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 [1; -20; 3] m₁ = 46 kg
A₂ [-20; 2; 9] m₂ = 81 kg
A₃ [9; -2; -10] m₃ = 59 kg
A₄ [3; 18; -14] m₄ = 91 kg
A₅ [6; -12; -19] m₅ = 48 kg
A₆ [5; 4; -18] m₆ = 72 kg
A₇ [-14; 3; 19] m₇ = 21 kg

Correct answer:

x₀ =  -0.9952
y₀ =  1.2847
z₀ =  -6.7129

Step-by-step explanation:

$y_0={\displaystyle \frac{M_y}{m}}={\displaystyle \frac{537}{418}}=1\frac{119}{418}=1.2847$

$z_0={\displaystyle \frac{M_z}{m}}={\displaystyle \frac{(-2806)}{418}}=-{\displaystyle \frac{1403}{209}}=-6\frac{149}{209}=-6.7129$

Try another example

Related math problems and questions:

• Speed of Slovakian trains
  Rudolf decided to take the train from the station 'Ostratice' to 'Horné Ozorovce'. In the train timetables found train Os 5409 : km 0 Chynorany 15:17 5 Ostratice 15:23 15:23 8 Rybany 15:27 15:27 10 Dolné Naštice 15:31 15:31 14 Bánovce nad Bebravou 15:35 1
• The raw
  The raw data presented here are the scores (out of 100 marks) of a market survey regarding the acceptability of new product launched by a company for random sample of 50 respondents: 40 45 41 45 45 30 30 8 48 25 26 9 23 24 26 29 8 40 41 42 39 35 18 25 35
• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• Standard deviation
  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
• Chickens and rabbits
  In the yard were chickens and rabbits. Together they had 18 heads and 56 legs. How many chickens and how many rabbits were in the yard?
• City market
  Apples were sold at contractual prices at the city market. Calculate the average price of 1 kg of apples sold: Stand, Sale kg, Price CZK/kg 1 325 6.20 2 194 7.00 3 258 6.50 4 870 5.90 5 275 6.40
• Here is
  Here is a data set (n=117) that has been sorted. 10.4 12.2 14.3 15.3 17.1 17.8 18 18.6 19.1 19.9 19.9 20.3 20.6 20.7 20.7 21.2 21.3 22 22.1 22.3 22.8 23 23 23.1 23.5 24.1 24.1 24.4 24.5 24.8 24.9 25.4 25.4 25.5 25.7 25.9 26 26.1 26.2 26.7 26.8 27.5 27.6 2
• CoG center
  Find the position of the center of gravity of a system of four mass points having masses, m₁, m₂ = 2 m1, m₃ = 3 m1, and m₄ = 4 m₁, if they lie at the vertices of an isosceles tetrahedron. (in all cases, between adjacent material points, the distance
• Barrel with liquid
  Barrel with grain weight 297 kg. When it shed 48% of grain, ha weight 174 kg. What is the weight of empty barrel?
• Dataset:
  Dataset: 35 22 18 54 22 46 28 31 43 22 14 17 25 19 33 14. 1 Group the data into a grouped distribution using 6 classes of equal width. 2. Determine the mean, median, and mode using the raw data. 3. Draw an Ogive curve corresponding to the data and use it
• Dried fruit
  The manufacturer produces a mixture of dried fruit. He purchased: 10kg pineapple for 200 Kc/kg 2kg papaya for 180 kc/kg 1kg of banana for 400 Kc/kg How many kgs of raisin for 80 Kc/kg must be put into the mix by the manufacturer so that the production pri
• Barrel with water
  The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
• Centroid - two bodies
  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 gravi
• Reverse Pythagorean theorem
  Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ... Δ DEF: 55 dm, 82 dm, 61 dm ... Δ GHI: 24 mm, 25 mm, 7 mm ... Δ JKL: 32 dm, 51 dm, 82 dm ... Δ MNO: 51 dm, 45 dm,
• Barrel 3
  Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel?
• Car
  At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.)
• Candies
  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?