Worksheet: Resolution of Forces into Two Given Directions

In this worksheet, we will practice solving problems on the resolution of a force into two directions using the properties of a parallelogram and applying the sine rule.

Q1:

The diagram shows a body of weight 69 N suspended by 2 light, inextensible strings, 𝐴 𝐶 and 𝐵 𝐶 . Both strings make an angle of 3 7 with the horizontal. Resolve the weight of the body into two components in the direction of 𝐴 𝐶 and in the direction of 𝐵 𝐶 . Give your answers to the nearest newton.

  • A 𝑊 = 4 3 N , 𝑊 = 4 3 N
  • B 𝑊 = 6 9 N , 𝑊 = 6 9 N
  • C 𝑊 = 8 3 N , 𝑊 = 8 3 N
  • D 𝑊 = 5 7 N , 𝑊 = 5 7 N

Q2:

A force of magnitude 96 N acts vertically downwards. 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 = 9 6 . 0 0 N , 𝐹 = 6 4 . 2 4 N
  • B 𝐹 = 1 0 6 . 6 2 N , 𝐹 = 1 4 3 . 4 7 N
  • C 𝐹 = 8 6 . 4 4 N , 𝐹 = 7 1 . 3 4 N
  • D 𝐹 = 8 6 . 4 4 N , 𝐹 = 1 2 9 . 1 8 N

Q3:

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

Q4:

The angle between two forces, 𝑎 and 𝑎 is 7 5 . Their resultant is 2,900 N and makes an angle of 4 5 with 𝑎 . Find the forces 𝑎 and 𝑎 . Give your answers to two decimal places.

  • A 𝑎 = 2 , 0 5 0 . 6 1 N , 𝑎 = 4 , 1 0 1 . 2 2 N
  • B 𝑎 = 2 , 6 0 0 . 0 7 N , 𝑎 = 2 , 1 2 2 . 9 5 N
  • C 𝑎 = 2 , 0 5 0 . 6 1 N , 𝑎 = 2 , 5 1 1 . 4 7 N
  • D 𝑎 = 1 , 5 0 1 . 1 5 N , 𝑎 = 2 , 1 2 2 . 9 5 N

Q5:

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 = 2 1 8 . 0 7 N
  • D 𝐹 = 1 3 1 . 2 4 N , 𝐹 = 1 9 6 . 0 0 N
  • E 𝐹 = 2 1 8 . 0 7 N , 𝐹 = 1 3 1 . 2 4 N

Q6:

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

  • A ,
  • B ,
  • C ,
  • D ,

Q7:

The diagram shows a body of weight 58 N suspended by 2 light, inextensible strings, 𝐴 𝐶 and 𝐵 𝐶 . Both strings make an angle of 5 1 with the horizontal. Resolve the weight of the body into two components in the direction of 𝐴 𝐶 and in the direction of 𝐵 𝐶 . Give your answers to the nearest newton.

  • A 𝑊 = 4 6 N , 𝑊 = 4 6 N
  • B 𝑊 = 5 8 N , 𝑊 = 5 8 N
  • C 𝑊 = 9 0 N , 𝑊 = 9 0 N
  • D 𝑊 = 3 7 N , 𝑊 = 3 7 N

Q8:

The diagram shows a body of weight 54 N suspended by 2 light, inextensible strings, 𝐴 𝐶 and 𝐵 𝐶 . Both strings make an angle of 5 2 with the horizontal. Resolve the weight of the body into two components in the direction of 𝐴 𝐶 and in the direction of 𝐵 𝐶 . Give your answers to the nearest newton.

  • A 𝑊 = 4 4 N , 𝑊 = 4 4 N
  • B 𝑊 = 5 4 N , 𝑊 = 5 4 N
  • C 𝑊 = 8 5 N , 𝑊 = 8 5 N
  • D 𝑊 = 3 4 N , 𝑊 = 3 4 N

Q9:

A force of magnitude 59 N acts vertically downwards. 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 = 5 9 . 0 0 N , 𝐹 = 3 4 . 6 8 N
  • B 𝐹 = 8 1 . 2 1 N , 𝐹 = 1 0 0 . 3 8 N
  • C 𝐹 = 4 2 . 8 7 N , 𝐹 = 4 7 . 7 3 N
  • D 𝐹 = 4 2 . 8 7 N , 𝐹 = 7 2 . 9 3 N

Q10:

A force of magnitude 27 N acts vertically downwards. 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 7 . 0 0 N , 𝐹 = 1 4 . 7 1 N
  • B 𝐹 = 4 1 . 5 8 N , 𝐹 = 4 9 . 5 7 N
  • C 𝐹 = 1 7 . 5 3 N , 𝐹 = 2 2 . 6 4 N
  • D 𝐹 = 1 7 . 5 3 N , 𝐹 = 3 2 . 1 9 N

Q11:

A force of magnitude 89 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 = 6 2 . 9 3 N , F = 6 2 . 9 3 N
  • B F = 2 4 3 . 1 5 N , F = 4 6 . 0 7 N
  • C F = 1 2 5 . 8 7 N , F = 1 2 5 . 8 7 N
  • D F = 6 5 . 1 5 N , F = 4 6 . 0 7 N

Q12:

A force of magnitude 10 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 = 7 . 0 7 N , F = 7 . 0 7 N
  • B F = 2 7 . 3 2 N , F = 5 . 1 8 N
  • C F = 1 4 . 1 4 N , F = 1 4 . 1 4 N
  • D F = 7 . 3 2 N , F = 5 . 1 8 N

Q13:

A force 𝐹 of magnitude 137 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 6 1 7 . 7 0 N , 𝐹 = 1 7 5 1 . 5 9 N
  • B 𝐹 = 8 6 . 2 2 N , 𝐹 = 9 1 . 6 7 N
  • C 𝐹 = 1 6 4 7 . 3 7 N , 𝐹 = 2 6 1 7 . 7 0 N
  • D 𝐹 = 1 6 4 7 . 3 7 N , 𝐹 = 1 7 5 1 . 5 9 N
  • E 𝐹 = 2 6 1 7 . 7 0 N , 𝐹 = 1 6 4 7 . 3 7 N

Q14:

A force 𝐹 of magnitude 157 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 = 6 9 7 . 9 3 N , 𝐹 = 5 4 9 . 9 8 N
  • B 𝐹 = 9 8 . 8 0 N , 𝐹 = 1 2 3 . 7 2 N
  • C 𝐹 = 4 3 9 . 2 2 N , 𝐹 = 6 9 7 . 9 3 N
  • D 𝐹 = 4 3 9 . 2 2 N , 𝐹 = 5 4 9 . 9 8 N
  • E 𝐹 = 6 9 7 . 9 3 N , 𝐹 = 4 3 9 . 2 2 N

Q15:

The angle between two forces, 𝑎 and 𝑎 is 1 0 5 . Their resultant is 6,200 N and makes an angle of 4 5 with 𝑎 . Find the forces 𝑎 and 𝑎 . Give your answers to two decimal places.

  • A 𝑎 = 7 , 5 9 3 . 4 2 N , 𝑎 = 5 , 0 6 2 . 2 8 N
  • B 𝑎 = 3 , 2 0 9 . 3 6 N , 𝑎 = 4 , 5 3 8 . 7 2 N
  • C 𝑎 = 4 , 3 8 4 . 0 6 N , 𝑎 = 3 , 1 0 0 N
  • D 𝑎 = 5 , 5 5 8 . 7 7 N , 𝑎 = 4 , 5 3 8 . 7 2 N

Q16:

The angle between two forces, 𝑎 and 𝑎 is 9 0 . Their resultant is 2,600 N and makes an angle of 6 0 with 𝑎 . Find the forces 𝑎 and 𝑎 . Give your answers to two decimal places.

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

Q17:

A force , acting in a northerly direction, is the resultant of two forces and . The force has a magnitude of 186 N and is acting north of east, and the force acts in a westerly direction. Find the magnitudes and .

  • A ,
  • B ,
  • C ,
  • D ,

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