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 result:

x0 =  -0.9952
y0 =  1.2847
z0 =  -6.7129

Solution:

x1=1;y1=20;z1=3 m1=46 x2=20;y2=2;z2=9 m2=81 x3=9;y3=2;z3=10 m3=59 x4=3;y4=18;z4=14 m4=91 x5=6;y5=12;z5=19 m5=48 x6=5;y6=4;z6=18 m6=72 x7=14;y7=3;z7=19 m7=21 m=m1+m2+m3+m4+m5+m6+m7=46+81+59+91+48+72+21=418  Mx=m1 x1+m2 x2+m3 x3+m4 x4+m5 x5+m6 x6+m7 x7=46 1+81 (20)+59 9+91 3+48 6+72 5+21 (14)=416  My=m1 y1+m2 y2+m3 y3+m4 y4+m5 y5+m6 y6+m7 y7=46 (20)+81 2+59 (2)+91 18+48 (12)+72 4+21 3=537  Mz=m1 z1+m2 z2+m3 z3+m4 z4+m5 z5+m6 z6+m7 z7=46 3+81 9+59 (10)+91 (14)+48 (19)+72 (18)+21 19=2806  x0=Mxm=(416)418=208209=0.9952
y0=Mym=537418=1.2847
z0=Mzm=(2806)418=1403209=6.7129



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
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?

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Here is
    calc 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
  • Complaints
    statistics The table is given: days complaints 0-4 2 5-9 4 10-14 8 15-19 6 20-24 4 25-29 3 30-34 3 1.1 What percentage of complaints were resolved within 2weeks? 1.2 calculate the mean number of days to resolve these complaints. 1.3 calculate the modal number of day
  • Coordinates of a centroind
    triangle_234 Let’s A = [3, 2, 0], B = [1, -2, 4] and C = [1, 1, 1] be 3 points in space. Calculate the coordinates of the centroid of △ABC (the intersection of the medians).
  • 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 gravi
  • City market
    vaha 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
  • Tennis aces
    tenis The number of aces served by Novak Djokovic in the last 20 tournaments that he has participated in, is shown below. 12 17 13 7 8 14 11 14 10 12 15 9 11 13 6 15 18 5 19 24 1.1 using the raw, determine the range. 1.2 Group the data into a frequency distribu
  • 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].
  • Vinegar 2
    ocet How many percentage of getvinegar solution, if we mix to 3.5 liters of 5.8% and 5 liters of 7.6% vinegar?
  • Center
    center_triangle In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].
  • Weight of air
    weighting What is the weight of air in the living room measuring width 10 m length 3 m and height 3.3 m? Air density is ρ = 1.2 kg/m3.
  • Ring
    prsten The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm3. How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3
  • Plasticine ball
    p_balls Plasticine balls have radius r1=85 cm, r2=60 mm, r3=59 cm, r4=86 cm, r5=20 cm, r6=76 mm, r7=81 mm, r8=25 mm, r9=19 mm, r10=14 cm. For these balls
  • Intersections 3
    intersect_circles Find the intersections of the circles x2 + y2 + 6 x - 10 y + 9 = 0 and x2 + y2 + 18 x + 4 y + 21 = 0
  • Pool
    pool If water flows into the pool by two inlets, fill the whole for 19 hours. The first inlet filled pool 5 hour longer than the second. How long pool take to fill with two inlets separately?
  • The triangle
    triangles The triangle is given by three vertices: A [0.0] B [-4.2] C [-6.0] Calculate V (intersection of heights), T (center of gravity), O - center of a circle circumscribed
  • Contestants
    avg_1 In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contestant
  • Normal Distribution
    normal_d At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5?