) with the box still on the truck, the truck attains its maximum velocity. as the truck comes to a stop at the next stop light, what is the magnitude of the maximum deceleration the truck can have without the box sliding?
When the truck starts decelerating a force starts acting on a box. In order for the box to start sliding force acting on it has to be bigger than a static force of friction. If the trucks declaration is we have the following force acting on the box: [tex]F=ma[/tex] This force has to be smaller than static friction force: [tex]F_f=mg\mu[/tex] Where [tex]\mu[/tex] is static friction coefficient. Now we can find an answer: [tex]ma\leq mg\mu\\
a\leq g\mu[/tex]
