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.

  • A 𝐹 = 9 5  N , 𝐹 = 9 5 √ 3  N
  • B 𝐹 = 9 5 √ 3  N , 𝐹 = 9 5  N
  • C 𝐹 = 1 9 0 √ 3  N , 𝐹 = 1 9 0  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.

  • A 𝐹 = 1 3 7 . 8 1  N , 𝐹 = 6 5 . 5 3  N
  • B 𝐹 = 4 7 . 6 1  N , 𝐹 = 6 5 . 5 3  N
  • C 𝐹 = 1 0 0 . 1 2  N , 𝐹 = 1 3 7 . 8 1  N
  • D 𝐹 = 4 7 . 6 1  N , 𝐹 = 1 3 7 . 8 1  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.

  • A 𝐹 = 3 6 √ 2  N , 𝐹 = 3 6 √ 2  N
  • B 𝐹 = 3 6 √ 2  N , 𝐹 = 3 6  N
  • C 𝐹 = 7 2 √ 2  N , 𝐹 = 7 2 √ 3  N
  • D 𝐹 = 3 6  N , 𝐹 = 3 6  N

Q4:

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

  • A 𝐹 = 2 4 √ 2  N , 𝐹 = 2 4 √ 2  N
  • B 𝐹 = 4 8 √ 2  N , 𝐹 = 4 8 √ 2  N
  • C 𝐹 = 2 4  N , 𝐹 = 2 4 √ 2  N
  • D 𝐹 = 4 8  N , 𝐹 = 4 8 √ 2  N
  • E 𝐹 = 2 4  N , 𝐹 = 2 4  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.

  • A 𝐹 = 3 4 . 5  N , 𝐹 = 3 4 . 5  N
  • B 𝐹 = 4 1 . 4  N , 𝐹 = 5 5 . 2  N
  • C 𝐹 = 5 5 . 2  N , 𝐹 = 5 5 . 2  N
  • D 𝐹 = 5 5 . 2  N , 𝐹 = 4 1 . 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.

  • A ο€» βˆ’ 4 √ 6 βˆ’ 4 √ 2  i j N
  • B ο€» 2 √ 6 βˆ’ 2 √ 2  i j N
  • C ο€» βˆ’ 2 √ 6 βˆ’ 2 √ 2  i j N
  • D ο€» βˆ’ 2 √ 2 βˆ’ 2 √ 6  i j N
  • E ο€Ώ βˆ’ √ 3 2 βˆ’ 1 2  i j 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.

  • A 𝐹 = 1 5 8 . 3 5  N , 𝐹 = 7 9 . 1 3  N
  • B 𝐹 = 7 6 . 4 1  N , 𝐹 = 7 9 . 1 3  N
  • C 𝐹 = 1 5 2 . 9 2  N , 𝐹 = 1 5 8 . 3 5  N
  • D 𝐹 = 7 6 . 4 1  N , 𝐹 = 1 5 8 . 3 5  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.

  • A 𝐹 = 1 8 0 . 3 5  N , 𝐹 = 8 9 . 9 6  N
  • B 𝐹 = 8 3 . 8 9  N , 𝐹 = 8 9 . 9 6  N
  • C 𝐹 = 1 6 8 . 1 8  N , 𝐹 = 1 8 0 . 3 5  N
  • D 𝐹 = 8 3 . 8 9  N , 𝐹 = 1 8 0 . 3 5  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.

  • A 𝐹 = 9  N , 𝐹 = 9 √ 3  N
  • B 𝐹 = 9 √ 3  N , 𝐹 = 3 6 √ 3  N
  • C 𝐹 = 3 6  N , 𝐹 = 9 √ 3  N
  • D 𝐹 = 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.

  • A 𝐹 = 6 √ 3  N , 𝐹 = 6  N
  • B 𝐹 = 6 √ 3  N , 𝐹 = 2 4 √ 3  N
  • C 𝐹 = 6 √ 3  N , 𝐹 = 2 4  N
  • D 𝐹 = 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.

  • A 𝐹 = 2 2 √ 2  N , 𝐹 = 2 2  N
  • B 𝐹 = 2 2 √ 2  N , 𝐹 = 2 2 √ 2  N
  • C 𝐹 = 2 2  N , 𝐹 = 2 2 √ 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.

  • A 𝐹 = 5 √ 3  N , 𝐹 = 5  N
  • B 𝐹 = 5  N , 𝐹 = 5 √ 3  N
  • C 𝐹 = 1 0 √ 3  N , 𝐹 = 1 0  N

Q14:

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

  • A 𝐹 = 2 6 √ 2  N , 𝐹 = 2 6 √ 2  N
  • B 𝐹 = 5 2 √ 2  N , 𝐹 = 5 2 √ 2  N
  • C 𝐹 = 2 6  N , 𝐹 = 2 6 √ 2  N
  • D 𝐹 = 5 2  N , 𝐹 = 5 2 √ 2  N
  • E 𝐹 = 2 6  N , 𝐹 = 2 6  N

Q15:

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

  • A 𝐹 = 9 8 √ 2  N , 𝐹 = 9 8 √ 2  N
  • B 𝐹 = 1 9 6 √ 2  N , 𝐹 = 1 9 6 √ 2  N
  • C 𝐹 = 9 8  N , 𝐹 = 9 8 √ 2  N
  • D 𝐹 = 1 9 6  N , 𝐹 = 1 9 6 √ 2  N
  • E 𝐹 = 9 8  N , 𝐹 = 9 8  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.

  • A F  = 5 7 . 9 8 N , F  = 5 7 . 9 8 N
  • B F  = 3 0 . 0 1 N , F  = 3 6 . 7 6 N
  • C F  = 2 8 . 9 9 N , F  = 2 8 . 9 9 N
  • D F  = 1 1 2 . 0 1 N , F  = 3 6 . 7 6 N

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.

  • A F  = 2 1 8 . 0 7 N , F  = 1 9 6 . 0 0 N
  • B F  = 5 9 . 5 8 N , F  = 8 8 . 9 8 N
  • C F  = 1 3 1 . 2 4 N , F  = 1 9 6 . 0 0 N
  • D F  = 1 3 1 . 2 4 N , F  = 2 1 8 . 0 7 N
  • E F  = 2 1 8 . 0 7 N , F  = 1 3 1 . 2 4 N

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.

  • A π‘Ž = 2 , 0 5 0 . 6 1  N , π‘Ž = 4 , 1 0 1 . 2 2  N
  • B π‘Ž = 2 , 0 5 0 . 6 1  N , π‘Ž = 2 , 5 1 1 . 4 7  N
  • C π‘Ž = 1 , 5 0 1 . 1 5  N , π‘Ž = 2 , 1 2 2 . 9 5  N
  • D π‘Ž = 2 , 6 0 0 . 0 7  N , π‘Ž = 2 , 1 2 2 . 9 5  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.

  • A 𝐹 = 8 6 . 4 4  N , 𝐹 = 1 2 9 . 1 8  N
  • B 𝐹 = 8 6 . 4 4  N , 𝐹 = 7 1 . 3 4  N
  • C 𝐹 = 9 6 . 0 0  N , 𝐹 = 6 4 . 2 4  N
  • D 𝐹 = 1 0 6 . 6 2  N , 𝐹 = 1 4 3 . 4 7  N

Q20:

A force F, acting in a northerly direction, is the resultant of two forces βƒ‘πΉοŠ§ and βƒ‘πΉοŠ¨. The force βƒ‘πΉοŠ§ has a magnitude of 172 N and is acting 60∘ north of east, and the force βƒ‘πΉοŠ¨ acts in a westerly direction. Find the magnitudes 𝐹 and 𝐹.

  • A 𝐹 = 8 6 √ 3 N , 𝐹 = 8 6 √ 3  N
  • B 𝐹 = 1 7 2 N , 𝐹 = 8 6 √ 3  N
  • C 𝐹 = 8 6 √ 3 N , 𝐹 = 8 6  N
  • D 𝐹 = 8 6 N , 𝐹 = 8 6 √ 3  N

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