# Center of Mass Rowboat Question

• sweetpete28
In summary: Same answer.In summary, the center of mass of the boy, girl, and empty rowboat system is located 0.0514 m ahead of the center of the empty boat. This can be calculated by using the equation for center of mass and considering the empty boat's mass to be located at the middle of the boat.
sweetpete28

When empty, a 166 kg rowboat is symmetrical. A boy of mass 70.5 kg sits 2.1 m from the center of mass of the rowboat toward the front of the boat, and a girl of mass 68.8 kg sits 2.38 m from the center of mass of the rowboat toward the rear of the boat. Find x, distance from center mass of the emptyt rowboat to the center of mass of the rowboat-plus-kids system.

I know the equation for center of mass [xcm = m1x1 + m2x2 + ... / m1 + m2 + ...] but I don't know where to start since the L of the rowboat is not given.

Welcome to PF,

L of the boat doesn't really matter. The empty boat is symmetric, meaning that its mass is evenly distributed. That means that the centre of mass of the empty boat is right in the middle of the boat (at the geometric centre).

For convenience, you can measure positions from this point i.e. take x = 0 to be at the middle of the boat.

The other thing to note that the centre of mass is the point where you can consider all the mass to be located (i.e. the system is equivalent to a single mass at that point, in some sense). Therefore, the entire mass of the boat can be considered to be located at x = 0. That takes care of one of the three masses. The other two (the boy and the girl) are located at the stated positions relative to x = 0. So, you can solve for the position of centre of mass of this three-body system, which is what the problem is asking for.

Thanks! That's what I thought, but I wasn't sure...

Ok. So: [(0)(166) + (2.1)(70.5) + (-2.38)(68.8)] / [166 + 70.5 + 68.8] = -.0514

So magnitude of distance b/t center of mass of empty boat and center of mass of rowboat + kids system = .0514...right?

sweetpete28 said:
Thanks! That's what I thought, but I wasn't sure...

Ok. So: [(0)(166) + (2.1)(70.5) + (-2.38)(68.8)] / [166 + 70.5 + 68.8] = -.0514

So magnitude of distance b/t center of mass of empty boat and center of mass of rowboat + kids system = .0514...right?

I think that's the right way to do it.

A check that gives me confidence in your answer: say instead of using the COM of the empty boat as x = 0, we instead decide to use the half-way point between the boy and the girl as x = 0. In this case, since the distance between them is 4.48 m, the half-way point is 2.24 m back from where the boy is. This means that the centre of the boat is 0.14 m ahead of the half-way point between the boy and the girl, like so:

Code:
B|------|----|-----------|G
COM  x=0

Using this different coordinate system, the expression for the centre of mass is:

(2.24*(70.5) + (-2.24)*(68.8) + 166*(0.14)) / (70.5 + 68.8 + 166)

= 0.0885948248

So the centre of mass of the total system is 0.089 m ahead of the half-way point between the two people. This means its distance from the centre of the boat is:

0.14 - 0.0885948248 = 0.0514051752

## 1. What is the "Center of Mass Rowboat Question"?

The "Center of Mass Rowboat Question" is a thought experiment that involves a rowboat with two people sitting on opposite ends. The question asks whether the rowboat will tip over when one person moves towards the center of the boat.

## 2. Why is this question important in science?

This question is important in science because it teaches us about the concept of center of mass and how it affects the stability of objects. Understanding center of mass is crucial in fields such as physics and engineering.

## 3. How can we determine the center of mass of an object?

The center of mass of an object can be determined by balancing the object on a point and drawing a vertical line from the point to the ground. The point where the object balances is the center of mass.

## 4. What factors affect the stability of an object's center of mass?

The stability of an object's center of mass is affected by the distribution of mass and its shape. Objects with a wider base and lower center of mass are more stable than those with a narrow base and higher center of mass.

## 5. How does the "Center of Mass Rowboat Question" relate to real-world situations?

The "Center of Mass Rowboat Question" can be applied to real-world situations, such as designing stable structures or balancing loads on vehicles. It also helps us understand the concept of balance and stability in various objects and systems.

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