Center of gravity

The mass points are distributed in space as follows - specify by coordinates and weight. Find the center of gravity of the mass points system:

A1 [14; -2; 5] m1 = 10.2 kg
A2 [-2; -16; 7] m2 = 13.6 kg
A3 [14; 6; 20] m3 = 16.5 kg
A4 [2; 20; 19] m4 = 15.8 kg
A5 [9; -5; 16] m5 = 1.6 kg
A6 [-3; 6; -4] m6 = 3.6 kg
A7 [-20; 12; 19] m7 = 12.5 kg
A8 [-5; -11; -16] m8 = 5.2 kg


Result

x =  1.339
y =  3.587
z =  11.923
=:  0

Solution:

x=10.214+13.6(2)+16.514+15.82+1.69+3.6(3)+12.5(20)+5.2(5)10.2+13.6+16.5+15.8+1.6+3.6+12.5+5.2 x=1.339x = \dfrac{ 10.2\cdot 14 + 13.6\cdot (-2) + 16.5\cdot 14 + 15.8\cdot 2 + 1.6\cdot 9 + 3.6\cdot (-3) + 12.5\cdot (-20) + 5.2\cdot (-5) }{ 10.2 + 13.6 + 16.5 + 15.8 + 1.6 + 3.6 + 12.5 + 5.2} \ \\ x= 1.339
y=10.2(2)+13.6(16)+16.56+15.820+1.6(5)+3.66+12.512+5.2(11)10.2+13.6+16.5+15.8+1.6+3.6+12.5+5.2 y=3.587y = \dfrac{ 10.2\cdot (-2) + 13.6\cdot (-16) + 16.5\cdot 6 + 15.8\cdot 20 + 1.6\cdot (-5) + 3.6\cdot 6 + 12.5\cdot 12 + 5.2\cdot (-11) }{ 10.2 + 13.6 + 16.5 + 15.8 + 1.6 + 3.6 + 12.5 + 5.2} \ \\ y = 3.587
z=10.25+13.67+16.520+15.819+1.616+3.6(4)+12.519+5.2(16)10.2+13.6+16.5+15.8+1.6+3.6+12.5+5.2 z=11.923z = \dfrac{ 10.2\cdot 5 + 13.6\cdot 7 + 16.5\cdot 20 + 15.8\cdot 19 + 1.6\cdot 16 + 3.6\cdot (-4) + 12.5\cdot 19 + 5.2\cdot (-16) }{ 10.2 + 13.6 + 16.5 + 15.8 + 1.6 + 3.6 + 12.5 + 5.2} \ \\ z = 11.923

= 0

Calculated by our linear equations calculator.



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Looking for help with calculating arithmetic mean?
For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc.
Looking for a statistical calculator?

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Centroid - two bodies
    sphere_bar_2 A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravit
  2. Center
    triangle_axis Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[11,4] B[13,-7] C[-17,-18].
  3. Three friends
    vaha_1 Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor.
  4. Life expectancy
    normal_d The life expectancy of batteries has a normal distribution with a mean of 350 minutes and standard deviation of 10 minutes. What the range in minutes 68% of the batteries will last? What is the range in minutes approximately 99.7% of batteries will last?
  5. Harmonic and arithmetic means
    Plot_harmonic_mean The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff: Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20 Calcula
  6. Median and modus
    dice_3 Radka made 50 throws with a dice. The table saw fit individual dice's wall frequency: Wall Number: 1 2 3 4 5 6 frequency: 8 7 5 11 6 13 Calculate the modus and median of the wall numbers that Radka fell.
  7. 75th percentile (quartille Q3)
    statistics Find 75th percentile for 30,42,42,46,46,46,50,50,54
  8. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  9. Standard deviation
    standard-dev_1 Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
  10. Carpenters
    time_15 Carpenters 1 and 2 spend 10 days and 5 days respectively to make one table. If 50 tables were made by the first carpenter and 30 tables were made by the second carpenter, What is the average time spent on the products?
  11. Kerosine and petrol
    kerosene if 4 litres of petrol containing 15% kerosine are added to another 7 litres of petrol containing 10% kerosine, what percentage of the petrol is kerosine?
  12. Average
    chart If the average(arithmetic mean) of three numbers x,y,z is 50. What is the average of there numbers (3x +10), (3y +10), (3z+10) ?
  13. Average speed 4
    uphill Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip?
  14. Box and whisker plot
    box-whisker-plot Construct a box and whisker plot for the given data. 56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43
  15. Std-deviation
    standard-dev Calculate standard deviation for file: 63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90
  16. Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  17. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.