Worksheet: Resolution of Forces

In this worksheet, we will practice solving problems about the resolution of a force into two directions.

Q1:

A force of magnitude 190 N acts at the origin making an angle of 30∘ above the π‘₯-axis. Find 𝐹 and 𝐹, its components in the π‘₯ and 𝑦 directions.

  • A𝐹=95N, 𝐹=95√3N
  • B𝐹=95√3N, 𝐹=95N
  • C𝐹=190√3N, 𝐹=190N

Q2:

Resolve a force of 81 N into two perpendicular components 𝐹 and 𝐹 as shown in the figure. Give your answer correct to two decimal places.

  • A𝐹=137.81N, 𝐹=65.53N
  • B𝐹=47.61N, 𝐹=65.53N
  • C𝐹=100.12N, 𝐹=137.81N
  • D𝐹=47.61N, 𝐹=137.81N

Q3:

A body weighing 72 N is placed on a plane that is inclined at 45∘ to the horizontal. Resolve its weight into two components 𝐹 and 𝐹, where 𝐹 is the component in the direction of the plane and 𝐹 is the component normal to the plane.

  • A𝐹=36√2N, 𝐹=36√2N
  • B𝐹=36√2N, 𝐹=36N
  • C𝐹=72√2N, 𝐹=72√3N
  • D𝐹=36N, 𝐹=36N

Q4:

Resolve a force of magnitude 48 N acting northwest into two components, 𝐹 and 𝐹, acting north and west respectively.

  • A𝐹=24√2N, 𝐹=24√2N
  • B𝐹=48√2N, 𝐹=48√2N
  • C𝐹=24N, 𝐹=24√2N
  • D𝐹=48N, 𝐹=48√2N
  • E𝐹=24N, 𝐹=24N

Q5:

A particle weighing 69 N is placed on a plane inclined at an angle πœƒ to the horizontal, where tanπœƒ=43. Resolve the weight of the particle into two components, 𝐹 and 𝐹, where 𝐹 is parallel to a line of greatest slope and 𝐹 is perpendicular to 𝐹.

  • A𝐹=34.5N, 𝐹=34.5N
  • B𝐹=41.4N, 𝐹=55.2N
  • C𝐹=55.2N, 𝐹=55.2N
  • D𝐹=55.2N, 𝐹=41.4N

Q6:

An object weighing 50 newtons rests on a ramp that is inclined 19∘ to the horizontal. Find the magnitude of the components of the force parallel and perpendicular to the ramp, giving your answer correct to three decimal places if necessary.

  • Aparallel: 52.881 newtons, perpendicular: 153.578 newtons
  • Bparallel: 153.578 newtons, perpendicular: 52.881 newtons
  • Cparallel: 16.278 newtons, perpendicular: 47.276 newtons
  • Dparallel: 47.276 newtons, perpendicular: 16.278 newtons
  • Eparallel: 50 newtons, perpendicular: 50 newtons

Q7:

A force of magnitude 4√2 N acts on a particle in a direction 30∘ south of west. i and j are two units vectors in the east and north directions, respectively. Express the force in terms of i and j.

  • Aο€»βˆ’4√6βˆ’4√2ij N
  • Bο€»2√6βˆ’2√2ij N
  • Cο€»βˆ’2√6βˆ’2√2ij N
  • Dο€»βˆ’2√2βˆ’2√6ij N
  • Eο€Ώβˆ’βˆš32βˆ’12ij N

Q8:

Resolve a force of 110 N into two perpendicular components 𝐹 and 𝐹 as shown in the figure. Give your answer correct to two decimal places.

  • A𝐹=158.35N, 𝐹=79.13N
  • B𝐹=76.41N, 𝐹=79.13N
  • C𝐹=152.92N, 𝐹=158.35N
  • D𝐹=76.41N, 𝐹=158.35N

Q9:

Resolve a force of 123 N into two perpendicular components 𝐹 and 𝐹 as shown in the figure. Give your answer correct to two decimal places.

  • A𝐹=180.35N, 𝐹=89.96N
  • B𝐹=83.89N, 𝐹=89.96N
  • C𝐹=168.18N, 𝐹=180.35N
  • D𝐹=83.89N, 𝐹=180.35N

Q10:

A body weighing 18 N is placed on a plane that is inclined at 30∘ to the horizontal. Resolve its weight into two components 𝐹 and 𝐹, where 𝐹 is the component in the direction of the plane and 𝐹 is the component normal to the plane.

  • A𝐹=9N, 𝐹=9√3N
  • B𝐹=9√3N, 𝐹=36√3N
  • C𝐹=36N, 𝐹=9√3N
  • D𝐹=9N, 𝐹=9N

Q11:

A body weighing 12 N is placed on a plane that is inclined at 60∘ to the horizontal. Resolve its weight into two components 𝐹 and 𝐹, where 𝐹 is the component in the direction of the plane and 𝐹 is the component normal to the plane.

  • A𝐹=6√3N, 𝐹=6N
  • B𝐹=6√3N, 𝐹=24√3N
  • C𝐹=6√3N, 𝐹=24N
  • D𝐹=6N, 𝐹=6N

Q12:

A force of magnitude 44 N acts at the origin making an angle of 45∘ above the π‘₯-axis. Find 𝐹 and 𝐹, its components in the π‘₯ and 𝑦 directions.

  • A𝐹=22√2N, 𝐹=22N
  • B𝐹=22√2N, 𝐹=22√2N
  • C𝐹=22N, 𝐹=22√2N

Q13:

A force of magnitude 10 N acts at the origin making an angle of 60∘ above the π‘₯-axis. Find 𝐹 and 𝐹, its components in the π‘₯ and 𝑦 directions.

  • A𝐹=5√3N, 𝐹=5N
  • B𝐹=5N, 𝐹=5√3N
  • C𝐹=10√3N, 𝐹=10N

Q14:

Resolve a force of magnitude 52 N acting northwest into two components, 𝐹 and 𝐹, acting north and west respectively.

  • A𝐹=26√2N, 𝐹=26√2N
  • B𝐹=52√2N, 𝐹=52√2N
  • C𝐹=26N, 𝐹=26√2N
  • D𝐹=52N, 𝐹=52√2N
  • E𝐹=26N, 𝐹=26N

Q15:

Resolve a force of magnitude 196 N acting northwest into two components, 𝐹 and 𝐹, acting north and west respectively.

  • A𝐹=98√2N, 𝐹=98√2N
  • B𝐹=196√2N, 𝐹=196√2N
  • C𝐹=98N, 𝐹=98√2N
  • D𝐹=196N, 𝐹=196√2N
  • E𝐹=98N, 𝐹=98N

Q16:

A force of magnitude 41 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of F and F. Give your answer to two decimal places.

  • AF=57.98N, F=57.98N
  • BF=30.01N, F=36.76N
  • CF=28.99N, F=28.99N
  • DF=112.01N, F=36.76N

Q17:

A force F of magnitude 99 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of F and F giving values to two decimal places.

  • AF=218.07N, F=196.00N
  • BF=59.58N, F=88.98N
  • CF=131.24N, F=196.00N
  • DF=131.24N, F=218.07N
  • EF=218.07N, F=131.24N

Q18:

The angle between two forces, π‘ŽοŠ§ and π‘ŽοŠ¨ is 75∘. Their resultant is 2,900 N and makes an angle of 45∘ with π‘ŽοŠ§. Find the forces π‘ŽοŠ§ and π‘ŽοŠ¨. Give your answers to two decimal places.

  • Aπ‘Ž=2,050.61N, π‘Ž=4,101.22N
  • Bπ‘Ž=2,050.61N, π‘Ž=2,511.47N
  • Cπ‘Ž=1,501.15N, π‘Ž=2,122.95N
  • Dπ‘Ž=2,600.07N, π‘Ž=2,122.95N

Q19:

A force of magnitude 96 N acts vertically downward. It is resolved into two components as shown on the diagram. Find the magnitudes of 𝐹 and 𝐹 giving values to two decimal places.

  • A𝐹=86.44N, 𝐹=129.18N
  • B𝐹=86.44N, 𝐹=71.34N
  • C𝐹=96.00N, 𝐹=64.24N
  • D𝐹=106.62N, 𝐹=143.47N

Q20:

A force F, acting in a northerly direction, is the resultant of two forces F and F. The force F has a magnitude of 172 N and is acting 60∘ north of east, and the force F acts in a westerly direction. Find the magnitudes F and F.

  • A||=86√3FN, ||=86√3FN
  • B||=172FN, ||=86√3FN
  • C||=86√3FN, ||=86FN
  • D||=86FN, ||=86√3FN

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