fbpx

Determine vector components

Solved problems in vectorsdetermine vector components

1. A force of 20 Newton makes an angle of 30o with the x-axis. Find both the x and y component of the force.

Solving vectors problems – determine vector components 1Solution

Fx = F cos 30o = (20)(cos 30o) = (20)(0.53) = 103 Newton

Fy = F sin 30o = (20)(sin 30o) = (20)(0.5) = 10 Newton

See also  Kinetic theory of gases - problems and solutions

2. F1 = 20 Newton makes an angle of 30o with the y axis and F2 = 30 Newton makes an angle of 60o with the -x axis. Find both the x and y components of F1 and F2.

Solving vectors problems – determine vector components 2Solution

F1x = F1 cos 60o = (20)(cos 60o) = (20)(0.5) = -10 Newton (negative because it has same direction with -x axis)

F2x = F2 cos 60o = (30)(cos 60o) = (30)(0.5) = -15 Newton (negative because it has same direction with -x axis)

F1y = F1 sin 60o = (20)(sin 60o) = (20)(0.53) = 103 Newton (positive because it has same direction with y axis)

F2y = F2 sin 60o = (30)(sin 60o) = (30)(0.53) = -153 Newton (negative because it has same direction with -y axis)

See also  Bodies connected by the cord and pulley - application of Newton's law of motion problems and solutions

3. F1 = 2 N, F2 = 4 N, F3 = 6 N. Find both the x and y components of F1, F2 and F3!

Solving vectors problems – determine vector components 3Solution

F1x = F1 cos 60o = (2)(cos 60o) = (2)(0.5) = 1 Newton (positive because it has the same direction with x axis)

F2x = F2 cos 30o = (4)(cos 30o) = (4)(0.53) = -23 Newton (negative because it has the same direction with -x axis)

F3x = F3 cos 60o = (6)(cos 60o) = (6)(0.5) = 3 Newton (positive because it has the same direction with x axis)

F1y = F1 sin 60o = (2)(sin 60o) = (2)(0.53) = 3 Newton (positive because it has the same direction with y axis)

F2y = F2 sin 30o = (4)(sin 30o) = (4)(0.5) = 2 Newton (positive because it has the same direction with y axis)

F3y = F3 sin 60o = (6)(sin 60o) = (6)(0.53) = -33 Newton (negative because it has the same direction with -y axis)

See also  Dynamics Object connected by cord over pulley Atwood machine - Problems and Solutions

[wpdm_package id=’542′]

[wpdm_package id=’554′]

  1. Determine the resultant of in a line vector
  2. Determine vector components
  3. Determine resultant of two vectors using Pythagorean theorem
  4. Determine resultant of two vectors using cosines equation
  5. Determine resultant of two vectors using components of vectors

Print Friendly, PDF & Email

Leave a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Discover more from Physics

Subscribe now to keep reading and get access to the full archive.

Continue reading