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Worksheet: Resolution of a Force into Two Perpendicular Directions

Q1:

A force of magnitude 190 N acts at the origin making an angle of 3 0 ∘ above the π‘₯ -axis. Find 𝐹 π‘₯ and 𝐹 𝑦 , its components in the π‘₯ and 𝑦 directions.

  • A 𝐹 = 1 9 0 √ 3 π‘₯ N , 𝐹 = 1 9 0 𝑦 N
  • B 𝐹 = 9 5 π‘₯ N , 𝐹 = 9 5 √ 3 𝑦 N
  • C 𝐹 = 9 5 √ 3 π‘₯ N , 𝐹 = 9 5 𝑦 N

Q2:

A force of magnitude 44 N acts at the origin making an angle of 4 5 ∘ above the π‘₯ -axis. Find 𝐹 π‘₯ and 𝐹 𝑦 , its components in the π‘₯ and 𝑦 directions.

  • A 𝐹 = 2 2 π‘₯ N , 𝐹 = 2 2 √ 2 𝑦 N
  • B 𝐹 = 2 2 √ 2 π‘₯ N , 𝐹 = 2 2 𝑦 N
  • C 𝐹 = 2 2 √ 2 π‘₯ N , 𝐹 = 2 2 √ 2 𝑦 N

Q3:

A force of magnitude 28 N acts at the origin making an angle of 6 0 ∘ above the π‘₯ -axis. Find 𝐹 π‘₯ and 𝐹 𝑦 , its components in the π‘₯ and 𝑦 directions.

  • A 𝐹 = 2 8 √ 3 π‘₯ N , 𝐹 = 2 8 𝑦 N
  • B 𝐹 = 1 4 √ 3 π‘₯ N , 𝐹 = 1 4 𝑦 N
  • C 𝐹 = 1 4 π‘₯ N , 𝐹 = 1 4 √ 3 𝑦 N

Q4:

Resolve a force of 81 N into two perpendicular components 𝐹 1 and 𝐹 2 as shown in the figure. Give your answer correct to two decimal places.

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

Q5:

Resolve a force of 110 N into two perpendicular components 𝐹 1 and 𝐹 2 as shown in the figure. Give your answer correct to two decimal places.

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

Q6:

Resolve a force of 123 N into two perpendicular components 𝐹 1 and 𝐹 2 as shown in the figure. Give your answer correct to two decimal places.

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

Q7:

A body weighing 72 N is placed on a plane that is inclined at 4 5 ∘ to the horizontal. Resolve its weight into two components 𝐹 1 and 𝐹 2 , where 𝐹 1 is the component in the direction of the plane and 𝐹 2 is the component normal to the plane.

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

Q8:

A body weighing 68 N is placed on a plane that is inclined at 4 5 ∘ to the horizontal. Resolve its weight into two components 𝐹 1 and 𝐹 2 , where 𝐹 1 is the component in the direction of the plane and 𝐹 2 is the component normal to the plane.

  • A 𝐹 = 3 4 1 N , 𝐹 = 3 4 2 N
  • B 𝐹 = 6 8 √ 2 1 N , 𝐹 = 6 8 √ 3 2 N
  • C 𝐹 = 3 4 √ 2 1 N , 𝐹 = 3 4 2 N
  • D 𝐹 = 3 4 √ 2 1 N , 𝐹 = 3 4 √ 2 2 N

Q9:

A body weighing 4 N is placed on a plane that is inclined at 4 5 ∘ to the horizontal. Resolve its weight into two components 𝐹 1 and 𝐹 2 , where 𝐹 1 is the component in the direction of the plane and 𝐹 2 is the component normal to the plane.

  • A 𝐹 = 2 1 N , 𝐹 = 2 2 N
  • B 𝐹 = 4 √ 2 1 N , 𝐹 = 4 √ 3 2 N
  • C 𝐹 = 2 √ 2 1 N , 𝐹 = 2 2 N
  • D 𝐹 = 2 √ 2 1 N , 𝐹 = 2 √ 2 2 N

Q10:

Resolve a force of magnitude 48 N acting northwest into two components, 𝐹 1 and 𝐹 2 , acting north and west respectively.

  • A 𝐹 = 2 4 1 N , 𝐹 = 2 4 √ 2 2 N
  • B 𝐹 = 2 4 1 N , 𝐹 = 2 4 2 N
  • C 𝐹 = 4 8 √ 2 1 N , 𝐹 = 4 8 √ 2 2 N
  • D 𝐹 = 2 4 √ 2 1 N , 𝐹 = 2 4 √ 2 2 N
  • E 𝐹 = 4 8 1 N , 𝐹 = 4 8 √ 2 2 N

Q11:

Resolve a force of magnitude 52 N acting northwest into two components, 𝐹 1 and 𝐹 2 , acting north and west respectively.

  • A 𝐹 = 2 6 1 N , 𝐹 = 2 6 √ 2 2 N
  • B 𝐹 = 2 6 1 N , 𝐹 = 2 6 2 N
  • C 𝐹 = 5 2 √ 2 1 N , 𝐹 = 5 2 √ 2 2 N
  • D 𝐹 = 2 6 √ 2 1 N , 𝐹 = 2 6 √ 2 2 N
  • E 𝐹 = 5 2 1 N , 𝐹 = 5 2 √ 2 2 N

Q12:

Resolve a force of magnitude 196 N acting northwest into two components, 𝐹 1 and 𝐹 2 , acting north and west respectively.

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

Q13:

A particle weighing 69 N is placed on a plane inclined at an angle πœƒ to the horizontal, where t a n πœƒ = 4 3 . Resolve the weight of the particle into two components, 𝐹 1 and 𝐹 2 , where 𝐹 1 is parallel to a line of greatest slope and 𝐹 2 is perpendicular to 𝐹 1 .

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

Q14:

An object weighing 50 newtons rests on a ramp that is inclined 1 9 ∘ 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.

  • A parallel: 52.881 newtons, perpendicular: 153.578 newtons
  • B parallel: 47.276 newtons, perpendicular: 16.278 newtons
  • C parallel: 153.578 newtons, perpendicular: 52.881 newtons
  • D parallel: 16.278 newtons, perpendicular: 47.276 newtons
  • E parallel: 50 newtons, perpendicular: 50 newtons

Q15:

A force of magnitude N acts on a particle in a direction south of west. and are two units vectors in the east and north directions, respectively. Express the force in terms of and .

  • A N
  • B N
  • C N
  • D N
  • E N