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:

$$\begin{gathered} F_1=50\text{ kN } \\ {F}_2=40\text{ kN } \\ {F}_3=40\text{ kN } \\ {a}_1=30^{\circ } \\ {a}_2=a_1+45=30+45=75^{\circ } \\ {a}_3=a_2+25=75+25=100^{\circ } \\ x=F_1\cdot \cos a_1^{\circ }+F_2\cdot \cos a_2^{\circ }+F_3\cdot \cos a_3^{\circ }=F_1\cdot \cos 30^{\circ }+F_2\cdot \cos 30^{\circ }+F_3\cdot \cos 30^{\circ }=50\cdot \cos 30^{\circ }+40\cdot \cos 30^{\circ }+40\cdot \cos 30^{\circ }=50\cdot 0.866025+40\cdot 0.866025+40\cdot 0.866025=46.7081 \\ y=F_1\cdot \sin a_1^{\circ }+F_2\cdot \sin a_2^{\circ }+F_3\cdot \sin a_3^{\circ }=F_1\cdot \sin 30^{\circ }+F_2\cdot \sin 30^{\circ }+F_3\cdot \sin 30^{\circ }=50\cdot \sin 30^{\circ }+40\cdot \sin 30^{\circ }+40\cdot \sin 30^{\circ }=50\cdot 0.5+40\cdot 0.5+40\cdot 0.5=103.02934 \\ F=\sqrt{x^2+y^2}=\sqrt{46.7081^2+103.0293^2}=113.1225\text{ kN} \end{gathered}$$

$f={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan (y\mathrm{/}x)={\displaystyle \frac{180^{\circ }}{\pi }}\cdot \arctan (103.0293\mathrm{/}46.7081)=65.613^{\circ }=65^{\circ }36^{\mathrm{\prime }}47\mathrm{"}$

Try another example

Showing 0 comments:

Next similar math problems:

• 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
• Two forces
  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
  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
  The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
• Triangle
  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
  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
  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
  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
  Using vector dot product calculate the angle of the body diagonals of the cube.
• Triangle SAS
  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
  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
  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
  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
  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
  Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
• Cone
  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
  Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.