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

Solution:

Solution in text x =
Solution in text y =
Solution in text z =







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

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




To solve this example are needed these knowledge from mathematics:

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?

Next similar examples:

  1. 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].
  2. Vegan shop
    zemiaky_2 To the shops brought together 23.2 kg of goods, fruits, vegetables and nuts. fruit was 4.7 kg more than vegetables, nuts was 1.5 kg less than the fruit. Determine the amount of fruits, vegetables and nuts.
  3. Candies
    bonbons_10 There are two types of candies in the store at 20 CZK/kg and 80 CZK/kg. How much will be cost a mix if we mix 22kg cheaper and 4kg more expensive candies?
  4. Energy
    energy In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of of 218 kWh. Find the consumption level separating the bottom 45% from the top 55%.
  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 Calculat
  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. Theorem prove
    thales_1 We want to prove the sentense: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  8. 75th percentile (quartille Q3)
    statistics Find 75th percentile for 30,42,42,46,46,46,50,50,54
  9. 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?
  10. 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
  11. 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?
  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. Sequence 3
    75 Write the first 5 members of an arithmetic sequence: a4=-35, a11=-105.
  15. Calculation of CN
    color_combinations Calculate: ?
  16. Final exam
    test_12 There are 5 learners in a class that has written a final exam Aleta scored 55% vera scored 36% and Sibusiso scored 88% if Thoko scored 71% and the class average was 63%. What was Davids score as a percentage?
  17. 5 people
    penize_49 5 people have $122000 and 1 person has $539000 How much should each person (equally) pay?