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?

Result

F =  60.335 N

Solution:

F1=42 N F2=35 N u=77+12/60=3865=77.2 ∘ x0=F1=42 y0=0 x=x0+F2⋅ cos⁡(u∘→ rad)=x0+F2⋅ cos⁡(u∘⋅ π180 )=42+35⋅ cos⁡(77.2∘⋅ 3.1415926180 )=49.7542 y=y0+F2⋅ sin⁡(u∘→ rad)=y0+F2⋅ sin⁡(u∘⋅ π180 )=0+35⋅ sin⁡(77.2∘⋅ 3.1415926180 )=34.13023 F=x2+y2=49.75422+34.13022≐60.3353≐60.335 NF_{1}=42 \ \text{N} \ \\ F_{2}=35 \ \text{N} \ \\ u=77+12/60=\dfrac{ 386 }{ 5 }=77.2 \ ^\circ \ \\ x_{0}=F_{1}=42 \ \\ y_{0}=0 \ \\ x=x_{0} + F_{2} \cdot \ \cos( u ^\circ \rightarrow\ \text{rad})=x_{0} + F_{2} \cdot \ \cos( u ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=42 + 35 \cdot \ \cos( 77.2 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=49.7542 \ \\ y=y_{0} + F_{2} \cdot \ \sin( u ^\circ \rightarrow\ \text{rad})=y_{0} + F_{2} \cdot \ \sin( u ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=0 + 35 \cdot \ \sin( 77.2 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=34.13023 \ \\ F=\sqrt{ x^2+y^2 }=\sqrt{ 49.7542^2+34.1302^2 } \doteq 60.3353 \doteq 60.335 \ \text{N}

Try another example


Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
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.

Following knowledge from mathematics are needed to solve this word math problem:

Next similar math problems:

  1. Cable car 2
    lanovka_1 Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car?
  2. One side
    angle_incline One side is 36 long with a 15° incline. What is the height at the end of that side?
  3. Bearing - navigation
    navigation A ship travels 84 km on a bearing of 17°, and then travels on a bearing of 107° for 135 km. Find the distance of the end of the trip from the starting point, to the nearest kilometer.
  4. Add vector
    vectors_2 Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.
  5. Vectors
    green For vector w is true: w = 2u-5v. Determine coordinates of vector w if u=(3, -1), v=(12, -10)
  6. Vertices of RT
    RightTriangleMidpoint_3 Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
  7. Reference angle
    anglemeter Find the reference angle of each angle:
  8. Building
    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?
  9. Steeple
    church_tower Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
  10. Flowerbed
    triangle_flowers.JPG Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex?
  11. Right triangle trigonometrics
    triangle2 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)
  12. Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  13. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  14. Trigonometry
    sinus Is true equality? ?
  15. Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  16. Triangle
    star Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
  17. The ladder
    rebrik The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?