Arturo O. answered • 11/17/17
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a = maximum acceleration of truck
f = static friction
m = mass of box = 4 kg
μ = 0.2
The static friction between the truck and the box is what drives the box to accelerate at the same rate as the truck. By Newton's 2nd law,
f = ma
f = μmg ⇒
μmg = ma
a = μg = (0.2)(9.8 m/s2) = 1.96 m/s2
amax = 1.96 m/s2
Note the answer does not depend on the mass of the box.
Arturo O.
In the horizontal direction, the only force acting on the box is static friction f.
f = μmg [you should have seen this in your physics class]
Hence,
F = f
ma = μmg
Report
11/18/17
Gnarls B.
But isn't the net force 0 since the box isn't sliding at that moment?
Report
11/25/17
Arturo O.
Do not confuse the box not sliding as meaning the box is not accelerating. While it is not moving relative to the truck, it is accelerating in the horizontal direction relative to the ground, with the ground at rest. The box is on the truck. The truck is accelerating. Therefore, the box is accelerating. Since it is not sliding on the truck, it is accelerating at the same rate as the truck. It has a net force acting on it by Newton's second law, and that force is the contact force between the surface of the truck and the surface of the box, i.e. the static friction between them. That is what accelerates the box at the rate of the truck. But if the acceleration of the the truck becomes too high, the friction between the truck and the box will not be enough to keep the box from sliding, since the friction depends only on weight and the coefficient of friction, and those are fixed.
Report
11/25/17
Gnarls B.
11/18/17