A box of mass 50 kg lies on the bed of truck traveling at 25 m/s. The coefficient of static friction between?

Question

the bed and box is 0.40. What is the maximum magnitude of deceleration that keeps that box from sliding across the bed?

Answer 1

The initial velocity is irrelevant. All that matters is acceleration (or deceleration, which is acceleration in the opposite direction).

If the box has a mass of 50 kg, the force of gravity on it is
50 kg x 9.8 N / kg = 490 N

And the maximum force that the truck bed can exert on the box is .40 x 490 = 196 N.

196 Newtons is the amount of force required to accelerate the 50 kg box at a rate of 196 / 50 = 3.92 m/sec.

So the maximum rate of deceleration that can occur before the box starts sliding is 3.92 m/sec, which is 0.4 g's. And when you really analyze it, it turns out that it doesn't matter what the mass of the box is. The answer (in terms of g's) is always equal to the coefficient of friction (0.4).

Incidentally, that rate of acceleration would get you from 0 to 60 (or 60 to 0) in about 7 seconds, which is pretty quick, but not really extreme.