Resultant force

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

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

Correct answer:

F =  113.1225 kN
f =  65.613 °

Step-by-step explanation:

$$\begin{gathered} F_1=50\text{ kN } \\ {F}_2=40\text{ kN } \\ {F}_3=40\text{ kN } \\ {a}_1=30\text{ ° } \\ {a}_2=a_1+45=30+45=75\text{ ° } \\ {a}_3=a_2+25=75+25=100\text{ ° } \\ x=F_1\cdot \cos a_1\mathrm{°}+F_2\cdot \cos a_2\mathrm{°}+F_3\cdot \cos a_3\mathrm{°}=F_1\cdot \cos 30\mathrm{°}+F_2\cdot \cos 75\mathrm{°}+F_3\cdot \cos 100\mathrm{°}=50\cdot \cos 30\mathrm{°}+40\cdot \cos 75\mathrm{°}+40\cdot \cos 100\mathrm{°}=50\cdot 0.866025+40\cdot 0.258819+40\cdot (-0.173648)=46.7081 \\ y=F_1\cdot \sin a_1\mathrm{°}+F_2\cdot \sin a_2\mathrm{°}+F_3\cdot \sin a_3\mathrm{°}=F_1\cdot \sin 30\mathrm{°}+F_2\cdot \sin 75\mathrm{°}+F_3\cdot \sin 100\mathrm{°}=50\cdot \sin 30\mathrm{°}+40\cdot \sin 75\mathrm{°}+40\cdot \sin 100\mathrm{°}=50\cdot 0.5+40\cdot 0.965926+40\cdot 0.984808=103.02934 \\ F=\sqrt{x^2+y^2}=\sqrt{46.7081^2+103.0293^2}=113.1225\text{ kN} \end{gathered}$$

Try another example

Related math problems and questions:

• Two forces
  Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer.
• 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.
• Mass point
  Two equal forces of 30 Newtons act on a mass point. Find the magnitude of the resultant force if these forces form an angle of 42°.
• 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'
• 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?
• Scalar dot product
  Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120°
• Diagonal
  Determine the dimensions of the cuboid, if diagonal long 53 dm has an angle with one edge 42° and with another edge 64°.
• Building
  The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
• Inner angles
  The inner angles of the triangle are 30°, 45° and 105° and its longest side is 10 cm. Calculate the length of the shortest side, write the result in cm up to two decimal places.
• Two forces
  The two forces F1 = 580N and F2 = 630N, have an angle of 59 degrees. Calculate their resultant force, F.
• Elevation angles
  From the endpoints of the base 240 m long and inclined at an angle of 18° 15 ', the top of the mountain can be seen at elevation angles of 43° and 51°. How high is the mountain?
• Right triangle trigonometrics
  Calculate the size of the remaining sides and angles of a right triangle ABC if it is given: b = 10 cm; c = 20 cm; angle alpha = 60° and the angle beta = 30° (use the Pythagorean theorem and functions sine, cosine, tangent, cotangent)
• Tetrahedral pyramid
  Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'.
• Quadrilateral oblique prism
  What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m, if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°.
• Area and two angles
  Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
• 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)?