Optimizing Truck Deceleration to Prevent Crate Sliding

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To prevent a crate from sliding in a truck while decelerating, the required acceleration can be calculated using the coefficient of friction. The formula a = μ(9.8) yields an acceleration of 3.92 m/s² when μ is 0.4. The initial speed of the truck at 20 m/s is irrelevant for determining the necessary deceleration. The focus is solely on the frictional force to maintain the crate's position. Understanding these principles is crucial for optimizing truck deceleration effectively.
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Homework Statement



A crate is sitting on the back of a truck at 20 m/s with a μ of 0.4. With what acceleration can the truck stop without having the crate slide?


Homework Equations



I'm not sure if I am supposed to use this equation:

a = μ(9.8)


The Attempt at a Solution



a = 0.4(9.8) = 3.92 m/s^2.
 
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That is correct, nice job.
 
So is the 20 m/s not needed?
 
That is correct. You are only asked for acceleration (or deceleration in this case), so initial velocity doesn't come into play.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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