes the motion of the plate. Depending on your numerical values, the plate might start moving to the RIGHT or to the LEFT. Also, be on your guard because slip can occur at ANY TIME if the required static friction force exceeds the maximum possible value.

[المتفيزق]

it is very easy ...
just have the accelleration differentiate s with respect to time twice to have a= 15t -2.6 m/s2
now ma = Fspring-friction
Fspring = -k. s
F friction = -mu. mg
as magnitudes:
Ftotal =k.s + mu.mg
now for the block to slip ma must be greate than F
we take the time when they are just equal ; i.e. Ftotal =ks + mu.mg = m(15t -2.6)
now solve to have t
once having t you can easily compute s from the equation s=2.5t^3-1.3t^2
and that is it .
والله اعلم

[physical]

Thank you very much

[المتفيزق]

for nothing... in fact, in spite of being easy, it is a good question...
thanks again...