How Do You Calculate the Center of Mass for a Club-Ax?

In summary, the Alley club-ax has a symmetrical 8 kg stone attached to the end of a uniform 2.5 kg stick. The center of mass of the system is located at 77.3 cm from the handle's end, with the coordinate system starting from the handle's end. This can be calculated using the formula xm=(mhxh+msxs)/(mh+ms), where xh is the handle's length and xs is the length of the stone.
  • #1
kathyt.25
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Homework Statement


"Alley club-ax consists of a symmetrical 8 kg
stone that is 18cm long, and is attached to the end of a uniform 2.5 kg
stick that is 98 cm long."

Homework Equations


cm = centre of mass

x(cm) = x1m1 + m2x2 / (m1+m2)


The Attempt at a Solution


m1=8
m2=2.5

x1=9
x2=40

This seems like a very straightforward question, but I can't seem to get it right... the answer is 77.3cm from the handle's end, and I keep on getting 18.52cm which is WAY off!
 
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  • #2
Formula is good, but the data you have put in it isn't. You say that the solution is 77.3 cm from the handle's end. Handle length is 80 cm and length of a stone is 18.
First, you have to define the coordinate system. In this case, we'll say that coordinate system starts from the handle's end. That means that the handle's CM is located at 40 cm (xh=40cm). CM of the stone is at 89 cm because coordinate system starts from the handle's end, so you have to add handle's length which is 80 cm plus 9 cm from the stone (xs=89cm).

xm=(mhxh+msxs)/(mh+ms)=(2.5*40+8*89)/(2.5+8)=77,3333cm
 
  • #3




Finding the center of mass in this situation requires using the equation x(cm) = (x1m1 + x2m2) / (m1+m2). In this case, we have two masses, the 8 kg stone and the 2.5 kg stick, with their respective distances from the handle being 18 cm and 98 cm. Plugging in the values, we get x(cm) = (18 cm * 8 kg + 98 cm * 2.5 kg) / (8 kg + 2.5 kg) = 77.3 cm. This is the correct answer and is located 77.3 cm from the handle's end. It is important to carefully check your calculations and units to ensure accuracy in solving for the center of mass.
 

FAQ: How Do You Calculate the Center of Mass for a Club-Ax?

1. What is the definition of centre of mass?

The centre of mass is the point at which an object's mass can be considered to be concentrated and from which all external forces act on the object.

2. How do you calculate the centre of mass?

The centre of mass can be calculated by finding the weighted average of the individual masses of all the particles that make up an object, with their respective positions taken into account.

3. Why is finding the centre of mass important?

Finding the centre of mass is important because it helps in understanding the overall motion and stability of an object, as well as predicting how it will respond to external forces.

4. Can the centre of mass be outside of an object?

Yes, the centre of mass can be outside of an object if the object has an irregular shape or if it is made up of multiple parts with varying masses.

5. How does the centre of mass relate to an object's balance?

The centre of mass is directly related to an object's balance. If the centre of mass is located above the base of support, the object will be in stable equilibrium. If the centre of mass is outside the base of support, the object will be in unstable equilibrium.

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