Question

A truck is carrying a 120-kg refrigerator, which is 2.20 m tall and 85.0 cm wide has its center of mass at its geometrical center. The refrigerator 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?

Answer 1

The maximum acceleration that the truck can have before the refrigerator begins to tip over is calculated using the tipping point at which the force of gravity causes a greater torque than the force of friction. Using the given dimensions and the constant for gravity, the maximum acceleration is found to be 1.89 m/s².

Step-by-step explanation:

The maximum acceleration that the truck can have before the refrigerator begins to tip over can be calculated using the concepts of torque and static equilibrium. The tipping point occurs when the torque caused by the refrigerator's weight about the point of rotation (the edge of the short strip) exceeds the stabilizing torque due to the friction between the refrigerator and the truck bed. The refrigerator will start to tip when the component of the gravitational force acting to rotate it about its edge equals the force of friction acting to keep it in place. Assuming no slipping occurs due to the strip, the maximum acceleration (a_max) can be found using the formula:

a_max = (g * width) / (2 * height)

where g is the acceleration due to gravity (9.81 m/s²), width is the width of the refrigerator (0.85 m), and height is the height to the center of mass (1.10 m, which is half its total height). Substituting the values, we get:

a_max = (9.81 m/s² * 0.85 m) / (2 * 2.20 m) = 1.89 m/s²

Hence, the maximum acceleration without tipping is 1.89 m/s².

Answer 2

The maximum acceleration that the truck can have before the refrigerator begins to tip over is 3.79 m/s^2

Step-by-step explanation:

Mass of refrigerator, m = 120 kg

Refrigerator height, h = 2.2 m

Width of refrigerator, w = 85 cm = 0.85 m

acceleration due to gravity, g = 9.81 m/s^2

From the principles of moments, the refrigerator will start to tip at the point when the forces are balanced at the edge of the width.

Therefore, taking moments about the edge, where the weight acts at the geometric center, we have

m×g×w/2 = m×a×h/2

120×9.81×0.85/2 = 120×a×2.2/2

or a = 3.79 m/s^2