HELP Simple center of Gravity problem

In summary, the conversation discusses the calculation of where to support a uniform board in order to balance a 10g mass, a 60kg mass, and a 40kg mass placed 30cm away from the 10g mass. To find the answer, the units are converted to kilograms and meters, and the center of mass equation is used. The correct answer is 0.511m, but the person in the conversation is unsure where they went wrong as they got a higher number.
  • #1
Rha1828
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0
2) A Uniform Boars has a mass of 1.5kg and length of 100cm, Note the Weight is negligible.

A) Where should it be supported so that it will balance a 10g mass places at an end, a 60kg mass on the other end, and a 40kg mass placed 30 cm to the 10g mass?

The answer should be 0.511m


a. First you need to convert all g to kg and cm to m

Therefore,

(10g)(1X10-3kg1g) = 0,010kg

(40g)(1X10-3kg/1g) = 0.040kg

(60g)(1X10-3kg/1g) = 0.060kg

(30cm)(1X10-2m/1cm) = 0.30m

(100cm)(1x10-2m/1cm) = 1.0m

(0cm)(1x10-2m/1cm)= 0 m



Using the center of mass equation you get

Xcg = W1X1 + W2X2 + W3X3 / W1 + W2 + W3
0A


Therefore,

Xcg = (0.010kg)(0m) + (0.060kg)(1.0m) + (0.040kg)(0.30) / (0.010kg) + (0.060kg) + (0.040kg)


= 0.0720kg.m / 0.110 kg

= 0.645 m


I am not sure where I went wrong and why I have a higher number then the answer. Any help would be great!

thank you!
 
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  • #2
Sorry, I don't understand your units. What are they g's or kg? They looked mixed in your use of them.

Also the mass of the board is not insignificant. Is this another typo?
 
  • #3


I would first check your calculations to make sure they are correct. It is possible that you may have made a mistake in converting the units or in the calculations themselves. If you are still getting a different answer, it could be due to rounding errors or a mistake in the given answer. I would also suggest checking the formula you used for center of mass to make sure it is the correct one for this problem. If you are still having trouble, you could consult with a colleague or teacher for assistance. Remember to always double check your work and to use reliable sources for information.
 

1. What is the center of gravity?

The center of gravity is the point at which all the weight of an object is concentrated, and all forces acting on the object can be considered to act through this point.

2. How is the center of gravity determined?

The center of gravity can be determined by finding the balance point of an object, where it would be perfectly balanced if placed on a fulcrum. It can also be calculated by taking the average of all the individual weights and their distances from a reference point.

3. Why is the center of gravity important?

The center of gravity is important because it affects the stability and balance of an object. If the center of gravity is not properly positioned, the object may tip over or become unstable. It is also important in designing structures and vehicles to ensure they are safe and functional.

4. How does the shape of an object affect its center of gravity?

The shape of an object can greatly impact its center of gravity. Objects with irregular shapes or uneven weight distribution will have a more complex center of gravity, while objects with symmetrical shapes and uniform weight distribution will have a simpler center of gravity.

5. Can the center of gravity change?

Yes, the center of gravity of an object can change depending on its position, orientation, or distribution of weight. For example, if an object is picked up and tilted, its center of gravity will shift. Additionally, adding or removing weight from an object will also change its center of gravity.

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