# How to find the center of mass and unknown weight

• JakeD23
In summary, the man and woman, with masses of 65 kg and 57 kg respectively, are initially positioned 4.0 m apart on a canoe with a mass of 38 kg. When they switch places, the canoe shifts a distance of 0.20 m relative to the water. Using the equation mr=Ʃmiri and the known positions of the individuals and the canoe, the woman's mass can be found to be 57 kg.
JakeD23

## Homework Statement

A canoe of mass 38 kg lies at rest in still water. A man and a woman are at opposite ends of the canoe 4.0 m apart and symmetrically located with respect to the canoe’s centre (which is also its centre of mass). The mass of the man is 65 kg and the woman’s mass is smaller.

The two people then change places and the man observes that the canoe shifts a distance 0.20 m relative to the water. What is the woman’s mass? [57 kg]

mr=Ʃmiri

## The Attempt at a Solution

I'm guessing the solution is found through a quadratic. I tried substituting in the know data for before and after the boat and making the position of the center of mass negative for the second equation but nothing seemed to help. I've done the problem 4 times and am no closer to solving it no matter how I visual the problem. I just can't seem to find the right answer

Last edited:

ehild

mman⋅xman+mwoman⋅xwoman+mcanoe⋅xcanoe=(mman+mwoman+mcanoe)⋅xcm
mman<mwoman
mman⋅(xman+4m+0,20m)+mwoman⋅(xwoman-4m+0,20m)+mcanoe⋅(xcanoe+0,20m)=(mman+mwoman+mcanoe)⋅xcm
mman>mwoman
mman⋅(xman+4m-0,20m)+mwoman⋅(xwoman-4m-0,20m)+mcanoe⋅(xcanoe-0,20m)=(mman+mwoman+mcanoe)⋅xcm
mman⋅xman+mwoman⋅xwoman+mcanoe⋅xcanoe=mman⋅(xman+3,8m)+mwoman⋅(xwoman-4,2m)+mcanoe⋅(xcanoe-0,20m)

## 1. How do I find the center of mass of an object?

The center of mass of an object can be found by balancing the object on a pivot point and marking the point where it balances. This point is the center of mass.

## 2. What is the formula for calculating the center of mass?

The formula for calculating the center of mass is: xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn), where xcm is the center of mass, m is the mass of each individual part, and x is the distance of each part from a chosen reference point.

## 3. How do I find the unknown weight of an object using the center of mass?

To find the unknown weight of an object using the center of mass, you will need to know the mass and distance from the reference point of at least one other part of the object. Using the formula for calculating the center of mass, you can solve for the unknown weight.

## 4. Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object. This can occur when the object is irregularly shaped or has a non-uniform mass distribution. It is important to remember that the center of mass represents the average location of the object's mass and may not always be located within the physical boundaries of the object.

## 5. How can I use the center of mass to determine stability?

The center of mass can be used to determine stability by analyzing its position relative to the object's base of support. If the center of mass is located above the base of support, the object will be stable. However, if the center of mass is located outside of the base of support, the object will be unstable and may tip over.

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