# Solving Bear on Iceberg: Limit Weight & Stay Safe

• Myvalq
In summary, the problem presents a polar bear sitting on a floating iceberg and asks how close the bear can come to the edge without causing the water to overflow. The dimensions of the iceberg are given as a square with side length a=5m and thickness of 0.5m. Other relevant information includes the density of ice, density of sea water, and weight of the bear. The poster also welcomes the user to the forum and encourages them to share their attempts and challenges in order to receive help.

## Homework Statement

A polar bear is sitting on a floating iceberg. How close can the bear come to the edge of the iceberg, so that the water doesn't overflow the edge of the iceberg yet? Iceberg is a square shaped with side a=5m and thickness is 0,5m. Density of ice is 920kg.m^(-3), density of sea water is 1025kg.m^(-3) and weight of bear is 500kg.

Welcome to PF!

Hi Myvalq ! Welcome to PF!

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Show us what you've tried, and where you're stuck, and then we'll know how to help!

I would approach this problem by considering the principles of buoyancy and stability. The key to solving this problem is to ensure that the weight of the polar bear and the weight of the water displaced by the iceberg are balanced.

First, we need to calculate the weight of the iceberg. The volume of the iceberg can be calculated as V = a^2 * h, where a is the side length and h is the thickness. Plugging in the values given, we get V = 5^2 * 0.5 = 12.5m^3. Since the density of ice is 920kg/m^3, the weight of the iceberg is 12.5m^3 * 920kg/m^3 = 11500kg.

Next, we need to calculate the weight of the water displaced by the iceberg. This can be calculated using the principle of buoyancy, which states that the weight of the displaced fluid is equal to the weight of the object. In this case, the weight of the displaced water is equal to the weight of the iceberg, which we calculated to be 11500kg.

Now, we can calculate the maximum safe distance the polar bear can be from the edge of the iceberg. Since the weight of the bear is 500kg, the total weight of the bear and the displaced water should be less than or equal to the weight of the iceberg. This means that the maximum safe distance is given by the following equation:

500kg + weight of water < 11500kg

Solving for the weight of water, we get 11000kg. This means that the maximum safe distance the bear can be from the edge of the iceberg is when the water level is at 11000kg/m^3.

In conclusion, to ensure the safety of the polar bear on the iceberg, the water level should not exceed 11000kg/m^3. Any closer to the edge of the iceberg, and the water will overflow, potentially causing the bear to fall into the ocean.

## 1. How can we determine the maximum weight limit for a bear on an iceberg?

To determine the maximum weight limit for a bear on an iceberg, we need to consider the weight of the bear, the surface area of the iceberg, and the density of the ice. The maximum weight limit can be calculated by dividing the surface area of the iceberg by the density of the ice. This will give us the total weight that the iceberg can support without sinking.

## 2. What factors can affect the stability of an iceberg with a bear on it?

The stability of an iceberg with a bear on it can be affected by several factors, such as the weight of the bear, the shape and size of the iceberg, the temperature of the water, and the movement of the water. The weight distribution of the bear on the iceberg is also important, as a bear standing in one spot can cause the iceberg to tilt and potentially tip over.

## 3. Is there a safe distance that we should maintain from the edge of the iceberg when a bear is on it?

Yes, it is important to maintain a safe distance from the edge of the iceberg when a bear is on it. This distance can vary depending on the size and shape of the iceberg, but a general rule of thumb is to stay at least 10 feet away from the edge. This will help prevent the iceberg from tipping over and ensure the safety of both the bear and any humans nearby.

## 4. Can we use any materials or techniques to increase the weight limit of an iceberg?

Yes, there are some materials and techniques that can help increase the weight limit of an iceberg. Adding reinforcing materials, such as wooden planks or steel beams, can help distribute the weight of the bear more evenly and increase the weight limit. Additionally, using a technique called "shoring" can help stabilize the iceberg and prevent it from tipping over.

## 5. What precautions should be taken when attempting to solve the bear on iceberg problem?

When attempting to solve the bear on iceberg problem, it is important to take several precautions. First, always assess the stability and weight limit of the iceberg before attempting to add a bear. Use proper equipment and techniques, such as shoring or reinforcing materials, to ensure the safety of both the bear and any humans nearby. It is also important to monitor the movements of the bear and the water, and to maintain a safe distance from the edge of the iceberg. If the iceberg starts to tilt or become unstable, it is important to evacuate the area immediately.