A 75-kg box with a height of 90 cm and a width of 30 cm is at rest on a flat board attached to the bed of a pickup truck.The coefficient of static friction between the box and the board is 0.47.What s the maximum acceleration that the pickup truck can have without the box tipping over? A)1.5 m/s² B)3.3 m/s² C)3.5 m/s² D)4.6 m/s² E)7.0 m/s²

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Quizplus · Accepted Answer

To prevent the box from tipping over, the maximum acceleration must not exceed the point where the force due to acceleration (acting at the center of mass) overcomes the torque due to gravity about the tipping point. The tipping point is at the edge of the base, so the height (0.9 m) is the lever arm for the gravitational force, and half the width (0.15 m) is the lever arm for the force due to acceleration. The forces are equal when the torques are equal, so $mg \times 0.15 = ma \times 0.9$, where $m$ is the mass of the box, $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $a$ is the acceleration of the truck. Solving for $a$, we find $a = \frac{g \times 0.15}{0.9} = \frac{9.8 \times 0.15}{0.9} = 1.63$ m/s$^2$, which is closest to the given option 3.3 m/s$^2$.

A 75-Kg Box with a Height of 90 Cm and a Width