Lesson: Resolution of Forces into Two Given Directions

In this lesson, we will learn how to solve problems on the resolution of a force into two directions using the properties of a parallelogram and applying the sine rule.

Sample Question Videos

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  • 03:33

Worksheet: Resolution of Forces into Two Given Directions • 17 Questions • 2 Videos

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.

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 1 and 𝐹 2 giving values to two decimal places.

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 1 and 𝐹 2 . Give your answer to two decimal places.

Q4:

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.

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 1 and 𝐹 2 giving values to two decimal places.

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 .

Q7:

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.

Q8:

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.

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 1 and 𝐹 2 giving values to two decimal places.

Q10:

A force of magnitude 143 N acts vertically downwards. 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.

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 1 and 𝐹 2 . Give your answer to two decimal places.

Q12:

A force of magnitude 133 N acts due south. It is resolved into two components as shown on the diagram. Find the magnitudes of 𝐹 1 and 𝐹 2 . Give your answer to two decimal places.

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 1 and 𝐹 2 giving values to two decimal places.

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 1 and 𝐹 2 giving values to two decimal places.

Q15:

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.

Q16:

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.

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 .

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