Rotation Kinematics and a stupid fridge

[Jester0722]

Problem as stated:
-A refrigerator is approximately a uniform parallelepiped h = 7 ft tall, w = 4 ft wide, and d = 2 ft deep. It sits upright on a truck with its 4 ft dimension in the direction of travel. Assume that the refrigerator cannot slide on the truck and that its mass is 110 kg. For the first three parts of this problem, the rope shown in the picture is not there.
Question:
-What is the maximum acceleration the truck can have such that the refrigerator does not tip over?
* It gave help hints: (1)Since the fridge is not rotating, the sum of all the torques about an axis through the CM must be zero.(2) for the maximum acceleration, assume that the fridge is just starting to tip, so that the point of contact with the floor of the truck is at the back corner.
Any help would be great.

 

[D H]

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[m2003]

Based on the given information, we can use the principles of rotation kinematics to determine the maximum acceleration that the truck can have without the refrigerator tipping over. First, we need to consider the forces acting on the refrigerator. Since the refrigerator cannot slide on the truck, the only external force acting on it is the normal force from the truck's floor. The weight of the refrigerator, which is equal to its mass multiplied by the acceleration due to gravity, also acts downwards.

Using the first hint, we can set up an equation for the sum of all the torques about an axis through the center of mass (CM) of the refrigerator. Since the refrigerator is not rotating, this sum must be equal to zero. We can choose the axis to be at the point of contact between the refrigerator and the truck's floor, as suggested in the second hint.

Next, we need to consider the direction of the torque caused by the weight of the refrigerator. Since the point of contact is at the back corner, the weight will create a clockwise torque. To counteract this, the normal force from the truck's floor must create an equal and opposite counterclockwise torque.

We can use the equation for torque (torque = force x lever arm) to solve for the maximum acceleration. The lever arm, in this case, is the distance from the point of contact to the back corner of the refrigerator. We know the weight of the refrigerator and can calculate the normal force using the equation for Newton's Second Law (force = mass x acceleration). Setting the two torques equal to each other and solving for the acceleration gives us the maximum acceleration that the truck can have without the refrigerator tipping over.

In summary, we can use the principles of rotation kinematics and the given information to determine the maximum acceleration that the truck can have without the refrigerator tipping over. This can help ensure the safe transportation of the refrigerator and prevent any unwanted accidents.