# Center of Mass for 8 kg Stone & 2.5 kg Stick

• tascja
In summary, the problem involves determining the center of mass of a symmetrical club-ax consisting of an 8 kg stone and a 2.5 kg stick that is 98 cm long. To find the center of mass, you can take the integral of the handle and add the moment of the stone at the end, using the formula Xcm = (xh*mh + L*ms)/(mh + ms).
tascja

## Homework Statement

alley club-ax consists of a symmetrical 8 kg stone attached to the end of a uniform 2.5 kg stick that is 98 cm long. How far is the center of mass from the angle end of the club-ax?

## Homework Equations

Xcm = (sum) x*m / m

## The Attempt at a Solution

I don't know how to approach this.. do i put the ax on a coordinate plane?
and it says that it is it is symmetrical and of uniform weight, does that give extra information that i should be using?

Not sure which is the angle end, but say it is the handle. You can reverse it if not.

The handle is .98m and uniform density. You could take the integral of that to find the center of mass of just the handle, but I'm sure you know already it's in the middle for the handle part. To complete the sum of the moments for the whole shillelagh, then add the moment of the stone at the end.

So with ms the mass of the stone, mh the mass of the handle, and xh the center of mass of the handle,

Xcm = (xh*mh + L*ms)/(mh + ms)

As a scientist, we can approach this problem by using the formula for calculating the center of mass: Xcm = (sum) x*m / m. In this case, the "x" represents the distance from the reference point (in this case, the angle end of the club-ax) to the center of mass, and "m" represents the mass at that distance.

Since the club-ax is symmetrical, we can assume that the center of mass is located at the midpoint of the stick, which is 49 cm from the angle end. Therefore, we can plug in the values for the mass and distance into the formula:

Xcm = (8 kg * 49 cm + 2.5 kg * 49 cm) / (8 kg + 2.5 kg)

Simplifying, we get Xcm = (392 cm + 122.5 cm) / 10.5 kg = 50.24 cm.

Therefore, the center of mass for this club-ax is located 50.24 cm from the angle end of the club-ax. This information can be useful for understanding the balance and stability of the club-ax and its potential for use in activities such as chopping wood or playing a game of golf.

## 1. What is the formula for calculating the center of mass for an object?

The formula for calculating the center of mass for an object is:
x = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn)
y = (m1y1 + m2y2 + ... + mny2) / (m1 + m2 + ... + mn)
Where m represents the mass of each individual component and x and y represent the coordinates in the x and y directions, respectively.

## 2. How do you determine the center of mass for an irregularly shaped object?

To determine the center of mass for an irregularly shaped object, you can use the principle of moments. This involves suspending the object from a point and finding the intersection of the lines of action for the forces acting on the object. This point is the center of mass.

## 3. What units are used to measure the center of mass?

The center of mass is typically measured in meters (m) or centimeters (cm) for the x and y coordinates. The mass of each individual component is typically measured in kilograms (kg).

## 4. How does the distribution of mass affect the position of the center of mass?

The distribution of mass in an object affects the position of the center of mass. An object with more mass in one area will have a center of mass closer to that area. If the mass is evenly distributed, the center of mass will be at the geometric center of the object.

## 5. What is the significance of the center of mass for an object?

The center of mass is an important concept in physics as it helps determine an object's stability, balance, and motion. It also plays a role in understanding the forces acting on an object and predicting its behavior.

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