Effect of centre of gravity on lift & calculations

Centre of gravity

Weight of a body is acting at a single point is known as it's centre of gravity. Where we can experience all weight of the body is acting in a single point downwards to the earth . 

Effect of centre of gravity on lift

  For simple lifts with one upper lifting hook block always position above the centre of gravity for stable lifting.

If the body is lifting without the consideration of C.O.G point , it will align itself to maintain the centre of gravity . In most of the case it will  take a position itself liner towards the hoisting hook.

Calculation of the center of gravity (Method 1)

Calculation of the center of gravity is based on the fact that a torque exerted by the weight of a system is the same as if it's total weight were located at the center of gravity. This point is the average or mean of the distribution of the moment arms of the object.

The calculation of the center of gravity of an object involves the summation of the weights times their separations from a starting point divided by the total weight of the object.

In the case of a highly irregular object, the weights can consist of individual particles or even atoms. Calculus is then used to integrate the product of these weights and the differential separations.

If the object is made up of regular parts, such as squares or circles, you can use the fact that each has a CG at its geometric center. This is seen in the illustration below:



Calculating CG of weights

The center of gravity in the illustration is at the following separation from the arbitrary zero-point:


CG = (aM + bN + cP)/(M + N + P)

For example, if:
a = 1 ft
b = 4 ft
c = 8 ft
M = 1 lb
N = 2 lb
P = 4 lb


CG = (1*1 + 4*2 + 8*4)/(1 + 2 + 4)

CG = 41/7

CG = 5.9 ft from the zero point

The approximate CG is shown in the illustration.

How to calculate centre of gravity (method 2)

1. Calculate the weight of the object. When you're calculating the center of gravity, the first thing you should do is to find the weight of the object. Let's say that you're calculating the weight of a see-saw that has a mass of 30 lbs. Since it's a symmetrical object, its center of gravity will be exactly in its center if it's empty. But if the see-saw has people of different masses sitting on it, then the problem is a bit more complicated.
   
2. Calculate the additional weights. To find the center of gravity of the see-saw with two children on it, you'll need to individually find the weight of the children on it. The first child has a mass of 40 lbs. and the second child's is 60 lbs.
   
3. Choose a datum. The datum is an arbitrary starting point placed on one end of the see-saw. You can place the datum on one end of the see-saw or the other. Let's say the see-saw is 16 feet long. Let's place the datum on the left side of the see-saw, close to the first child.
   
4. Measure the datum's distance from the center of the main object as well as from the two additional weights. Let's say the children are each sitting 1 foot away from each end of the see-saw. The center of the see-saw is the midpoint of the see-saw, or at 8 feet, since 16 feet divided by 2 is 8. Here are the distances from the center of the main object and the two additional weights form the datum:
   • Center of see-saw = 8 feet away from datum.
   • Child 1 = 1 foot away from datum
   • Child 2 = 15 feet away from datum
     
5. Multiply each object's distance from the datum by its weight to find its moment.This gives you the moment for each object. Here's how to multiply each object's distance from the datum by its weight:
   • The see-saw: 30 lb. x 8 ft. = 240 ft. x lb.
   • Child 1 = 40 lb. x 1 ft. = 40 ft. x lb.
   • Child 2 = 60 lb. x 15 ft. = 900 ft. x lb.
     
     
     
6. Add up the three moments. Simply do the math: 240 ft. x lb. + 40 ft. x lb. + 900 ft. x lb = 1180 ft. x lb. The total moment is 1180 ft. x lb.
   
7. Add the weights of all the objects. Find the sum of the weights of the seesaw, the first child, and the second child. To do this, add up the weights: 30 lbs. + 40 lbs. + 60 lbs. = 130 lbs.
   
8. Divide the total moment by the total weight. This will give you the distance from the datum to the center of gravity of the object. To do this, simply divide 1180 ft. x lb. by 130 lbs.
   • 1180 ft. x lb. ÷ 130 lbs = 9.08 ft.
   • The center of gravity is 9.08 feet from the datum, or measured 9.08 feet from the end of the left side of the see-saw, which is where the datum was placed.