Resultant force

Calculate mathematically and graphically the resultant of a three forces with a common centre if:

F1 = 50 kN α1 = 30°
F2 = 40 kN α2 = 45°
F3 = 40 kN α3 = 25°

Correct result:

F =  113.1225 kN
f =  65.613 °

Solution:

F1=50 kN F2=40 kN F3=40 kN a1=30 a2=a1+45=30+45=75 a3=a2+25=75+25=100 x=F1 cosa1+F2 cosa2+F3 cosa3=F1 cos30 +F2 cos30 +F3 cos30 =50 cos30 +40 cos30 +40 cos30 =50 0.866025+40 0.866025+40 0.866025=46.7081 y=F1 sina1+F2 sina2+F3 sina3=F1 sin30 +F2 sin30 +F3 sin30 =50 sin30 +40 sin30 +40 sin30 =50 0.5+40 0.5+40 0.5=103.02934  F=x2+y2=46.70812+103.02932=113.1225 kN
f=180πarctan(y/x)=180πarctan(103.0293/46.7081)=65.613=653647"



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
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.
Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

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
  • Two forces
    vector-add Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
  • Forces
    vectors_4 Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant?
  • Two forces
    forces_1 The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
  • Triangle
    sedlo Triangle KLM is given by plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3]. Calculate its area and its interior angles.
  • Three vectors
    vectors_sum0 The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point so that they are in balance. Determine the angles of the each two forces.
  • Forces
    ijk In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
  • Bearing
    compass A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
  • Angle of the body diagonals
    body_diagonals_angle Using vector dot product calculate the angle of the body diagonals of the cube.
  • Triangle SAS
    triangle_iron Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
  • Space diagonal angles
    kvadr_diagonal Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28cm, b = 45cm and c = 73cm. Then, find the angle between the body diagonal and the plane of the base ABCD.
  • Airplane navigation
    triangle_airplane An airplane leaves an airport and flies to west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
  • Distance of points
    jehlan_4b_obdelnik_1 A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S.
  • Square pyramid
    pyramid_4 Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
  • Cube - angles
    cube_diagonal_1 Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
  • Cone
    cone-blue Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
  • Right triangle
    right_triangles Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.