A truck is carrying a refrigerator that is 2.0 m tall and 0.8 m wide. The centre of mass of the refrigerator is at its geometric centre. It is facing sideways and a short strip on the bed of the truck keeps the refrigerator from sliding. What is the maximum acceleration that the truck can have before the refrigerator begins to tip over?

Question

Quizplus · Accepted Answer

The maximum acceleration before the refrigerator begins to tip over can be calculated using the formula for static equilibrium and tipping points. The tipping point occurs when the line of action of the gravitational force (which goes through the center of mass) reaches the edge of the base. The maximum acceleration $a_{max}$ can be found using the equation derived from the torque balance: $a_{max} = g \cdot \frac{h}{w}$, where $g$ is the acceleration due to gravity (9.8 m/s$^2$), $h$ is the height of the center of mass from the base (1.0 m, half of the total height since the center of mass is at the geometric center), and $w$ is the width of the base (0.8 m). Substituting the given values, $a_{max} = 9.8 \cdot \frac{1.0}{0.8} = 12.25$ m/s$^2$. However, this calculation mistake led to an answer not provided in the options, indicating a misunderstanding in the application of the formula. The correct approach should consider the physical scenario and the principles of rotational equilibrium more accurately. The correct formula for the maximum acceleration before tipping occurs, considering the geometry of the situation, is $a_{max} = g \cdot \frac{w}{2h}$. Correcting the explanation to align with the provided options and the principles of physics, the maximum acceleration is calculated based on the conditions for tipping over, considering the height and width of the refrigerator and the acceleration due to gravity. The correct calculation involves understanding the relationship between the center of mass, the base of support, and the acceleration that causes a shift in the center of mass leading to tipping.

A Truck Is Carrying a Refrigerator That Is 2