Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Resolution of Forces into Two Given Directions

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:

The diagram shows a body of weight 77 N suspended by 2 light, inextensible strings, 𝐴 𝐶 and 𝐵 𝐶 . Both strings make an angle of 4 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 = 5 6 N , 𝑊 = 5 6 N
  • B 𝑊 = 7 7 N , 𝑊 = 7 7 N
  • C 𝑊 = 1 1 3 N , 𝑊 = 1 1 3 N
  • D 𝑊 = 5 3 N , 𝑊 = 5 3 N

Q3:

The diagram shows a body of weight 41 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 = 3 3 N , 𝑊 = 3 3 N
  • B 𝑊 = 4 1 N , 𝑊 = 4 1 N
  • C 𝑊 = 6 4 N , 𝑊 = 6 4 N
  • D 𝑊 = 2 6 N , 𝑊 = 2 6 N

Q4:

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 1 and 𝐹 2 giving values to two decimal places.

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

Q5:

A force of magnitude 59 N acts vertically downward. It is resolved into two components as shown on the diagram. Find the magnitudes of 𝐹 1 and 𝐹 2 giving values to two decimal places.

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

Q6:

A force of magnitude 143 N acts vertically downward. It is resolved into two components as shown on the diagram. Find the magnitudes of 𝐹 1 and 𝐹 2 giving values to two decimal places.

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

Q7:

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

  • A ,
  • B ,
  • C ,
  • D ,

Q8:

A force of magnitude 89 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and . Give your answer to two decimal places.

  • A ,
  • B ,
  • C ,
  • D ,

Q9:

A force of magnitude 133 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and . Give your answer to two decimal places.

  • A ,
  • B ,
  • C ,
  • D ,

Q10:

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

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q11:

A force of magnitude 137 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q12:

A force of magnitude 157 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of and giving values to two decimal places.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q13:

The angle between two forces, 𝑎 1 and 𝑎 2 is 7 5 . Their resultant is 2 900 N and makes an angle of 4 5 with 𝑎 1 . Find the forces 𝑎 1 and 𝑎 2 . Give your answers to two decimal places.

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

Q14:

The angle between two forces, 𝑎 1 and 𝑎 2 is 1 0 5 . Their resultant is 6 200 N and makes an angle of 4 5 with 𝑎 1 . Find the forces 𝑎 1 and 𝑎 2 . Give your answers to two decimal places.

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

Q15:

The angle between two forces, 𝑎 1 and 𝑎 2 is 9 0 . Their resultant is 2 600 N and makes an angle of 6 0 with 𝑎 1 . Find the forces 𝑎 1 and 𝑎 2 . Give your answers to two decimal places.

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

Q16:

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 ,

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 ,